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Early Stopping is Nonparametric Variational Inference | stat.ML cs.LG | We show that unconverged stochastic gradient descent can be interpreted as a
procedure that samples from a nonparametric variational approximate posterior
distribution. This distribution is implicitly defined as the transformation of
an initial distribution by a sequence of optimization updates. By tracking the
change in entropy over this sequence of transformations during optimization, we
form a scalable, unbiased estimate of the variational lower bound on the log
marginal likelihood. We can use this bound to optimize hyperparameters instead
of using cross-validation. This Bayesian interpretation of SGD suggests
improved, overfitting-resistant optimization procedures, and gives a
theoretical foundation for popular tricks such as early stopping and
ensembling. We investigate the properties of this marginal likelihood estimator
on neural network models.
| Dougal Maclaurin, David Duvenaud, Ryan P. Adams | null | 1504.01344 | null | null |
PASSCoDe: Parallel ASynchronous Stochastic dual Co-ordinate Descent | cs.LG | Stochastic Dual Coordinate Descent (SDCD) has become one of the most
efficient ways to solve the family of $\ell_2$-regularized empirical risk
minimization problems, including linear SVM, logistic regression, and many
others. The vanilla implementation of DCD is quite slow; however, by
maintaining primal variables while updating dual variables, the time complexity
of SDCD can be significantly reduced. Such a strategy forms the core algorithm
in the widely-used LIBLINEAR package. In this paper, we parallelize the SDCD
algorithms in LIBLINEAR. In recent research, several synchronized parallel SDCD
algorithms have been proposed, however, they fail to achieve good speedup in
the shared memory multi-core setting. In this paper, we propose a family of
asynchronous stochastic dual coordinate descent algorithms (ASDCD). Each thread
repeatedly selects a random dual variable and conducts coordinate updates using
the primal variables that are stored in the shared memory. We analyze the
convergence properties when different locking/atomic mechanisms are applied.
For implementation with atomic operations, we show linear convergence under
mild conditions. For implementation without any atomic operations or locking,
we present the first {\it backward error analysis} for ASDCD under the
multi-core environment, showing that the converged solution is the exact
solution for a primal problem with perturbed regularizer. Experimental results
show that our methods are much faster than previous parallel coordinate descent
solvers.
| Cho-Jui Hsieh and Hsiang-Fu Yu and Inderjit S. Dhillon | null | 1504.01365 | null | null |
Information Recovery from Pairwise Measurements | cs.IT cs.DM cs.LG math.IT math.ST stat.ML stat.TH | This paper is concerned with jointly recovering $n$ node-variables $\left\{
x_{i}\right\}_{1\leq i\leq n}$ from a collection of pairwise difference
measurements. Imagine we acquire a few observations taking the form of
$x_{i}-x_{j}$; the observation pattern is represented by a measurement graph
$\mathcal{G}$ with an edge set $\mathcal{E}$ such that $x_{i}-x_{j}$ is
observed if and only if $(i,j)\in\mathcal{E}$. To account for noisy
measurements in a general manner, we model the data acquisition process by a
set of channels with given input/output transition measures. Employing
information-theoretic tools applied to channel decoding problems, we develop a
\emph{unified} framework to characterize the fundamental recovery criterion,
which accommodates general graph structures, alphabet sizes, and channel
transition measures. In particular, our results isolate a family of
\emph{minimum} \emph{channel divergence measures} to characterize the degree of
measurement corruption, which together with the size of the minimum cut of
$\mathcal{G}$ dictates the feasibility of exact information recovery. For
various homogeneous graphs, the recovery condition depends almost only on the
edge sparsity of the measurement graph irrespective of other graphical metrics;
alternatively, the minimum sample complexity required for these graphs scales
like \[ \text{minimum sample complexity }\asymp\frac{n\log
n}{\mathsf{Hel}_{1/2}^{\min}} \] for certain information metric
$\mathsf{Hel}_{1/2}^{\min}$ defined in the main text, as long as the alphabet
size is not super-polynomial in $n$. We apply our general theory to three
concrete applications, including the stochastic block model, the outlier model,
and the haplotype assembly problem. Our theory leads to order-wise tight
recovery conditions for all these scenarios.
| Yuxin Chen, Changho Suh, Andrea J. Goldsmith | null | 1504.01369 | null | null |
Totally Corrective Boosting with Cardinality Penalization | cs.LG quant-ph | We propose a totally corrective boosting algorithm with explicit cardinality
regularization. The resulting combinatorial optimization problems are not known
to be efficiently solvable with existing classical methods, but emerging
quantum optimization technology gives hope for achieving sparser models in
practice. In order to demonstrate the utility of our algorithm, we use a
distributed classical heuristic optimizer as a stand-in for quantum hardware.
Even though this evaluation methodology incurs large time and resource costs on
classical computing machinery, it allows us to gauge the potential gains in
generalization performance and sparsity of the resulting boosted ensembles. Our
experimental results on public data sets commonly used for benchmarking of
boosting algorithms decidedly demonstrate the existence of such advantages. If
actual quantum optimization were to be used with this algorithm in the future,
we would expect equivalent or superior results at much smaller time and energy
costs during training. Moreover, studying cardinality-penalized boosting also
sheds light on why unregularized boosting algorithms with early stopping often
yield better results than their counterparts with explicit convex
regularization: Early stopping performs suboptimal cardinality regularization.
The results that we present here indicate it is beneficial to explicitly solve
the combinatorial problem still left open at early termination.
| Vasil S. Denchev, Nan Ding, Shin Matsushima, S.V.N. Vishwanathan,
Hartmut Neven | null | 1504.01446 | null | null |
Deep Recurrent Neural Networks for Acoustic Modelling | cs.LG cs.CL cs.NE stat.ML | We present a novel deep Recurrent Neural Network (RNN) model for acoustic
modelling in Automatic Speech Recognition (ASR). We term our contribution as a
TC-DNN-BLSTM-DNN model, the model combines a Deep Neural Network (DNN) with
Time Convolution (TC), followed by a Bidirectional Long Short-Term Memory
(BLSTM), and a final DNN. The first DNN acts as a feature processor to our
model, the BLSTM then generates a context from the sequence acoustic signal,
and the final DNN takes the context and models the posterior probabilities of
the acoustic states. We achieve a 3.47 WER on the Wall Street Journal (WSJ)
eval92 task or more than 8% relative improvement over the baseline DNN models.
| William Chan, Ian Lane | null | 1504.01482 | null | null |
Transferring Knowledge from a RNN to a DNN | cs.LG cs.CL cs.NE stat.ML | Deep Neural Network (DNN) acoustic models have yielded many state-of-the-art
results in Automatic Speech Recognition (ASR) tasks. More recently, Recurrent
Neural Network (RNN) models have been shown to outperform DNNs counterparts.
However, state-of-the-art DNN and RNN models tend to be impractical to deploy
on embedded systems with limited computational capacity. Traditionally, the
approach for embedded platforms is to either train a small DNN directly, or to
train a small DNN that learns the output distribution of a large DNN. In this
paper, we utilize a state-of-the-art RNN to transfer knowledge to small DNN. We
use the RNN model to generate soft alignments and minimize the Kullback-Leibler
divergence against the small DNN. The small DNN trained on the soft RNN
alignments achieved a 3.93 WER on the Wall Street Journal (WSJ) eval92 task
compared to a baseline 4.54 WER or more than 13% relative improvement.
| William Chan and Nan Rosemary Ke and Ian Lane | null | 1504.01483 | null | null |
Efficient SDP Inference for Fully-connected CRFs Based on Low-rank
Decomposition | cs.CV cs.LG stat.ML | Conditional Random Fields (CRF) have been widely used in a variety of
computer vision tasks. Conventional CRFs typically define edges on neighboring
image pixels, resulting in a sparse graph such that efficient inference can be
performed. However, these CRFs fail to model long-range contextual
relationships. Fully-connected CRFs have thus been proposed. While there are
efficient approximate inference methods for such CRFs, usually they are
sensitive to initialization and make strong assumptions. In this work, we
develop an efficient, yet general algorithm for inference on fully-connected
CRFs. The algorithm is based on a scalable SDP algorithm and the low- rank
approximation of the similarity/kernel matrix. The core of the proposed
algorithm is a tailored quasi-Newton method that takes advantage of the
low-rank matrix approximation when solving the specialized SDP dual problem.
Experiments demonstrate that our method can be applied on fully-connected CRFs
that cannot be solved previously, such as pixel-level image co-segmentation.
| Peng Wang, Chunhua Shen, Anton van den Hengel | 10.1109/CVPR.2015.7298942 | 1504.01492 | null | null |
Bidirectional Recurrent Neural Networks as Generative Models -
Reconstructing Gaps in Time Series | cs.LG cs.NE | Bidirectional recurrent neural networks (RNN) are trained to predict both in
the positive and negative time directions simultaneously. They have not been
used commonly in unsupervised tasks, because a probabilistic interpretation of
the model has been difficult. Recently, two different frameworks, GSN and NADE,
provide a connection between reconstruction and probabilistic modeling, which
makes the interpretation possible. As far as we know, neither GSN or NADE have
been studied in the context of time series before. As an example of an
unsupervised task, we study the problem of filling in gaps in high-dimensional
time series with complex dynamics. Although unidirectional RNNs have recently
been trained successfully to model such time series, inference in the negative
time direction is non-trivial. We propose two probabilistic interpretations of
bidirectional RNNs that can be used to reconstruct missing gaps efficiently.
Our experiments on text data show that both proposed methods are much more
accurate than unidirectional reconstructions, although a bit less accurate than
a computationally complex bidirectional Bayesian inference on the
unidirectional RNN. We also provide results on music data for which the
Bayesian inference is computationally infeasible, demonstrating the scalability
of the proposed methods.
| Mathias Berglund, Tapani Raiko, Mikko Honkala, Leo K\"arkk\"ainen,
Akos Vetek, Juha Karhunen | null | 1504.01575 | null | null |
Tensor machines for learning target-specific polynomial features | cs.LG stat.ML | Recent years have demonstrated that using random feature maps can
significantly decrease the training and testing times of kernel-based
algorithms without significantly lowering their accuracy. Regrettably, because
random features are target-agnostic, typically thousands of such features are
necessary to achieve acceptable accuracies. In this work, we consider the
problem of learning a small number of explicit polynomial features. Our
approach, named Tensor Machines, finds a parsimonious set of features by
optimizing over the hypothesis class introduced by Kar and Karnick for random
feature maps in a target-specific manner. Exploiting a natural connection
between polynomials and tensors, we provide bounds on the generalization error
of Tensor Machines. Empirically, Tensor Machines behave favorably on several
real-world datasets compared to other state-of-the-art techniques for learning
polynomial features, and deliver significantly more parsimonious models.
| Jiyan Yang and Alex Gittens | null | 1504.01697 | null | null |
Autonomous CRM Control via CLV Approximation with Deep Reinforcement
Learning in Discrete and Continuous Action Space | cs.LG | The paper outlines a framework for autonomous control of a CRM (customer
relationship management) system. First, it explores how a modified version of
the widely accepted Recency-Frequency-Monetary Value system of metrics can be
used to define the state space of clients or donors. Second, it describes a
procedure to determine the optimal direct marketing action in discrete and
continuous action space for the given individual, based on his position in the
state space. The procedure involves the use of model-free Q-learning to train a
deep neural network that relates a client's position in the state space to
rewards associated with possible marketing actions. The estimated value
function over the client state space can be interpreted as customer lifetime
value, and thus allows for a quick plug-in estimation of CLV for a given
client. Experimental results are presented, based on KDD Cup 1998 mailing
dataset of donation solicitations.
| Yegor Tkachenko | null | 1504.01840 | null | null |
Data Mining for Prediction of Human Performance Capability in the
Software-Industry | cs.LG | The recruitment of new personnel is one of the most essential business
processes which affect the quality of human capital within any company. It is
highly essential for the companies to ensure the recruitment of right talent to
maintain a competitive edge over the others in the market. However IT companies
often face a problem while recruiting new people for their ongoing projects due
to lack of a proper framework that defines a criteria for the selection
process. In this paper we aim to develop a framework that would allow any
project manager to take the right decision for selecting new talent by
correlating performance parameters with the other domain-specific attributes of
the candidates. Also, another important motivation behind this project is to
check the validity of the selection procedure often followed by various big
companies in both public and private sectors which focus only on academic
scores, GPA/grades of students from colleges and other academic backgrounds. We
test if such a decision will produce optimal results in the industry or is
there a need for change that offers a more holistic approach to recruitment of
new talent in the software companies. The scope of this work extends beyond the
IT domain and a similar procedure can be adopted to develop a recruitment
framework in other fields as well. Data-mining techniques provide useful
information from the historical projects depending on which the hiring-manager
can make decisions for recruiting high-quality workforce. This study aims to
bridge this hiatus by developing a data-mining framework based on an
ensemble-learning technique to refocus on the criteria for personnel selection.
The results from this research clearly demonstrated that there is a need to
refocus on the selection-criteria for quality objectives.
| Gaurav Singh Thakur, Anubhav Gupta and Sangita Gupta | null | 1504.01934 | null | null |
Adaptive Diffusion Schemes for Heterogeneous Networks | cs.SY cs.LG | In this paper, we deal with distributed estimation problems in diffusion
networks with heterogeneous nodes, i.e., nodes that either implement different
adaptive rules or differ in some other aspect such as the filter structure or
length, or step size. Although such heterogeneous networks have been considered
from the first works on diffusion networks, obtaining practical and robust
schemes to adaptively adjust the combiners in different scenarios is still an
open problem. In this paper, we study a diffusion strategy specially designed
and suited to heterogeneous networks. Our approach is based on two key
ingredients: 1) the adaptation and combination phases are completely decoupled,
so that network nodes keep purely local estimations at all times; and 2)
combiners are adapted to minimize estimates of the network mean-square-error.
Our scheme is compared with the standard Adapt-then-Combine scheme and
theoretically analyzed using energy conservation arguments. Several experiments
involving networks with heterogeneous nodes show that the proposed decoupled
Adapt-then-Combine approach with adaptive combiners outperforms other
state-of-the-art techniques, becoming a competitive approach in these
scenarios.
| Jesus Fernandez-Bes, Jer\'onimo Arenas-Garc\'ia, Magno T. M. Silva,
Luis A. Azpicueta-Ruiz | 10.1109/TSP.2017.2740199 | 1504.01982 | null | null |
Pixel-wise Deep Learning for Contour Detection | cs.CV cs.LG cs.NE | We address the problem of contour detection via per-pixel classifications of
edge point. To facilitate the process, the proposed approach leverages with
DenseNet, an efficient implementation of multiscale convolutional neural
networks (CNNs), to extract an informative feature vector for each pixel and
uses an SVM classifier to accomplish contour detection. In the experiment of
contour detection, we look into the effectiveness of combining per-pixel
features from different CNN layers and verify their performance on BSDS500.
| Jyh-Jing Hwang and Tyng-Luh Liu | null | 1504.01989 | null | null |
A Chaotic Dynamical System that Paints | nlin.CD cs.LG | Can a dynamical system paint masterpieces such as Da Vinci's Mona Lisa or
Monet's Water Lilies? Moreover, can this dynamical system be chaotic in the
sense that although the trajectories are sensitive to initial conditions, the
same painting is created every time? Setting aside the creative aspect of
painting a picture, in this work, we develop a novel algorithm to reproduce
paintings and photographs. Combining ideas from ergodic theory and control
theory, we construct a chaotic dynamical system with predetermined statistical
properties. If one makes the spatial distribution of colors in the picture the
target distribution, akin to a human, the algorithm first captures large scale
features and then goes on to refine small scale features. Beyond reproducing
paintings, this approach is expected to have a wide variety of applications
such as uncertainty quantification, sampling for efficient inference in
scalable machine learning for big data, and developing effective strategies for
search and rescue. In particular, our preliminary studies demonstrate that this
algorithm provides significant acceleration and higher accuracy than competing
methods for Markov Chain Monte Carlo (MCMC).
| Tuhin Sahai, George Mathew and Amit Surana | null | 1504.02010 | null | null |
The Computational Power of Optimization in Online Learning | cs.LG cs.GT | We consider the fundamental problem of prediction with expert advice where
the experts are "optimizable": there is a black-box optimization oracle that
can be used to compute, in constant time, the leading expert in retrospect at
any point in time. In this setting, we give a novel online algorithm that
attains vanishing regret with respect to $N$ experts in total
$\widetilde{O}(\sqrt{N})$ computation time. We also give a lower bound showing
that this running time cannot be improved (up to log factors) in the oracle
model, thereby exhibiting a quadratic speedup as compared to the standard,
oracle-free setting where the required time for vanishing regret is
$\widetilde{\Theta}(N)$. These results demonstrate an exponential gap between
the power of optimization in online learning and its power in statistical
learning: in the latter, an optimization oracle---i.e., an efficient empirical
risk minimizer---allows to learn a finite hypothesis class of size $N$ in time
$O(\log{N})$. We also study the implications of our results to learning in
repeated zero-sum games, in a setting where the players have access to oracles
that compute, in constant time, their best-response to any mixed strategy of
their opponent. We show that the runtime required for approximating the minimax
value of the game in this setting is $\widetilde{\Theta}(\sqrt{N})$, yielding
again a quadratic improvement upon the oracle-free setting, where
$\widetilde{\Theta}(N)$ is known to be tight.
| Elad Hazan, Tomer Koren | null | 1504.02089 | null | null |
Residential Demand Response Applications Using Batch Reinforcement
Learning | cs.SY cs.LG | Driven by recent advances in batch Reinforcement Learning (RL), this paper
contributes to the application of batch RL to demand response. In contrast to
conventional model-based approaches, batch RL techniques do not require a
system identification step, which makes them more suitable for a large-scale
implementation. This paper extends fitted Q-iteration, a standard batch RL
technique, to the situation where a forecast of the exogenous data is provided.
In general, batch RL techniques do not rely on expert knowledge on the system
dynamics or the solution. However, if some expert knowledge is provided, it can
be incorporated by using our novel policy adjustment method. Finally, we tackle
the challenge of finding an open-loop schedule required to participate in the
day-ahead market. We propose a model-free Monte-Carlo estimator method that
uses a metric to construct artificial trajectories and we illustrate this
method by finding the day-ahead schedule of a heat-pump thermostat. Our
experiments show that batch RL techniques provide a valuable alternative to
model-based controllers and that they can be used to construct both closed-loop
and open-loop policies.
| Frederik Ruelens, Bert Claessens, Stijn Vandael, Bart De Schutter,
Robert Babuska and Ronnie Belmans | null | 1504.02125 | null | null |
Detecting Falls with X-Factor Hidden Markov Models | cs.LG cs.AI | Identification of falls while performing normal activities of daily living
(ADL) is important to ensure personal safety and well-being. However, falling
is a short term activity that occurs infrequently. This poses a challenge to
traditional classification algorithms, because there may be very little
training data for falls (or none at all). This paper proposes an approach for
the identification of falls using a wearable device in the absence of training
data for falls but with plentiful data for normal ADL. We propose three
`X-Factor' Hidden Markov Model (XHMMs) approaches. The XHMMs model unseen falls
using "inflated" output covariances (observation models). To estimate the
inflated covariances, we propose a novel cross validation method to remove
"outliers" from the normal ADL that serve as proxies for the unseen falls and
allow learning the XHMMs using only normal activities. We tested the proposed
XHMM approaches on two activity recognition datasets and show high detection
rates for falls in the absence of fall-specific training data. We show that the
traditional method of choosing a threshold based on maximum of negative of
log-likelihood to identify unseen falls is ill-posed for this problem. We also
show that supervised classification methods perform poorly when very limited
fall data are available during the training phase.
| Shehroz S. Khan, Michelle E. Karg, Dana Kulic, Jesse Hoey | 10.1016/j.asoc.2017.01.034 | 1504.02141 | null | null |
Unwrapping ADMM: Efficient Distributed Computing via Transpose Reduction | cs.DC cs.LG | Recent approaches to distributed model fitting rely heavily on consensus
ADMM, where each node solves small sub-problems using only local data. We
propose iterative methods that solve {\em global} sub-problems over an entire
distributed dataset. This is possible using transpose reduction strategies that
allow a single node to solve least-squares over massive datasets without
putting all the data in one place. This results in simple iterative methods
that avoid the expensive inner loops required for consensus methods. To
demonstrate the efficiency of this approach, we fit linear classifiers and
sparse linear models to datasets over 5 Tb in size using a distributed
implementation with over 7000 cores in far less time than previous approaches.
| Tom Goldstein, Gavin Taylor, Kawika Barabin, Kent Sayre | null | 1504.02147 | null | null |
Projective simulation with generalization | cs.AI cs.LG stat.ML | The ability to generalize is an important feature of any intelligent agent.
Not only because it may allow the agent to cope with large amounts of data, but
also because in some environments, an agent with no generalization capabilities
cannot learn. In this work we outline several criteria for generalization, and
present a dynamic and autonomous machinery that enables projective simulation
agents to meaningfully generalize. Projective simulation, a novel, physical
approach to artificial intelligence, was recently shown to perform well in
standard reinforcement learning problems, with applications in advanced
robotics as well as quantum experiments. Both the basic projective simulation
model and the presented generalization machinery are based on very simple
principles. This allows us to provide a full analytical analysis of the agent's
performance and to illustrate the benefit the agent gains by generalizing.
Specifically, we show that already in basic (but extreme) environments,
learning without generalization may be impossible, and demonstrate how the
presented generalization machinery enables the projective simulation agent to
learn.
| Alexey A. Melnikov, Adi Makmal, Vedran Dunjko and Hans J. Briegel | 10.1038/s41598-017-14740-y | 1504.02247 | null | null |
Kernel Manifold Alignment | stat.ML cs.LG | We introduce a kernel method for manifold alignment (KEMA) and domain
adaptation that can match an arbitrary number of data sources without needing
corresponding pairs, just few labeled examples in all domains. KEMA has
interesting properties: 1) it generalizes other manifold alignment methods, 2)
it can align manifolds of very different complexities, performing a sort of
manifold unfolding plus alignment, 3) it can define a domain-specific metric to
cope with multimodal specificities, 4) it can align data spaces of different
dimensionality, 5) it is robust to strong nonlinear feature deformations, and
6) it is closed-form invertible which allows transfer across-domains and data
synthesis. We also present a reduced-rank version for computational efficiency
and discuss the generalization performance of KEMA under Rademacher principles
of stability. KEMA exhibits very good performance over competing methods in
synthetic examples, visual object recognition and recognition of facial
expressions tasks.
| Devis Tuia and Gustau Camps-Valls | 10.1371/journal.pone.0148655 | 1504.02338 | null | null |
When Face Recognition Meets with Deep Learning: an Evaluation of
Convolutional Neural Networks for Face Recognition | cs.CV cs.LG cs.NE | Deep learning, in particular Convolutional Neural Network (CNN), has achieved
promising results in face recognition recently. However, it remains an open
question: why CNNs work well and how to design a 'good' architecture. The
existing works tend to focus on reporting CNN architectures that work well for
face recognition rather than investigate the reason. In this work, we conduct
an extensive evaluation of CNN-based face recognition systems (CNN-FRS) on a
common ground to make our work easily reproducible. Specifically, we use public
database LFW (Labeled Faces in the Wild) to train CNNs, unlike most existing
CNNs trained on private databases. We propose three CNN architectures which are
the first reported architectures trained using LFW data. This paper
quantitatively compares the architectures of CNNs and evaluate the effect of
different implementation choices. We identify several useful properties of
CNN-FRS. For instance, the dimensionality of the learned features can be
significantly reduced without adverse effect on face recognition accuracy. In
addition, traditional metric learning method exploiting CNN-learned features is
evaluated. Experiments show two crucial factors to good CNN-FRS performance are
the fusion of multiple CNNs and metric learning. To make our work reproducible,
source code and models will be made publicly available.
| Guosheng Hu, Yongxin Yang, Dong Yi, Josef Kittler, William Christmas,
Stan Z. Li and Timothy Hospedales | null | 1504.02351 | null | null |
Deciding when to stop: Efficient stopping of active learning guided
drug-target prediction | q-bio.QM cs.LG stat.ML | Active learning has shown to reduce the number of experiments needed to
obtain high-confidence drug-target predictions. However, in order to actually
save experiments using active learning, it is crucial to have a method to
evaluate the quality of the current prediction and decide when to stop the
experimentation process. Only by applying reliable stoping criteria to active
learning, time and costs in the experimental process can be actually saved. We
compute active learning traces on simulated drug-target matrices in order to
learn a regression model for the accuracy of the active learner. By analyzing
the performance of the regression model on simulated data, we design stopping
criteria for previously unseen experimental matrices. We demonstrate on four
previously characterized drug effect data sets that applying the stopping
criteria can result in upto 40% savings of the total experiments for highly
accurate predictions.
| Maja Temerinac-Ott and Armaghan W. Naik and Robert F. Murphy | null | 1504.02406 | null | null |
A Group Theoretic Perspective on Unsupervised Deep Learning | cs.LG cs.NE stat.ML | Why does Deep Learning work? What representations does it capture? How do
higher-order representations emerge? We study these questions from the
perspective of group theory, thereby opening a new approach towards a theory of
Deep learning.
One factor behind the recent resurgence of the subject is a key algorithmic
step called {\em pretraining}: first search for a good generative model for the
input samples, and repeat the process one layer at a time. We show deeper
implications of this simple principle, by establishing a connection with the
interplay of orbits and stabilizers of group actions. Although the neural
networks themselves may not form groups, we show the existence of {\em shadow}
groups whose elements serve as close approximations.
Over the shadow groups, the pre-training step, originally introduced as a
mechanism to better initialize a network, becomes equivalent to a search for
features with minimal orbits. Intuitively, these features are in a way the {\em
simplest}. Which explains why a deep learning network learns simple features
first. Next, we show how the same principle, when repeated in the deeper
layers, can capture higher order representations, and why representation
complexity increases as the layers get deeper.
| Arnab Paul, Suresh Venkatasubramanian | null | 1504.02462 | null | null |
Unsupervised Feature Learning from Temporal Data | cs.CV cs.LG | Current state-of-the-art classification and detection algorithms rely on
supervised training. In this work we study unsupervised feature learning in the
context of temporally coherent video data. We focus on feature learning from
unlabeled video data, using the assumption that adjacent video frames contain
semantically similar information. This assumption is exploited to train a
convolutional pooling auto-encoder regularized by slowness and sparsity. We
establish a connection between slow feature learning to metric learning and
show that the trained encoder can be used to define a more temporally and
semantically coherent metric.
| Ross Goroshin, Joan Bruna, Jonathan Tompson, David Eigen, Yann LeCun | null | 1504.02518 | null | null |
Learning Arbitrary Statistical Mixtures of Discrete Distributions | cs.LG cs.DS | We study the problem of learning from unlabeled samples very general
statistical mixture models on large finite sets. Specifically, the model to be
learned, $\vartheta$, is a probability distribution over probability
distributions $p$, where each such $p$ is a probability distribution over $[n]
= \{1,2,\dots,n\}$. When we sample from $\vartheta$, we do not observe $p$
directly, but only indirectly and in very noisy fashion, by sampling from $[n]$
repeatedly, independently $K$ times from the distribution $p$. The problem is
to infer $\vartheta$ to high accuracy in transportation (earthmover) distance.
We give the first efficient algorithms for learning this mixture model
without making any restricting assumptions on the structure of the distribution
$\vartheta$. We bound the quality of the solution as a function of the size of
the samples $K$ and the number of samples used. Our model and results have
applications to a variety of unsupervised learning scenarios, including
learning topic models and collaborative filtering.
| Jian Li, Yuval Rabani, Leonard J. Schulman, Chaitanya Swamy | null | 1504.02526 | null | null |
Maximum Entropy Linear Manifold for Learning Discriminative
Low-dimensional Representation | cs.LG | Representation learning is currently a very hot topic in modern machine
learning, mostly due to the great success of the deep learning methods. In
particular low-dimensional representation which discriminates classes can not
only enhance the classification procedure, but also make it faster, while
contrary to the high-dimensional embeddings can be efficiently used for visual
based exploratory data analysis.
In this paper we propose Maximum Entropy Linear Manifold (MELM), a
multidimensional generalization of Multithreshold Entropy Linear Classifier
model which is able to find a low-dimensional linear data projection maximizing
discriminativeness of projected classes. As a result we obtain a linear
embedding which can be used for classification, class aware dimensionality
reduction and data visualization. MELM provides highly discriminative 2D
projections of the data which can be used as a method for constructing robust
classifiers.
We provide both empirical evaluation as well as some interesting theoretical
properties of our objective function such us scale and affine transformation
invariance, connections with PCA and bounding of the expected balanced accuracy
error.
| Wojciech Marian Czarnecki, Rafa{\l} J\'ozefowicz, Jacek Tabor | null | 1504.02622 | null | null |
Gradient of Probability Density Functions based Contrasts for Blind
Source Separation (BSS) | cs.LG cs.IT math.IT stat.ML | The article derives some novel independence measures and contrast functions
for Blind Source Separation (BSS) application. For the $k^{th}$ order
differentiable multivariate functions with equal hyper-volumes (region bounded
by hyper-surfaces) and with a constraint of bounded support for $k>1$, it
proves that equality of any $k^{th}$ order derivatives implies equality of the
functions. The difference between product of marginal Probability Density
Functions (PDFs) and joint PDF of a random vector is defined as Function
Difference (FD) of a random vector. Assuming the PDFs are $k^{th}$ order
differentiable, the results on generalized functions are applied to the
independence condition. This brings new sets of independence measures and BSS
contrasts based on the $L^p$-Norm, $ p \geq 1$ of - FD, gradient of FD (GFD)
and Hessian of FD (HFD). Instead of a conventional two stage indirect
estimation method for joint PDF based BSS contrast estimation, a single stage
direct estimation of the contrasts is desired. The article targets both the
efficient estimation of the proposed contrasts and extension of the potential
theory for an information field. The potential theory has a concept of
reference potential and it is used to derive closed form expression for the
relative analysis of potential field. Analogous to it, there are introduced
concepts of Reference Information Potential (RIP) and Cross Reference
Information Potential (CRIP) based on the potential due to kernel functions
placed at selected sample points as basis in kernel methods. The quantities are
used to derive closed form expressions for information field analysis using
least squares. The expressions are used to estimate $L^2$-Norm of FD and
$L^2$-Norm of GFD based contrasts.
| Dharmani Bhaveshkumar C | null | 1504.02712 | null | null |
Diffusion Component Analysis: Unraveling Functional Topology in
Biological Networks | q-bio.MN cs.LG cs.SI stat.ML | Complex biological systems have been successfully modeled by biochemical and
genetic interaction networks, typically gathered from high-throughput (HTP)
data. These networks can be used to infer functional relationships between
genes or proteins. Using the intuition that the topological role of a gene in a
network relates to its biological function, local or diffusion based
"guilt-by-association" and graph-theoretic methods have had success in
inferring gene functions. Here we seek to improve function prediction by
integrating diffusion-based methods with a novel dimensionality reduction
technique to overcome the incomplete and noisy nature of network data. In this
paper, we introduce diffusion component analysis (DCA), a framework that plugs
in a diffusion model and learns a low-dimensional vector representation of each
node to encode the topological properties of a network. As a proof of concept,
we demonstrate DCA's substantial improvement over state-of-the-art
diffusion-based approaches in predicting protein function from molecular
interaction networks. Moreover, our DCA framework can integrate multiple
networks from heterogeneous sources, consisting of genomic information,
biochemical experiments and other resources, to even further improve function
prediction. Yet another layer of performance gain is achieved by integrating
the DCA framework with support vector machines that take our node vector
representations as features. Overall, our DCA framework provides a novel
representation of nodes in a network that can be used as a plug-in architecture
to other machine learning algorithms to decipher topological properties of and
obtain novel insights into interactomes.
| Hyunghoon Cho, Bonnie Berger and Jian Peng | null | 1504.02719 | null | null |
Performance measures for classification systems with rejection | cs.CV cs.LG | Classifiers with rejection are essential in real-world applications where
misclassifications and their effects are critical. However, if no problem
specific cost function is defined, there are no established measures to assess
the performance of such classifiers. We introduce a set of desired properties
for performance measures for classifiers with rejection, based on which we
propose a set of three performance measures for the evaluation of the
performance of classifiers with rejection that satisfy the desired properties.
The nonrejected accuracy measures the ability of the classifier to accurately
classify nonrejected samples; the classification quality measures the correct
decision making of the classifier with rejector; and the rejection quality
measures the ability to concentrate all misclassified samples onto the set of
rejected samples. From the measures, we derive the concept of relative
optimality that allows us to connect the measures to a family of cost functions
that take into account the trade-off between rejection and misclassification.
We illustrate the use of the proposed performance measures on classifiers with
rejection applied to synthetic and real-world data.
| Filipe Condessa, Jelena Kovacevic, Jose Bioucas-Dias | null | 1504.02763 | null | null |
A Deep Embedding Model for Co-occurrence Learning | cs.LG | Co-occurrence Data is a common and important information source in many
areas, such as the word co-occurrence in the sentences, friends co-occurrence
in social networks and products co-occurrence in commercial transaction data,
etc, which contains rich correlation and clustering information about the
items. In this paper, we study co-occurrence data using a general energy-based
probabilistic model, and we analyze three different categories of energy-based
model, namely, the $L_1$, $L_2$ and $L_k$ models, which are able to capture
different levels of dependency in the co-occurrence data. We also discuss how
several typical existing models are related to these three types of energy
models, including the Fully Visible Boltzmann Machine (FVBM) ($L_2$), Matrix
Factorization ($L_2$), Log-BiLinear (LBL) models ($L_2$), and the Restricted
Boltzmann Machine (RBM) model ($L_k$). Then, we propose a Deep Embedding Model
(DEM) (an $L_k$ model) from the energy model in a \emph{principled} manner.
Furthermore, motivated by the observation that the partition function in the
energy model is intractable and the fact that the major objective of modeling
the co-occurrence data is to predict using the conditional probability, we
apply the \emph{maximum pseudo-likelihood} method to learn DEM. In consequence,
the developed model and its learning method naturally avoid the above
difficulties and can be easily used to compute the conditional probability in
prediction. Interestingly, our method is equivalent to learning a special
structured deep neural network using back-propagation and a special sampling
strategy, which makes it scalable on large-scale datasets. Finally, in the
experiments, we show that the DEM can achieve comparable or better results than
state-of-the-art methods on datasets across several application domains.
| Yelong Shen, Ruoming Jin, Jianshu Chen, Xiaodong He, Jianfeng Gao, Li
Deng | null | 1504.02824 | null | null |
Quick sensitivity analysis for incremental data modification and its
application to leave-one-out CV in linear classification problems | stat.ML cs.LG | We introduce a novel sensitivity analysis framework for large scale
classification problems that can be used when a small number of instances are
incrementally added or removed. For quickly updating the classifier in such a
situation, incremental learning algorithms have been intensively studied in the
literature. Although they are much more efficient than solving the optimization
problem from scratch, their computational complexity yet depends on the entire
training set size. It means that, if the original training set is large,
completely solving an incremental learning problem might be still rather
expensive. To circumvent this computational issue, we propose a novel framework
that allows us to make an inference about the updated classifier without
actually re-optimizing it. Specifically, the proposed framework can quickly
provide a lower and an upper bounds of a quantity on the unknown updated
classifier. The main advantage of the proposed framework is that the
computational cost of computing these bounds depends only on the number of
updated instances. This property is quite advantageous in a typical sensitivity
analysis task where only a small number of instances are updated. In this paper
we demonstrate that the proposed framework is applicable to various practical
sensitivity analysis tasks, and the bounds provided by the framework are often
sufficiently tight for making desired inferences.
| Shota Okumura and Yoshiki Suzuki and Ichiro Takeuchi | null | 1504.02870 | null | null |
Gradual Training Method for Denoising Auto Encoders | cs.LG cs.NE | Stacked denoising auto encoders (DAEs) are well known to learn useful deep
representations, which can be used to improve supervised training by
initializing a deep network. We investigate a training scheme of a deep DAE,
where DAE layers are gradually added and keep adapting as additional layers are
added. We show that in the regime of mid-sized datasets, this gradual training
provides a small but consistent improvement over stacked training in both
reconstruction quality and classification error over stacked training on MNIST
and CIFAR datasets.
| Alexander Kalmanovich and Gal Chechik | null | 1504.02902 | null | null |
Deep Transform: Cocktail Party Source Separation via Complex Convolution
in a Deep Neural Network | cs.SD cs.LG cs.NE | Convolutional deep neural networks (DNN) are state of the art in many
engineering problems but have not yet addressed the issue of how to deal with
complex spectrograms. Here, we use circular statistics to provide a convenient
probabilistic estimate of spectrogram phase in a complex convolutional DNN. In
a typical cocktail party source separation scenario, we trained a convolutional
DNN to re-synthesize the complex spectrograms of two source speech signals
given a complex spectrogram of the monaural mixture - a discriminative deep
transform (DT). We then used this complex convolutional DT to obtain
probabilistic estimates of the magnitude and phase components of the source
spectrograms. Our separation results are on a par with equivalent binary-mask
based non-complex separation approaches.
| Andrew J.R. Simpson | null | 1504.02945 | null | null |
Classification with Extreme Learning Machine and Ensemble Algorithms
Over Randomly Partitioned Data | cs.LG | In this age of Big Data, machine learning based data mining methods are
extensively used to inspect large scale data sets. Deriving applicable
predictive modeling from these type of data sets is a challenging obstacle
because of their high complexity. Opportunity with high data availability
levels, automated classification of data sets has become a critical and
complicated function. In this paper, the power of applying MapReduce based
Distributed AdaBoosting of Extreme Learning Machine (ELM) are explored to build
reliable predictive bag of classification models. Thus, (i) dataset ensembles
are build; (ii) ELM algorithm is used to build weak classification models; and
(iii) build a strong classification model from a set of weak classification
models. This training model is applied to the publicly available knowledge
discovery and data mining datasets.
| Ferhat \"Ozg\"ur \c{C}atak | null | 1504.02975 | null | null |
Robobarista: Object Part based Transfer of Manipulation Trajectories
from Crowd-sourcing in 3D Pointclouds | cs.RO cs.AI cs.LG | There is a large variety of objects and appliances in human environments,
such as stoves, coffee dispensers, juice extractors, and so on. It is
challenging for a roboticist to program a robot for each of these object types
and for each of their instantiations. In this work, we present a novel approach
to manipulation planning based on the idea that many household objects share
similarly-operated object parts. We formulate the manipulation planning as a
structured prediction problem and design a deep learning model that can handle
large noise in the manipulation demonstrations and learns features from three
different modalities: point-clouds, language and trajectory. In order to
collect a large number of manipulation demonstrations for different objects, we
developed a new crowd-sourcing platform called Robobarista. We test our model
on our dataset consisting of 116 objects with 249 parts along with 250 language
instructions, for which there are 1225 crowd-sourced manipulation
demonstrations. We further show that our robot can even manipulate objects it
has never seen before.
| Jaeyong Sung, Seok Hyun Jin, Ashutosh Saxena | null | 1504.03071 | null | null |
Convex Learning of Multiple Tasks and their Structure | cs.LG | Reducing the amount of human supervision is a key problem in machine learning
and a natural approach is that of exploiting the relations (structure) among
different tasks. This is the idea at the core of multi-task learning. In this
context a fundamental question is how to incorporate the tasks structure in the
learning problem.We tackle this question by studying a general computational
framework that allows to encode a-priori knowledge of the tasks structure in
the form of a convex penalty; in this setting a variety of previously proposed
methods can be recovered as special cases, including linear and non-linear
approaches. Within this framework, we show that tasks and their structure can
be efficiently learned considering a convex optimization problem that can be
approached by means of block coordinate methods such as alternating
minimization and for which we prove convergence to the global minimum.
| Carlo Ciliberto, Youssef Mroueh, Tomaso Poggio and Lorenzo Rosasco | null | 1504.03101 | null | null |
Learning Multiple Visual Tasks while Discovering their Structure | cs.LG cs.CV | Multi-task learning is a natural approach for computer vision applications
that require the simultaneous solution of several distinct but related
problems, e.g. object detection, classification, tracking of multiple agents,
or denoising, to name a few. The key idea is that exploring task relatedness
(structure) can lead to improved performances.
In this paper, we propose and study a novel sparse, non-parametric approach
exploiting the theory of Reproducing Kernel Hilbert Spaces for vector-valued
functions. We develop a suitable regularization framework which can be
formulated as a convex optimization problem, and is provably solvable using an
alternating minimization approach. Empirical tests show that the proposed
method compares favorably to state of the art techniques and further allows to
recover interpretable structures, a problem of interest in its own right.
| Carlo Ciliberto, Lorenzo Rosasco and Silvia Villa | null | 1504.03106 | null | null |
Real-world Object Recognition with Off-the-shelf Deep Conv Nets: How
Many Objects can iCub Learn? | cs.RO cs.CV cs.LG | The ability to visually recognize objects is a fundamental skill for robotics
systems. Indeed, a large variety of tasks involving manipulation, navigation or
interaction with other agents, deeply depends on the accurate understanding of
the visual scene. Yet, at the time being, robots are lacking good visual
perceptual systems, which often become the main bottleneck preventing the use
of autonomous agents for real-world applications.
Lately in computer vision, systems that learn suitable visual representations
and based on multi-layer deep convolutional networks are showing remarkable
performance in tasks such as large-scale visual recognition and image
retrieval. To this regard, it is natural to ask whether such remarkable
performance would generalize also to the robotic setting.
In this paper we investigate such possibility, while taking further steps in
developing a computational vision system to be embedded on a robotic platform,
the iCub humanoid robot. In particular, we release a new dataset ({\sc
iCubWorld28}) that we use as a benchmark to address the question: {\it how many
objects can iCub recognize?} Our study is developed in a learning framework
which reflects the typical visual experience of a humanoid robot like the iCub.
Experiments shed interesting insights on the strength and weaknesses of current
computer vision approaches applied in real robotic settings.
| Giulia Pasquale, Carlo Ciliberto, Francesca Odone, Lorenzo Rosasco and
Lorenzo Natale | null | 1504.03154 | null | null |
Tight Bounds on Low-degree Spectral Concentration of Submodular and XOS
functions | cs.DS cs.LG | Submodular and fractionally subadditive (or equivalently XOS) functions play
a fundamental role in combinatorial optimization, algorithmic game theory and
machine learning. Motivated by learnability of these classes of functions from
random examples, we consider the question of how well such functions can be
approximated by low-degree polynomials in $\ell_2$ norm over the uniform
distribution. This question is equivalent to understanding of the concentration
of Fourier weight on low-degree coefficients, a central concept in Fourier
analysis. We show that
1. For any submodular function $f:\{0,1\}^n \rightarrow [0,1]$, there is a
polynomial of degree $O(\log (1/\epsilon) / \epsilon^{4/5})$ approximating $f$
within $\epsilon$ in $\ell_2$, and there is a submodular function that requires
degree $\Omega(1/\epsilon^{4/5})$.
2. For any XOS function $f:\{0,1\}^n \rightarrow [0,1]$, there is a
polynomial of degree $O(1/\epsilon)$ and there exists an XOS function that
requires degree $\Omega(1/\epsilon)$.
This improves on previous approaches that all showed an upper bound of
$O(1/\epsilon^2)$ for submodular and XOS functions. The best previous lower
bound was $\Omega(1/\epsilon^{2/3})$ for monotone submodular functions. Our
techniques reveal new structural properties of submodular and XOS functions and
the upper bounds lead to nearly optimal PAC learning algorithms for these
classes of functions.
| Vitaly Feldman and Jan Vondrak | null | 1504.03391 | null | null |
HHCART: An Oblique Decision Tree | stat.ML cs.LG | Decision trees are a popular technique in statistical data classification.
They recursively partition the feature space into disjoint sub-regions until
each sub-region becomes homogeneous with respect to a particular class. The
basic Classification and Regression Tree (CART) algorithm partitions the
feature space using axis parallel splits. When the true decision boundaries are
not aligned with the feature axes, this approach can produce a complicated
boundary structure. Oblique decision trees use oblique decision boundaries to
potentially simplify the boundary structure. The major limitation of this
approach is that the tree induction algorithm is computationally expensive. In
this article we present a new decision tree algorithm, called HHCART. The
method utilizes a series of Householder matrices to reflect the training data
at each node during the tree construction. Each reflection is based on the
directions of the eigenvectors from each classes' covariance matrix.
Considering axis parallel splits in the reflected training data provides an
efficient way of finding oblique splits in the unreflected training data.
Experimental results show that the accuracy and size of the HHCART trees are
comparable with some benchmark methods in the literature. The appealing feature
of HHCART is that it can handle both qualitative and quantitative features in
the same oblique split.
| D. C. Wickramarachchi, B. L. Robertson, M. Reale, C. J. Price and J.
Brown | null | 1504.03415 | null | null |
Regret vs. Communication: Distributed Stochastic Multi-Armed Bandits and
Beyond | cs.LG stat.ML | In this paper, we consider the distributed stochastic multi-armed bandit
problem, where a global arm set can be accessed by multiple players
independently. The players are allowed to exchange their history of
observations with each other at specific points in time. We study the
relationship between regret and communication. When the time horizon is known,
we propose the Over-Exploration strategy, which only requires one-round
communication and whose regret does not scale with the number of players. When
the time horizon is unknown, we measure the frequency of communication through
a new notion called the density of the communication set, and give an exact
characterization of the interplay between regret and communication.
Specifically, a lower bound is established and stable strategies that match the
lower bound are developed. The results and analyses in this paper are specific
but can be translated into more general settings.
| Shuang Liu, Cheng Chen and Zhihua Zhang | null | 1504.03509 | null | null |
Learning to Compare Image Patches via Convolutional Neural Networks | cs.CV cs.LG cs.NE | In this paper we show how to learn directly from image data (i.e., without
resorting to manually-designed features) a general similarity function for
comparing image patches, which is a task of fundamental importance for many
computer vision problems. To encode such a function, we opt for a CNN-based
model that is trained to account for a wide variety of changes in image
appearance. To that end, we explore and study multiple neural network
architectures, which are specifically adapted to this task. We show that such
an approach can significantly outperform the state-of-the-art on several
problems and benchmark datasets.
| Sergey Zagoruyko and Nikos Komodakis | null | 1504.03641 | null | null |
Scale Up Nonlinear Component Analysis with Doubly Stochastic Gradients | cs.LG | Nonlinear component analysis such as kernel Principle Component Analysis
(KPCA) and kernel Canonical Correlation Analysis (KCCA) are widely used in
machine learning, statistics and data analysis, but they can not scale up to
big datasets. Recent attempts have employed random feature approximations to
convert the problem to the primal form for linear computational complexity.
However, to obtain high quality solutions, the number of random features should
be the same order of magnitude as the number of data points, making such
approach not directly applicable to the regime with millions of data points.
We propose a simple, computationally efficient, and memory friendly algorithm
based on the "doubly stochastic gradients" to scale up a range of kernel
nonlinear component analysis, such as kernel PCA, CCA and SVD. Despite the
\emph{non-convex} nature of these problems, our method enjoys theoretical
guarantees that it converges at the rate $\tilde{O}(1/t)$ to the global
optimum, even for the top $k$ eigen subspace. Unlike many alternatives, our
algorithm does not require explicit orthogonalization, which is infeasible on
big datasets. We demonstrate the effectiveness and scalability of our algorithm
on large scale synthetic and real world datasets.
| Bo Xie, Yingyu Liang, Le Song | null | 1504.03655 | null | null |
Probabilistic Clustering of Time-Evolving Distance Data | cs.LG stat.ML | We present a novel probabilistic clustering model for objects that are
represented via pairwise distances and observed at different time points. The
proposed method utilizes the information given by adjacent time points to find
the underlying cluster structure and obtain a smooth cluster evolution. This
approach allows the number of objects and clusters to differ at every time
point, and no identification on the identities of the objects is needed.
Further, the model does not require the number of clusters being specified in
advance -- they are instead determined automatically using a Dirichlet process
prior. We validate our model on synthetic data showing that the proposed method
is more accurate than state-of-the-art clustering methods. Finally, we use our
dynamic clustering model to analyze and illustrate the evolution of brain
cancer patients over time.
| Julia E. Vogt, Marius Kloft, Stefan Stark, Sudhir S. Raman, Sandhya
Prabhakaran, Volker Roth and Gunnar R\"atsch | null | 1504.03701 | null | null |
Bridging belief function theory to modern machine learning | cs.AI cs.LG | Machine learning is a quickly evolving field which now looks really different
from what it was 15 years ago, when classification and clustering were major
issues. This document proposes several trends to explore the new questions of
modern machine learning, with the strong afterthought that the belief function
framework has a major role to play.
| Thomas Burger | null | 1504.03874 | null | null |
Linear Maximum Margin Classifier for Learning from Uncertain Data | cs.LG | In this paper, we propose a maximum margin classifier that deals with
uncertainty in data input. More specifically, we reformulate the SVM framework
such that each training example can be modeled by a multi-dimensional Gaussian
distribution described by its mean vector and its covariance matrix -- the
latter modeling the uncertainty. We address the classification problem and
define a cost function that is the expected value of the classical SVM cost
when data samples are drawn from the multi-dimensional Gaussian distributions
that form the set of the training examples. Our formulation approximates the
classical SVM formulation when the training examples are isotropic Gaussians
with variance tending to zero. We arrive at a convex optimization problem,
which we solve efficiently in the primal form using a stochastic gradient
descent approach. The resulting classifier, which we name SVM with Gaussian
Sample Uncertainty (SVM-GSU), is tested on synthetic data and five publicly
available and popular datasets; namely, the MNIST, WDBC, DEAP, TV News Channel
Commercial Detection, and TRECVID MED datasets. Experimental results verify the
effectiveness of the proposed method.
| Christos Tzelepis, Vasileios Mezaris and Ioannis Patras | 10.1109/TPAMI.2017.2772235 | 1504.03892 | null | null |
Theory of Dual-sparse Regularized Randomized Reduction | cs.LG stat.ML | In this paper, we study randomized reduction methods, which reduce
high-dimensional features into low-dimensional space by randomized methods
(e.g., random projection, random hashing), for large-scale high-dimensional
classification. Previous theoretical results on randomized reduction methods
hinge on strong assumptions about the data, e.g., low rank of the data matrix
or a large separable margin of classification, which hinder their applications
in broad domains. To address these limitations, we propose dual-sparse
regularized randomized reduction methods that introduce a sparse regularizer
into the reduced dual problem. Under a mild condition that the original dual
solution is a (nearly) sparse vector, we show that the resulting dual solution
is close to the original dual solution and concentrates on its support set. In
numerical experiments, we present an empirical study to support the analysis
and we also present a novel application of the dual-sparse regularized
randomized reduction methods to reducing the communication cost of distributed
learning from large-scale high-dimensional data.
| Tianbao Yang, Lijun Zhang, Rong Jin, Shenghuo Zhu | null | 1504.03991 | null | null |
A Generative Model for Deep Convolutional Learning | stat.ML cs.LG cs.NE | A generative model is developed for deep (multi-layered) convolutional
dictionary learning. A novel probabilistic pooling operation is integrated into
the deep model, yielding efficient bottom-up (pretraining) and top-down
(refinement) probabilistic learning. Experimental results demonstrate powerful
capabilities of the model to learn multi-layer features from images, and
excellent classification results are obtained on the MNIST and Caltech 101
datasets.
| Yunchen Pu, Xin Yuan, Lawrence Carin | null | 1504.04054 | null | null |
Faster Algorithms for Testing under Conditional Sampling | cs.DS cs.CC cs.LG math.ST stat.TH | There has been considerable recent interest in distribution-tests whose
run-time and sample requirements are sublinear in the domain-size $k$. We study
two of the most important tests under the conditional-sampling model where each
query specifies a subset $S$ of the domain, and the response is a sample drawn
from $S$ according to the underlying distribution.
For identity testing, which asks whether the underlying distribution equals a
specific given distribution or $\epsilon$-differs from it, we reduce the known
time and sample complexities from $\tilde{\mathcal{O}}(\epsilon^{-4})$ to
$\tilde{\mathcal{O}}(\epsilon^{-2})$, thereby matching the information
theoretic lower bound. For closeness testing, which asks whether two
distributions underlying observed data sets are equal or different, we reduce
existing complexity from $\tilde{\mathcal{O}}(\epsilon^{-4} \log^5 k)$ to an
even sub-logarithmic $\tilde{\mathcal{O}}(\epsilon^{-5} \log \log k)$ thus
providing a better bound to an open problem in Bertinoro Workshop on Sublinear
Algorithms [Fisher, 2004].
| Moein Falahatgar and Ashkan Jafarpour and Alon Orlitsky and
Venkatadheeraj Pichapathi and Ananda Theertha Suresh | null | 1504.04103 | null | null |
Actively Learning to Attract Followers on Twitter | stat.ML cs.LG cs.SI | Twitter, a popular social network, presents great opportunities for on-line
machine learning research. However, previous research has focused almost
entirely on learning from passively collected data. We study the problem of
learning to acquire followers through normative user behavior, as opposed to
the mass following policies applied by many bots. We formalize the problem as a
contextual bandit problem, in which we consider retweeting content to be the
action chosen and each tweet (content) is accompanied by context. We design
reward signals based on the change in followers. The result of our month long
experiment with 60 agents suggests that (1) aggregating experience across
agents can adversely impact prediction accuracy and (2) the Twitter community's
response to different actions is non-stationary. Our findings suggest that
actively learning on-line can provide deeper insights about how to attract
followers than machine learning over passively collected data alone.
| Nir Levine, Timothy A. Mann, Shie Mannor | null | 1504.04114 | null | null |
Caffe con Troll: Shallow Ideas to Speed Up Deep Learning | cs.LG cs.CV stat.ML | We present Caffe con Troll (CcT), a fully compatible end-to-end version of
the popular framework Caffe with rebuilt internals. We built CcT to examine the
performance characteristics of training and deploying general-purpose
convolutional neural networks across different hardware architectures. We find
that, by employing standard batching optimizations for CPU training, we achieve
a 4.5x throughput improvement over Caffe on popular networks like CaffeNet.
Moreover, with these improvements, the end-to-end training time for CNNs is
directly proportional to the FLOPS delivered by the CPU, which enables us to
efficiently train hybrid CPU-GPU systems for CNNs.
| Stefan Hadjis, Firas Abuzaid, Ce Zhang, Christopher R\'e | null | 1504.04343 | null | null |
Non-Uniform Stochastic Average Gradient Method for Training Conditional
Random Fields | stat.ML cs.LG math.OC stat.CO | We apply stochastic average gradient (SAG) algorithms for training
conditional random fields (CRFs). We describe a practical implementation that
uses structure in the CRF gradient to reduce the memory requirement of this
linearly-convergent stochastic gradient method, propose a non-uniform sampling
scheme that substantially improves practical performance, and analyze the rate
of convergence of the SAGA variant under non-uniform sampling. Our experimental
results reveal that our method often significantly outperforms existing methods
in terms of the training objective, and performs as well or better than
optimally-tuned stochastic gradient methods in terms of test error.
| Mark Schmidt, Reza Babanezhad, Mohamed Osama Ahmed, Aaron Defazio, Ann
Clifton, Anoop Sarkar | null | 1504.04406 | null | null |
Mini-Batch Semi-Stochastic Gradient Descent in the Proximal Setting | cs.LG stat.ML | We propose mS2GD: a method incorporating a mini-batching scheme for improving
the theoretical complexity and practical performance of semi-stochastic
gradient descent (S2GD). We consider the problem of minimizing a strongly
convex function represented as the sum of an average of a large number of
smooth convex functions, and a simple nonsmooth convex regularizer. Our method
first performs a deterministic step (computation of the gradient of the
objective function at the starting point), followed by a large number of
stochastic steps. The process is repeated a few times with the last iterate
becoming the new starting point. The novelty of our method is in introduction
of mini-batching into the computation of stochastic steps. In each step,
instead of choosing a single function, we sample $b$ functions, compute their
gradients, and compute the direction based on this. We analyze the complexity
of the method and show that it benefits from two speedup effects. First, we
prove that as long as $b$ is below a certain threshold, we can reach any
predefined accuracy with less overall work than without mini-batching. Second,
our mini-batching scheme admits a simple parallel implementation, and hence is
suitable for further acceleration by parallelization.
| Jakub Kone\v{c}n\'y, Jie Liu, Peter Richt\'arik, Martin Tak\'a\v{c} | 10.1109/JSTSP.2015.2505682 | 1504.04407 | null | null |
The Nataf-Beta Random Field Classifier: An Extension of the Beta
Conjugate Prior to Classification Problems | cs.LG | This paper presents the Nataf-Beta Random Field Classifier, a discriminative
approach that extends the applicability of the Beta conjugate prior to
classification problems. The approach's key feature is to model the probability
of a class conditional on attribute values as a random field whose marginals
are Beta distributed, and where the parameters of marginals are themselves
described by random fields. Although the classification accuracy of the
approach proposed does not statistically outperform the best accuracies
reported in the literature, it ranks among the top tier for the six benchmark
datasets tested. The Nataf-Beta Random Field Classifier is suited as a general
purpose classification approach for real-continuous and real-integer attribute
value problems.
| James-A. Goulet | null | 1504.04588 | null | null |
Testing Closeness With Unequal Sized Samples | cs.LG cs.IT math.IT math.ST stat.ML stat.TH | We consider the problem of closeness testing for two discrete distributions
in the practically relevant setting of \emph{unequal} sized samples drawn from
each of them. Specifically, given a target error parameter $\varepsilon > 0$,
$m_1$ independent draws from an unknown distribution $p,$ and $m_2$ draws from
an unknown distribution $q$, we describe a test for distinguishing the case
that $p=q$ from the case that $||p-q||_1 \geq \varepsilon$. If $p$ and $q$ are
supported on at most $n$ elements, then our test is successful with high
probability provided $m_1\geq n^{2/3}/\varepsilon^{4/3}$ and $m_2 =
\Omega(\max\{\frac{n}{\sqrt m_1\varepsilon^2}, \frac{\sqrt
n}{\varepsilon^2}\});$ we show that this tradeoff is optimal throughout this
range, to constant factors. These results extend the recent work of Chan et al.
who established the sample complexity when the two samples have equal sizes,
and tightens the results of Acharya et al. by polynomials factors in both $n$
and $\varepsilon$. As a consequence, we obtain an algorithm for estimating the
mixing time of a Markov chain on $n$ states up to a $\log n$ factor that uses
$\tilde{O}(n^{3/2} \tau_{mix})$ queries to a "next node" oracle, improving upon
the $\tilde{O}(n^{5/3}\tau_{mix})$ query algorithm of Batu et al. Finally, we
note that the core of our testing algorithm is a relatively simple statistic
that seems to perform well in practice, both on synthetic data and on natural
language data.
| Bhaswar B. Bhattacharya and Gregory Valiant | null | 1504.04599 | null | null |
Performance Evaluation of Machine Learning Algorithms in Post-operative
Life Expectancy in the Lung Cancer Patients | cs.LG | The nature of clinical data makes it difficult to quickly select, tune and
apply machine learning algorithms to clinical prognosis. As a result, a lot of
time is spent searching for the most appropriate machine learning algorithms
applicable in clinical prognosis that contains either binary-valued or
multi-valued attributes. The study set out to identify and evaluate the
performance of machine learning classification schemes applied in clinical
prognosis of post-operative life expectancy in the lung cancer patients.
Multilayer Perceptron, J48, and the Naive Bayes algorithms were used to train
and test models on Thoracic Surgery datasets obtained from the University of
California Irvine machine learning repository. Stratified 10-fold
cross-validation was used to evaluate baseline performance accuracy of the
classifiers. The comparative analysis shows that multilayer perceptron
performed best with classification accuracy of 82.3%, J48 came out second with
classification accuracy of 81.8%, and Naive Bayes came out the worst with
classification accuracy of 74.4%. The quality and outcome of the chosen machine
learning algorithms depends on the ingenuity of the clinical miner.
| Kwetishe Joro Danjuma | null | 1504.04646 | null | null |
Deep Karaoke: Extracting Vocals from Musical Mixtures Using a
Convolutional Deep Neural Network | cs.SD cs.LG cs.NE | Identification and extraction of singing voice from within musical mixtures
is a key challenge in source separation and machine audition. Recently, deep
neural networks (DNN) have been used to estimate 'ideal' binary masks for
carefully controlled cocktail party speech separation problems. However, it is
not yet known whether these methods are capable of generalizing to the
discrimination of voice and non-voice in the context of musical mixtures. Here,
we trained a convolutional DNN (of around a billion parameters) to provide
probabilistic estimates of the ideal binary mask for separation of vocal sounds
from real-world musical mixtures. We contrast our DNN results with more
traditional linear methods. Our approach may be useful for automatic removal of
vocal sounds from musical mixtures for 'karaoke' type applications.
| Andrew J.R. Simpson, Gerard Roma, Mark D. Plumbley | null | 1504.04658 | null | null |
Unsupervised Dependency Parsing: Let's Use Supervised Parsers | cs.CL cs.LG | We present a self-training approach to unsupervised dependency parsing that
reuses existing supervised and unsupervised parsing algorithms. Our approach,
called `iterated reranking' (IR), starts with dependency trees generated by an
unsupervised parser, and iteratively improves these trees using the richer
probability models used in supervised parsing that are in turn trained on these
trees. Our system achieves 1.8% accuracy higher than the state-of-the-part
parser of Spitkovsky et al. (2013) on the WSJ corpus.
| Phong Le and Willem Zuidema | null | 1504.04666 | null | null |
Local, Private, Efficient Protocols for Succinct Histograms | cs.CR cs.DS cs.LG | We give efficient protocols and matching accuracy lower bounds for frequency
estimation in the local model for differential privacy. In this model,
individual users randomize their data themselves, sending differentially
private reports to an untrusted server that aggregates them.
We study protocols that produce a succinct histogram representation of the
data. A succinct histogram is a list of the most frequent items in the data
(often called "heavy hitters") along with estimates of their frequencies; the
frequency of all other items is implicitly estimated as 0.
If there are $n$ users whose items come from a universe of size $d$, our
protocols run in time polynomial in $n$ and $\log(d)$. With high probability,
they estimate the accuracy of every item up to error
$O\left(\sqrt{\log(d)/(\epsilon^2n)}\right)$ where $\epsilon$ is the privacy
parameter. Moreover, we show that this much error is necessary, regardless of
computational efficiency, and even for the simple setting where only one item
appears with significant frequency in the data set.
Previous protocols (Mishra and Sandler, 2006; Hsu, Khanna and Roth, 2012) for
this task either ran in time $\Omega(d)$ or had much worse error (about
$\sqrt[6]{\log(d)/(\epsilon^2n)}$), and the only known lower bound on error was
$\Omega(1/\sqrt{n})$.
We also adapt a result of McGregor et al (2010) to the local setting. In a
model with public coins, we show that each user need only send 1 bit to the
server. For all known local protocols (including ours), the transformation
preserves computational efficiency.
| Raef Bassily and Adam Smith | 10.1145/2746539.2746632 | 1504.04686 | null | null |
Fast optimization of Multithreshold Entropy Linear Classifier | cs.LG stat.ML | Multithreshold Entropy Linear Classifier (MELC) is a density based model
which searches for a linear projection maximizing the Cauchy-Schwarz Divergence
of dataset kernel density estimation. Despite its good empirical results, one
of its drawbacks is the optimization speed. In this paper we analyze how one
can speed it up through solving an approximate problem. We analyze two methods,
both similar to the approximate solutions of the Kernel Density Estimation
querying and provide adaptive schemes for selecting a crucial parameters based
on user-specified acceptable error. Furthermore we show how one can exploit
well known conjugate gradients and L-BFGS optimizers despite the fact that the
original optimization problem should be solved on the sphere. All above methods
and modifications are tested on 10 real life datasets from UCI repository to
confirm their practical usability.
| Rafal Jozefowicz, Wojciech Marian Czarnecki | 10.4467/20838476SI.14.005.3022 | 1504.04739 | null | null |
On the consistency of Multithreshold Entropy Linear Classifier | cs.LG stat.ML | Multithreshold Entropy Linear Classifier (MELC) is a recent classifier idea
which employs information theoretic concept in order to create a multithreshold
maximum margin model. In this paper we analyze its consistency over
multithreshold linear models and show that its objective function upper bounds
the amount of misclassified points in a similar manner like hinge loss does in
support vector machines. For further confirmation we also conduct some
numerical experiments on five datasets.
| Wojciech Marian Czarnecki | 10.4467/20838476SI.15.012.3034 | 1504.04740 | null | null |
Online Inference for Relation Extraction with a Reduced Feature Set | cs.CL cs.LG | Access to web-scale corpora is gradually bringing robust automatic knowledge
base creation and extension within reach. To exploit these large
unannotated---and extremely difficult to annotate---corpora, unsupervised
machine learning methods are required. Probabilistic models of text have
recently found some success as such a tool, but scalability remains an obstacle
in their application, with standard approaches relying on sampling schemes that
are known to be difficult to scale. In this report, we therefore present an
empirical assessment of the sublinear time sparse stochastic variational
inference (SSVI) scheme applied to RelLDA. We demonstrate that online inference
leads to relatively strong qualitative results but also identify some of its
pathologies---and those of the model---which will need to be overcome if SSVI
is to be used for large-scale relation extraction.
| Maxim Rabinovich, C\'edric Archambeau | null | 1504.04770 | null | null |
Compressing Neural Networks with the Hashing Trick | cs.LG cs.NE | As deep nets are increasingly used in applications suited for mobile devices,
a fundamental dilemma becomes apparent: the trend in deep learning is to grow
models to absorb ever-increasing data set sizes; however mobile devices are
designed with very little memory and cannot store such large models. We present
a novel network architecture, HashedNets, that exploits inherent redundancy in
neural networks to achieve drastic reductions in model sizes. HashedNets uses a
low-cost hash function to randomly group connection weights into hash buckets,
and all connections within the same hash bucket share a single parameter value.
These parameters are tuned to adjust to the HashedNets weight sharing
architecture with standard backprop during training. Our hashing procedure
introduces no additional memory overhead, and we demonstrate on several
benchmark data sets that HashedNets shrink the storage requirements of neural
networks substantially while mostly preserving generalization performance.
| Wenlin Chen and James T. Wilson and Stephen Tyree and Kilian Q.
Weinberger and Yixin Chen | null | 1504.04788 | null | null |
Exploring Bayesian Models for Multi-level Clustering of Hierarchically
Grouped Sequential Data | cs.LG cs.AI | A wide range of Bayesian models have been proposed for data that is divided
hierarchically into groups. These models aim to cluster the data at different
levels of grouping, by assigning a mixture component to each datapoint, and a
mixture distribution to each group. Multi-level clustering is facilitated by
the sharing of these components and distributions by the groups. In this paper,
we introduce the concept of Degree of Sharing (DoS) for the mixture components
and distributions, with an aim to analyze and classify various existing models.
Next we introduce a generalized hierarchical Bayesian model, of which the
existing models can be shown to be special cases. Unlike most of these models,
our model takes into account the sequential nature of the data, and various
other temporal structures at different levels while assigning mixture
components and distributions. We show one specialization of this model aimed at
hierarchical segmentation of news transcripts, and present a Gibbs Sampling
based inference algorithm for it. We also show experimentally that the proposed
model outperforms existing models for the same task.
| Adway Mitra | null | 1504.04850 | null | null |
F-SVM: Combination of Feature Transformation and SVM Learning via Convex
Relaxation | cs.LG cs.CV | The generalization error bound of support vector machine (SVM) depends on the
ratio of radius and margin, while standard SVM only considers the maximization
of the margin but ignores the minimization of the radius. Several approaches
have been proposed to integrate radius and margin for joint learning of feature
transformation and SVM classifier. However, most of them either require the
form of the transformation matrix to be diagonal, or are non-convex and
computationally expensive. In this paper, we suggest a novel approximation for
the radius of minimum enclosing ball (MEB) in feature space, and then propose a
convex radius-margin based SVM model for joint learning of feature
transformation and SVM classifier, i.e., F-SVM. An alternating minimization
method is adopted to solve the F-SVM model, where the feature transformation is
updatedvia gradient descent and the classifier is updated by employing the
existing SVM solver. By incorporating with kernel principal component analysis,
F-SVM is further extended for joint learning of nonlinear transformation and
classifier. Experimental results on the UCI machine learning datasets and the
LFW face datasets show that F-SVM outperforms the standard SVM and the existing
radius-margin based SVMs, e.g., RMM, R-SVM+ and R-SVM+{\mu}.
| Xiaohe Wu, Wangmeng Zuo, Yuanyuan Zhu, Liang Lin | null | 1504.05035 | null | null |
Nonparametric Nearest Neighbor Random Process Clustering | stat.ML cs.IT cs.LG math.IT | We consider the problem of clustering noisy finite-length observations of
stationary ergodic random processes according to their nonparametric generative
models without prior knowledge of the model statistics and the number of
generative models. Two algorithms, both using the L1-distance between estimated
power spectral densities (PSDs) as a measure of dissimilarity, are analyzed.
The first algorithm, termed nearest neighbor process clustering (NNPC), to the
best of our knowledge, is new and relies on partitioning the nearest neighbor
graph of the observations via spectral clustering. The second algorithm, simply
referred to as k-means (KM), consists of a single k-means iteration with
farthest point initialization and was considered before in the literature,
albeit with a different measure of dissimilarity and with asymptotic
performance results only. We show that both NNPC and KM succeed with high
probability under noise and even when the generative process PSDs overlap
significantly, all provided that the observation length is sufficiently large.
Our results quantify the tradeoff between the overlap of the generative process
PSDs, the noise variance, and the observation length. Finally, we present
numerical performance results for synthetic and real data.
| Michael Tschannen, Helmut B\"olcskei | 10.1109/ISIT.2015.7282647 | 1504.05059 | null | null |
Self-Adaptive Hierarchical Sentence Model | cs.CL cs.LG cs.NE | The ability to accurately model a sentence at varying stages (e.g.,
word-phrase-sentence) plays a central role in natural language processing. As
an effort towards this goal we propose a self-adaptive hierarchical sentence
model (AdaSent). AdaSent effectively forms a hierarchy of representations from
words to phrases and then to sentences through recursive gated local
composition of adjacent segments. We design a competitive mechanism (through
gating networks) to allow the representations of the same sentence to be
engaged in a particular learning task (e.g., classification), therefore
effectively mitigating the gradient vanishing problem persistent in other
recursive models. Both qualitative and quantitative analysis shows that AdaSent
can automatically form and select the representations suitable for the task at
hand during training, yielding superior classification performance over
competitor models on 5 benchmark data sets.
| Han Zhao, Zhengdong Lu, Pascal Poupart | null | 1504.05070 | null | null |
Optimal Nudging: Solving Average-Reward Semi-Markov Decision Processes
as a Minimal Sequence of Cumulative Tasks | cs.LG cs.AI | This paper describes a novel method to solve average-reward semi-Markov
decision processes, by reducing them to a minimal sequence of cumulative reward
problems. The usual solution methods for this type of problems update the gain
(optimal average reward) immediately after observing the result of taking an
action. The alternative introduced, optimal nudging, relies instead on setting
the gain to some fixed value, which transitorily makes the problem a
cumulative-reward task, solving it by any standard reinforcement learning
method, and only then updating the gain in a way that minimizes uncertainty in
a minmax sense. The rule for optimal gain update is derived by exploiting the
geometric features of the w-l space, a simple mapping of the space of policies.
The total number of cumulative reward tasks that need to be solved is shown to
be small. Some experiments are presented to explore the features of the
algorithm and to compare its performance with other approaches.
| Reinaldo Uribe Muriel, Fernando Lozando and Charles Anderson | null | 1504.05122 | null | null |
Poisson Matrix Recovery and Completion | cs.LG math.ST stat.ML stat.TH | We extend the theory of low-rank matrix recovery and completion to the case
when Poisson observations for a linear combination or a subset of the entries
of a matrix are available, which arises in various applications with count
data. We consider the usual matrix recovery formulation through maximum
likelihood with proper constraints on the matrix $M$ of size $d_1$-by-$d_2$,
and establish theoretical upper and lower bounds on the recovery error. Our
bounds for matrix completion are nearly optimal up to a factor on the order of
$\mathcal{O}(\log(d_1 d_2))$. These bounds are obtained by combing techniques
for compressed sensing for sparse vectors with Poisson noise and for analyzing
low-rank matrices, as well as adapting the arguments used for one-bit matrix
completion \cite{davenport20121} (although these two problems are different in
nature) and the adaptation requires new techniques exploiting properties of the
Poisson likelihood function and tackling the difficulties posed by the locally
sub-Gaussian characteristic of the Poisson distribution. Our results highlight
a few important distinctions of the Poisson case compared to the prior work
including having to impose a minimum signal-to-noise requirement on each
observed entry and a gap in the upper and lower bounds. We also develop a set
of efficient iterative algorithms and demonstrate their good performance on
synthetic examples and real data.
| Yang Cao and Yao Xie | 10.1109/TSP.2015.2500192 | 1504.05229 | null | null |
Decomposing Overcomplete 3rd Order Tensors using Sum-of-Squares
Algorithms | cs.DS cs.LG stat.ML | Tensor rank and low-rank tensor decompositions have many applications in
learning and complexity theory. Most known algorithms use unfoldings of tensors
and can only handle rank up to $n^{\lfloor p/2 \rfloor}$ for a $p$-th order
tensor in $\mathbb{R}^{n^p}$. Previously no efficient algorithm can decompose
3rd order tensors when the rank is super-linear in the dimension. Using ideas
from sum-of-squares hierarchy, we give the first quasi-polynomial time
algorithm that can decompose a random 3rd order tensor decomposition when the
rank is as large as $n^{3/2}/\textrm{polylog} n$.
We also give a polynomial time algorithm for certifying the injective norm of
random low rank tensors. Our tensor decomposition algorithm exploits the
relationship between injective norm and the tensor components. The proof relies
on interesting tools for decoupling random variables to prove better matrix
concentration bounds, which can be useful in other settings.
| Rong Ge, Tengyu Ma | null | 1504.05287 | null | null |
Distance-based species tree estimation: information-theoretic trade-off
between number of loci and sequence length under the coalescent | math.PR cs.LG math.ST q-bio.PE stat.TH | We consider the reconstruction of a phylogeny from multiple genes under the
multispecies coalescent. We establish a connection with the sparse signal
detection problem, where one seeks to distinguish between a distribution and a
mixture of the distribution and a sparse signal. Using this connection, we
derive an information-theoretic trade-off between the number of genes, $m$,
needed for an accurate reconstruction and the sequence length, $k$, of the
genes. Specifically, we show that to detect a branch of length $f$, one needs
$m = \Theta(1/[f^{2} \sqrt{k}])$.
| Elchanan Mossel, Sebastien Roch | null | 1504.05289 | null | null |
Instance Optimal Learning | cs.LG | We consider the following basic learning task: given independent draws from
an unknown distribution over a discrete support, output an approximation of the
distribution that is as accurate as possible in $\ell_1$ distance (i.e. total
variation or statistical distance). Perhaps surprisingly, it is often possible
to "de-noise" the empirical distribution of the samples to return an
approximation of the true distribution that is significantly more accurate than
the empirical distribution, without relying on any prior assumptions on the
distribution. We present an instance optimal learning algorithm which optimally
performs this de-noising for every distribution for which such a de-noising is
possible. More formally, given $n$ independent draws from a distribution $p$,
our algorithm returns a labelled vector whose expected distance from $p$ is
equal to the minimum possible expected error that could be obtained by any
algorithm that knows the true unlabeled vector of probabilities of distribution
$p$ and simply needs to assign labels, up to an additive subconstant term that
is independent of $p$ and goes to zero as $n$ gets large. One conceptual
implication of this result is that for large samples, Bayesian assumptions on
the "shape" or bounds on the tail probabilities of a distribution over discrete
support are not helpful for the task of learning the distribution.
As a consequence of our techniques, we also show that given a set of $n$
samples from an arbitrary distribution, one can accurately estimate the
expected number of distinct elements that will be observed in a sample of any
size up to $n \log n$. This sort of extrapolation is practically relevant,
particularly to domains such as genomics where it is important to understand
how much more might be discovered given larger sample sizes, and we are
optimistic that our approach is practically viable.
| Gregory Valiant, Paul Valiant | null | 1504.05321 | null | null |
Effective Discriminative Feature Selection with Non-trivial Solutions | cs.LG | Feature selection and feature transformation, the two main ways to reduce
dimensionality, are often presented separately. In this paper, a feature
selection method is proposed by combining the popular transformation based
dimensionality reduction method Linear Discriminant Analysis (LDA) and sparsity
regularization. We impose row sparsity on the transformation matrix of LDA
through ${\ell}_{2,1}$-norm regularization to achieve feature selection, and
the resultant formulation optimizes for selecting the most discriminative
features and removing the redundant ones simultaneously. The formulation is
extended to the ${\ell}_{2,p}$-norm regularized case: which is more likely to
offer better sparsity when $0<p<1$. Thus the formulation is a better
approximation to the feature selection problem. An efficient algorithm is
developed to solve the ${\ell}_{2,p}$-norm based optimization problem and it is
proved that the algorithm converges when $0<p\le 2$. Systematical experiments
are conducted to understand the work of the proposed method. Promising
experimental results on various types of real-world data sets demonstrate the
effectiveness of our algorithm.
| Hong Tao, Chenping Hou, Feiping Nie, Yuanyuan Jiao, Dongyun Yi | null | 1504.05408 | null | null |
Can FCA-based Recommender System Suggest a Proper Classifier? | cs.IR cs.LG stat.ML | The paper briefly introduces multiple classifier systems and describes a new
algorithm, which improves classification accuracy by means of recommendation of
a proper algorithm to an object classification. This recommendation is done
assuming that a classifier is likely to predict the label of the object
correctly if it has correctly classified its neighbors. The process of
assigning a classifier to each object is based on Formal Concept Analysis. We
explain the idea of the algorithm with a toy example and describe our first
experiments with real-world datasets.
| Yury Kashnitsky, Dmitry I. Ignatov | null | 1504.05473 | null | null |
Randomized Block Krylov Methods for Stronger and Faster Approximate
Singular Value Decomposition | cs.DS cs.LG cs.NA | Since being analyzed by Rokhlin, Szlam, and Tygert and popularized by Halko,
Martinsson, and Tropp, randomized Simultaneous Power Iteration has become the
method of choice for approximate singular value decomposition. It is more
accurate than simpler sketching algorithms, yet still converges quickly for any
matrix, independently of singular value gaps. After $\tilde{O}(1/\epsilon)$
iterations, it gives a low-rank approximation within $(1+\epsilon)$ of optimal
for spectral norm error.
We give the first provable runtime improvement on Simultaneous Iteration: a
simple randomized block Krylov method, closely related to the classic Block
Lanczos algorithm, gives the same guarantees in just
$\tilde{O}(1/\sqrt{\epsilon})$ iterations and performs substantially better
experimentally. Despite their long history, our analysis is the first of a
Krylov subspace method that does not depend on singular value gaps, which are
unreliable in practice.
Furthermore, while it is a simple accuracy benchmark, even $(1+\epsilon)$
error for spectral norm low-rank approximation does not imply that an algorithm
returns high quality principal components, a major issue for data applications.
We address this problem for the first time by showing that both Block Krylov
Iteration and a minor modification of Simultaneous Iteration give nearly
optimal PCA for any matrix. This result further justifies their strength over
non-iterative sketching methods.
Finally, we give insight beyond the worst case, justifying why both
algorithms can run much faster in practice than predicted. We clarify how
simple techniques can take advantage of common matrix properties to
significantly improve runtime.
| Cameron Musco and Christopher Musco | null | 1504.05477 | null | null |
Deep Convolutional Neural Networks Based on Semi-Discrete Frames | cs.LG cs.IT math.FA math.IT stat.ML | Deep convolutional neural networks have led to breakthrough results in
practical feature extraction applications. The mathematical analysis of these
networks was pioneered by Mallat, 2012. Specifically, Mallat considered
so-called scattering networks based on identical semi-discrete wavelet frames
in each network layer, and proved translation-invariance as well as deformation
stability of the resulting feature extractor. The purpose of this paper is to
develop Mallat's theory further by allowing for different and, most
importantly, general semi-discrete frames (such as, e.g., Gabor frames,
wavelets, curvelets, shearlets, ridgelets) in distinct network layers. This
allows to extract wider classes of features than point singularities resolved
by the wavelet transform. Our generalized feature extractor is proven to be
translation-invariant, and we develop deformation stability results for a
larger class of deformations than those considered by Mallat. For Mallat's
wavelet-based feature extractor, we get rid of a number of technical
conditions. The mathematical engine behind our results is continuous frame
theory, which allows us to completely detach the invariance and deformation
stability proofs from the particular algebraic structure of the underlying
frames.
| Thomas Wiatowski and Helmut B\"olcskei | null | 1504.05487 | null | null |
Online Learning Algorithm for Time Series Forecasting Suitable for Low
Cost Wireless Sensor Networks Nodes | cs.NI cs.LG cs.SY | Time series forecasting is an important predictive methodology which can be
applied to a wide range of problems. Particularly, forecasting the indoor
temperature permits an improved utilization of the HVAC (Heating, Ventilating
and Air Conditioning) systems in a home and thus a better energy efficiency.
With such purpose the paper describes how to implement an Artificial Neural
Network (ANN) algorithm in a low cost system-on-chip to develop an autonomous
intelligent wireless sensor network. The present paper uses a Wireless Sensor
Networks (WSN) to monitor and forecast the indoor temperature in a smart home,
based on low resources and cost microcontroller technology as the 8051MCU. An
on-line learning approach, based on Back-Propagation (BP) algorithm for ANNs,
has been developed for real-time time series learning. It performs the model
training with every new data that arrive to the system, without saving enormous
quantities of data to create a historical database as usual, i.e., without
previous knowledge. Consequently to validate the approach a simulation study
through a Bayesian baseline model have been tested in order to compare with a
database of a real application aiming to see the performance and accuracy. The
core of the paper is a new algorithm, based on the BP one, which has been
described in detail, and the challenge was how to implement a computational
demanding algorithm in a simple architecture with very few hardware resources.
| Juan Pardo and Francisco Zamora-Martinez and Paloma Botella-Rocamora | 10.3390/s150409277 | 1504.05517 | null | null |
Temporal-Difference Networks | cs.LG | We introduce a generalization of temporal-difference (TD) learning to
networks of interrelated predictions. Rather than relating a single prediction
to itself at a later time, as in conventional TD methods, a TD network relates
each prediction in a set of predictions to other predictions in the set at a
later time. TD networks can represent and apply TD learning to a much wider
class of predictions than has previously been possible. Using a random-walk
example, we show that these networks can be used to learn to predict by a fixed
interval, which is not possible with conventional TD methods. Secondly, we show
that if the inter-predictive relationships are made conditional on action, then
the usual learning-efficiency advantage of TD methods over Monte Carlo
(supervised learning) methods becomes particularly pronounced. Thirdly, we
demonstrate that TD networks can learn predictive state representations that
enable exact solution of a non-Markov problem. A very broad range of
inter-predictive temporal relationships can be expressed in these networks.
Overall we argue that TD networks represent a substantial extension of the
abilities of TD methods and bring us closer to the goal of representing world
knowledge in entirely predictive, grounded terms.
| Richard S. Sutton, Brian Tanner | null | 1504.05539 | null | null |
Learning Opposites with Evolving Rules | cs.NE cs.LG | The idea of opposition-based learning was introduced 10 years ago. Since then
a noteworthy group of researchers has used some notions of oppositeness to
improve existing optimization and learning algorithms. Among others,
evolutionary algorithms, reinforcement agents, and neural networks have been
reportedly extended into their opposition-based version to become faster and/or
more accurate. However, most works still use a simple notion of opposites,
namely linear (or type- I) opposition, that for each $x\in[a,b]$ assigns its
opposite as $\breve{x}_I=a+b-x$. This, of course, is a very naive estimate of
the actual or true (non-linear) opposite $\breve{x}_{II}$, which has been
called type-II opposite in literature. In absence of any knowledge about a
function $y=f(\mathbf{x})$ that we need to approximate, there seems to be no
alternative to the naivety of type-I opposition if one intents to utilize
oppositional concepts. But the question is if we can receive some level of
accuracy increase and time savings by using the naive opposite estimate
$\breve{x}_I$ according to all reports in literature, what would we be able to
gain, in terms of even higher accuracies and more reduction in computational
complexity, if we would generate and employ true opposites? This work
introduces an approach to approximate type-II opposites using evolving fuzzy
rules when we first perform opposition mining. We show with multiple examples
that learning true opposites is possible when we mine the opposites from the
training data to subsequently approximate $\breve{x}_{II}=f(\mathbf{x},y)$.
| Hamid R. Tizhoosh and Shahryar Rahnamayan | null | 1504.05619 | null | null |
Self-Tuned Deep Super Resolution | cs.LG cs.CV | Deep learning has been successfully applied to image super resolution (SR).
In this paper, we propose a deep joint super resolution (DJSR) model to exploit
both external and self similarities for SR. A Stacked Denoising Convolutional
Auto Encoder (SDCAE) is first pre-trained on external examples with proper data
augmentations. It is then fine-tuned with multi-scale self examples from each
input, where the reliability of self examples is explicitly taken into account.
We also enhance the model performance by sub-model training and selection. The
DJSR model is extensively evaluated and compared with state-of-the-arts, and
show noticeable performance improvements both quantitatively and perceptually
on a wide range of images.
| Zhangyang Wang, Yingzhen Yang, Zhaowen Wang, Shiyu Chang, Wei Han,
Jianchao Yang, and Thomas S. Huang | null | 1504.05632 | null | null |
Rebuilding Factorized Information Criterion: Asymptotically Accurate
Marginal Likelihood | cs.LG stat.ML | Factorized information criterion (FIC) is a recently developed approximation
technique for the marginal log-likelihood, which provides an automatic model
selection framework for a few latent variable models (LVMs) with tractable
inference algorithms. This paper reconsiders FIC and fills theoretical gaps of
previous FIC studies. First, we reveal the core idea of FIC that allows
generalization for a broader class of LVMs, including continuous LVMs, in
contrast to previous FICs, which are applicable only to binary LVMs. Second, we
investigate the model selection mechanism of the generalized FIC. Our analysis
provides a formal justification of FIC as a model selection criterion for LVMs
and also a systematic procedure for pruning redundant latent variables that
have been removed heuristically in previous studies. Third, we provide an
interpretation of FIC as a variational free energy and uncover a few
previously-unknown their relationships. A demonstrative study on Bayesian
principal component analysis is provided and numerical experiments support our
theoretical results.
| Kohei Hayashi, Shin-ichi Maeda, Ryohei Fujimaki | null | 1504.05665 | null | null |
On the Generalization Properties of Differential Privacy | cs.LG cs.CR | A new line of work, started with Dwork et al., studies the task of answering
statistical queries using a sample and relates the problem to the concept of
differential privacy. By the Hoeffding bound, a sample of size $O(\log
k/\alpha^2)$ suffices to answer $k$ non-adaptive queries within error $\alpha$,
where the answers are computed by evaluating the statistical queries on the
sample. This argument fails when the queries are chosen adaptively (and can
hence depend on the sample). Dwork et al. showed that if the answers are
computed with $(\epsilon,\delta)$-differential privacy then $O(\epsilon)$
accuracy is guaranteed with probability $1-O(\delta^\epsilon)$. Using the
Private Multiplicative Weights mechanism, they concluded that the sample size
can still grow polylogarithmically with the $k$.
Very recently, Bassily et al. presented an improved bound and showed that (a
variant of) the private multiplicative weights algorithm can answer $k$
adaptively chosen statistical queries using sample complexity that grows
logarithmically in $k$. However, their results no longer hold for every
differentially private algorithm, and require modifying the private
multiplicative weights algorithm in order to obtain their high probability
bounds.
We greatly simplify the results of Dwork et al. and improve on the bound by
showing that differential privacy guarantees $O(\epsilon)$ accuracy with
probability $1-O(\delta\log(1/\epsilon)/\epsilon)$. It would be tempting to
guess that an $(\epsilon,\delta)$-differentially private computation should
guarantee $O(\epsilon)$ accuracy with probability $1-O(\delta)$. However, we
show that this is not the case, and that our bound is tight (up to logarithmic
factors).
| Kobbi Nissim, Uri Stemmer | null | 1504.05800 | null | null |
Learning of Behavior Trees for Autonomous Agents | cs.RO cs.AI cs.LG | Definition of an accurate system model for Automated Planner (AP) is often
impractical, especially for real-world problems. Conversely, off-the-shelf
planners fail to scale up and are domain dependent. These drawbacks are
inherited from conventional transition systems such as Finite State Machines
(FSMs) that describes the action-plan execution generated by the AP. On the
other hand, Behavior Trees (BTs) represent a valid alternative to FSMs
presenting many advantages in terms of modularity, reactiveness, scalability
and domain-independence. In this paper, we propose a model-free AP framework
using Genetic Programming (GP) to derive an optimal BT for an autonomous agent
to achieve a given goal in unknown (but fully observable) environments. We
illustrate the proposed framework using experiments conducted with an open
source benchmark Mario AI for automated generation of BTs that can play the
game character Mario to complete a certain level at various levels of
difficulty to include enemies and obstacles.
| Michele Colledanchise, Ramviyas Parasuraman, and Petter \"Ogren | 10.1109/TG.2018.2816806 | 1504.05811 | null | null |
Normal Bandits of Unknown Means and Variances: Asymptotic Optimality,
Finite Horizon Regret Bounds, and a Solution to an Open Problem | stat.ML cs.LG | Consider the problem of sampling sequentially from a finite number of $N \geq
2$ populations, specified by random variables $X^i_k$, $ i = 1,\ldots , N,$ and
$k = 1, 2, \ldots$; where $X^i_k$ denotes the outcome from population $i$ the
$k^{th}$ time it is sampled. It is assumed that for each fixed $i$,
$\{ X^i_k \}_{k \geq 1}$ is a sequence of i.i.d. normal random variables,
with unknown mean $\mu_i$ and unknown variance $\sigma_i^2$.
The objective is to have a policy $\pi$ for deciding from which of the $N$
populations to sample form at any time $n=1,2,\ldots$ so as to maximize the
expected sum of outcomes of $n$ samples or equivalently to minimize the regret
due to lack on information of the parameters $\mu_i$ and $\sigma_i^2$. In this
paper, we present a simple inflated sample mean (ISM) index policy that is
asymptotically optimal in the sense of Theorem 4 below. This resolves a
standing open problem from Burnetas and Katehakis (1996). Additionally, finite
horizon regret bounds are given.
| Wesley Cowan and Junya Honda and Michael N. Katehakis | null | 1504.05823 | null | null |
Exploit Bounding Box Annotations for Multi-label Object Recognition | cs.CV cs.LG | Convolutional neural networks (CNNs) have shown great performance as general
feature representations for object recognition applications. However, for
multi-label images that contain multiple objects from different categories,
scales and locations, global CNN features are not optimal. In this paper, we
incorporate local information to enhance the feature discriminative power. In
particular, we first extract object proposals from each image. With each image
treated as a bag and object proposals extracted from it treated as instances,
we transform the multi-label recognition problem into a multi-class
multi-instance learning problem. Then, in addition to extracting the typical
CNN feature representation from each proposal, we propose to make use of
ground-truth bounding box annotations (strong labels) to add another level of
local information by using nearest-neighbor relationships of local regions to
form a multi-view pipeline. The proposed multi-view multi-instance framework
utilizes both weak and strong labels effectively, and more importantly it has
the generalization ability to even boost the performance of unseen categories
by partial strong labels from other categories. Our framework is extensively
compared with state-of-the-art hand-crafted feature based methods and CNN based
methods on two multi-label benchmark datasets. The experimental results
validate the discriminative power and the generalization ability of the
proposed framework. With strong labels, our framework is able to achieve
state-of-the-art results in both datasets.
| Hao Yang, Joey Tianyi Zhou, Yu Zhang, Bin-Bin Gao, Jianxin Wu, Jianfei
Cai | null | 1504.05843 | null | null |
On-the-fly Approximation of Multivariate Total Variation Minimization | cs.LG cs.NA math.OC | In the context of change-point detection, addressed by Total Variation
minimization strategies, an efficient on-the-fly algorithm has been designed
leading to exact solutions for univariate data. In this contribution, an
extension of such an on-the-fly strategy to multivariate data is investigated.
The proposed algorithm relies on the local validation of the Karush-Kuhn-Tucker
conditions on the dual problem. Showing that the non-local nature of the
multivariate setting precludes to obtain an exact on-the-fly solution, we
devise an on-the-fly algorithm delivering an approximate solution, whose
quality is controlled by a practitioner-tunable parameter, acting as a
trade-off between quality and computational cost. Performance assessment shows
that high quality solutions are obtained on-the-fly while benefiting of
computational costs several orders of magnitude lower than standard iterative
procedures. The proposed algorithm thus provides practitioners with an
efficient multivariate change-point detection on-the-fly procedure.
| Jordan Frecon, Nelly Pustelnik, Patrice Abry and Laurent Condat | 10.1109/TSP.2016.2516962 | 1504.05854 | null | null |
Spectral Norm of Random Kernel Matrices with Applications to Privacy | stat.ML cs.CR cs.LG | Kernel methods are an extremely popular set of techniques used for many
important machine learning and data analysis applications. In addition to
having good practical performances, these methods are supported by a
well-developed theory. Kernel methods use an implicit mapping of the input data
into a high dimensional feature space defined by a kernel function, i.e., a
function returning the inner product between the images of two data points in
the feature space. Central to any kernel method is the kernel matrix, which is
built by evaluating the kernel function on a given sample dataset.
In this paper, we initiate the study of non-asymptotic spectral theory of
random kernel matrices. These are n x n random matrices whose (i,j)th entry is
obtained by evaluating the kernel function on $x_i$ and $x_j$, where
$x_1,...,x_n$ are a set of n independent random high-dimensional vectors. Our
main contribution is to obtain tight upper bounds on the spectral norm (largest
eigenvalue) of random kernel matrices constructed by commonly used kernel
functions based on polynomials and Gaussian radial basis.
As an application of these results, we provide lower bounds on the distortion
needed for releasing the coefficients of kernel ridge regression under
attribute privacy, a general privacy notion which captures a large class of
privacy definitions. Kernel ridge regression is standard method for performing
non-parametric regression that regularly outperforms traditional regression
approaches in various domains. Our privacy distortion lower bounds are the
first for any kernel technique, and our analysis assumes realistic scenarios
for the input, unlike all previous lower bounds for other release problems
which only hold under very restrictive input settings.
| Shiva Prasad Kasiviswanathan and Mark Rudelson | null | 1504.05880 | null | null |
svcR: An R Package for Support Vector Clustering improved with Geometric
Hashing applied to Lexical Pattern Discovery | cs.LG cs.CL | We present a new R package which takes a numerical matrix format as data
input, and computes clusters using a support vector clustering method (SVC). We
have implemented an original 2D-grid labeling approach to speed up cluster
extraction. In this sense, SVC can be seen as an efficient cluster extraction
if clusters are separable in a 2-D map. Secondly we showed that this SVC
approach using a Jaccard-Radial base kernel can help to classify well enough a
set of terms into ontological classes and help to define regular expression
rules for information extraction in documents; our case study concerns a set of
terms and documents about developmental and molecular biology.
| Nicolas Turenne | null | 1504.06080 | null | null |
Collectively Embedding Multi-Relational Data for Predicting User
Preferences | cs.LG cs.IR | Matrix factorization has found incredible success and widespread application
as a collaborative filtering based approach to recommendations. Unfortunately,
incorporating additional sources of evidence, especially ones that are
incomplete and noisy, is quite difficult to achieve in such models, however, is
often crucial for obtaining further gains in accuracy. For example, additional
information about businesses from reviews, categories, and attributes should be
leveraged for predicting user preferences, even though this information is
often inaccurate and partially-observed. Instead of creating customized methods
that are specific to each type of evidences, in this paper we present a generic
approach to factorization of relational data that collectively models all the
relations in the database. By learning a set of embeddings that are shared
across all the relations, the model is able to incorporate observed information
from all the relations, while also predicting all the relations of interest.
Our evaluation on multiple Amazon and Yelp datasets demonstrates effective
utilization of additional information for held-out preference prediction, but
further, we present accurate models even for the cold-starting businesses and
products for which we do not observe any ratings or reviews. We also illustrate
the capability of the model in imputing missing information and jointly
visualizing words, categories, and attribute factors.
| Nitish Gupta, Sameer Singh | null | 1504.06165 | null | null |
A new approach for physiological time series | cs.LG stat.ML | We developed a new approach for the analysis of physiological time series. An
iterative convolution filter is used to decompose the time series into various
components. Statistics of these components are extracted as features to
characterize the mechanisms underlying the time series. Motivated by the
studies that show many normal physiological systems involve irregularity while
the decrease of irregularity usually implies the abnormality, the statistics
for "outliers" in the components are used as features measuring irregularity.
Support vector machines are used to select the most relevant features that are
able to differentiate the time series from normal and abnormal systems. This
new approach is successfully used in the study of congestive heart failure by
heart beat interval time series.
| Dong Mao, Yang Wang and Qiang Wu | null | 1504.06274 | null | null |
Regularization-free estimation in trace regression with symmetric
positive semidefinite matrices | stat.ML cs.LG stat.ME | Over the past few years, trace regression models have received considerable
attention in the context of matrix completion, quantum state tomography, and
compressed sensing. Estimation of the underlying matrix from
regularization-based approaches promoting low-rankedness, notably nuclear norm
regularization, have enjoyed great popularity. In the present paper, we argue
that such regularization may no longer be necessary if the underlying matrix is
symmetric positive semidefinite (\textsf{spd}) and the design satisfies certain
conditions. In this situation, simple least squares estimation subject to an
\textsf{spd} constraint may perform as well as regularization-based approaches
with a proper choice of the regularization parameter, which entails knowledge
of the noise level and/or tuning. By contrast, constrained least squares
estimation comes without any tuning parameter and may hence be preferred due to
its simplicity.
| Martin Slawski, Ping Li, Matthias Hein | null | 1504.06305 | null | null |
Analysis of Stopping Active Learning based on Stabilizing Predictions | cs.LG cs.CL stat.ML | Within the natural language processing (NLP) community, active learning has
been widely investigated and applied in order to alleviate the annotation
bottleneck faced by developers of new NLP systems and technologies. This paper
presents the first theoretical analysis of stopping active learning based on
stabilizing predictions (SP). The analysis has revealed three elements that are
central to the success of the SP method: (1) bounds on Cohen's Kappa agreement
between successively trained models impose bounds on differences in F-measure
performance of the models; (2) since the stop set does not have to be labeled,
it can be made large in practice, helping to guarantee that the results
transfer to previously unseen streams of examples at test/application time; and
(3) good (low variance) sample estimates of Kappa between successive models can
be obtained. Proofs of relationships between the level of Kappa agreement and
the difference in performance between consecutive models are presented.
Specifically, if the Kappa agreement between two models exceeds a threshold T
(where $T>0$), then the difference in F-measure performance between those
models is bounded above by $\frac{4(1-T)}{T}$ in all cases. If precision of the
positive conjunction of the models is assumed to be $p$, then the bound can be
tightened to $\frac{4(1-T)}{(p+1)T}$.
| Michael Bloodgood and John Grothendieck | null | 1504.06329 | null | null |
Strategic Teaching and Learning in Games | cs.GT cs.AI cs.LG | It is known that there are uncoupled learning heuristics leading to Nash
equilibrium in all finite games. Why should players use such learning
heuristics and where could they come from? We show that there is no uncoupled
learning heuristic leading to Nash equilibrium in all finite games that a
player has an incentive to adopt, that would be evolutionary stable or that
could "learn itself". Rather, a player has an incentive to strategically teach
such a learning opponent in order secure at least the Stackelberg leader
payoff. The impossibility result remains intact when restricted to the classes
of generic games, two-player games, potential games, games with strategic
complements or 2x2 games, in which learning is known to be "nice". More
generally, it also applies to uncoupled learning heuristics leading to
correlated equilibria, rationalizable outcomes, iterated admissible outcomes,
or minimal curb sets. A possibility result restricted to "strategically
trivial" games fails if some generic games outside this class are considered as
well.
| Burkhard C. Schipper | null | 1504.06341 | null | null |
Use of Ensembles of Fourier Spectra in Capturing Recurrent Concepts in
Data Streams | cs.AI cs.LG | In this research, we apply ensembles of Fourier encoded spectra to capture
and mine recurring concepts in a data stream environment. Previous research
showed that compact versions of Decision Trees can be obtained by applying the
Discrete Fourier Transform to accurately capture recurrent concepts in a data
stream. However, in highly volatile environments where new concepts emerge
often, the approach of encoding each concept in a separate spectrum is no
longer viable due to memory overload and thus in this research we present an
ensemble approach that addresses this problem. Our empirical results on real
world data and synthetic data exhibiting varying degrees of recurrence reveal
that the ensemble approach outperforms the single spectrum approach in terms of
classification accuracy, memory and execution time.
| Sripirakas Sakthithasan, Russel Pears, Albert Bifet and Bernhard
Pfahringer | null | 1504.06366 | null | null |
Social Trust Prediction via Max-norm Constrained 1-bit Matrix Completion | cs.SI cs.LG stat.ML | Social trust prediction addresses the significant problem of exploring
interactions among users in social networks. Naturally, this problem can be
formulated in the matrix completion framework, with each entry indicating the
trustness or distrustness. However, there are two challenges for the social
trust problem: 1) the observed data are with sign (1-bit) measurements; 2) they
are typically sampled non-uniformly. Most of the previous matrix completion
methods do not well handle the two issues. Motivated by the recent progress of
max-norm, we propose to solve the problem with a 1-bit max-norm constrained
formulation. Since max-norm is not easy to optimize, we utilize a reformulation
of max-norm which facilitates an efficient projected gradient decent algorithm.
We demonstrate the superiority of our formulation on two benchmark datasets.
| Jing Wang and Jie Shen and Huan Xu | null | 1504.06394 | null | null |
Discriminative Switching Linear Dynamical Systems applied to
Physiological Condition Monitoring | cs.LG | We present a Discriminative Switching Linear Dynamical System (DSLDS) applied
to patient monitoring in Intensive Care Units (ICUs). Our approach is based on
identifying the state-of-health of a patient given their observed vital signs
using a discriminative classifier, and then inferring their underlying
physiological values conditioned on this status. The work builds on the
Factorial Switching Linear Dynamical System (FSLDS) (Quinn et al., 2009) which
has been previously used in a similar setting. The FSLDS is a generative model,
whereas the DSLDS is a discriminative model. We demonstrate on two real-world
datasets that the DSLDS is able to outperform the FSLDS in most cases of
interest, and that an $\alpha$-mixture of the two models achieves higher
performance than either of the two models separately.
| Konstantinos Georgatzis, Christopher K. I. Williams | null | 1504.06494 | null | null |
Sampling Correctors | cs.DS cs.LG math.PR | In many situations, sample data is obtained from a noisy or imperfect source.
In order to address such corruptions, this paper introduces the concept of a
sampling corrector. Such algorithms use structure that the distribution is
purported to have, in order to allow one to make "on-the-fly" corrections to
samples drawn from probability distributions. These algorithms then act as
filters between the noisy data and the end user.
We show connections between sampling correctors, distribution learning
algorithms, and distribution property testing algorithms. We show that these
connections can be utilized to expand the applicability of known distribution
learning and property testing algorithms as well as to achieve improved
algorithms for those tasks.
As a first step, we show how to design sampling correctors using proper
learning algorithms. We then focus on the question of whether algorithms for
sampling correctors can be more efficient in terms of sample complexity than
learning algorithms for the analogous families of distributions. When
correcting monotonicity, we show that this is indeed the case when also granted
query access to the cumulative distribution function. We also obtain sampling
correctors for monotonicity without this stronger type of access, provided that
the distribution be originally very close to monotone (namely, at a distance
$O(1/\log^2 n)$). In addition to that, we consider a restricted error model
that aims at capturing "missing data" corruptions. In this model, we show that
distributions that are close to monotone have sampling correctors that are
significantly more efficient than achievable by the learning approach.
We also consider the question of whether an additional source of independent
random bits is required by sampling correctors to implement the correction
process.
| Cl\'ement Canonne, Themis Gouleakis and Ronitt Rubinfeld | null | 1504.06544 | null | null |
Classifying Relations by Ranking with Convolutional Neural Networks | cs.CL cs.LG cs.NE | Relation classification is an important semantic processing task for which
state-ofthe-art systems still rely on costly handcrafted features. In this work
we tackle the relation classification task using a convolutional neural network
that performs classification by ranking (CR-CNN). We propose a new pairwise
ranking loss function that makes it easy to reduce the impact of artificial
classes. We perform experiments using the the SemEval-2010 Task 8 dataset,
which is designed for the task of classifying the relationship between two
nominals marked in a sentence. Using CRCNN, we outperform the state-of-the-art
for this dataset and achieve a F1 of 84.1 without using any costly handcrafted
features. Additionally, our experimental results show that: (1) our approach is
more effective than CNN followed by a softmax classifier; (2) omitting the
representation of the artificial class Other improves both precision and
recall; and (3) using only word embeddings as input features is enough to
achieve state-of-the-art results if we consider only the text between the two
target nominals.
| Cicero Nogueira dos Santos, Bing Xiang, Bowen Zhou | null | 1504.06580 | null | null |
Handling oversampling in dynamic networks using link prediction | cs.SI cs.LG physics.soc-ph | Oversampling is a common characteristic of data representing dynamic
networks. It introduces noise into representations of dynamic networks, but
there has been little work so far to compensate for it. Oversampling can affect
the quality of many important algorithmic problems on dynamic networks,
including link prediction. Link prediction seeks to predict edges that will be
added to the network given previous snapshots. We show that not only does
oversampling affect the quality of link prediction, but that we can use link
prediction to recover from the effects of oversampling. We also introduce a
novel generative model of noise in dynamic networks that represents
oversampling. We demonstrate the results of our approach on both synthetic and
real-world data.
| Benjamin Fish, Rajmonda S. Caceres | null | 1504.06667 | null | null |
Online Convex Optimization Using Predictions | cs.LG | Making use of predictions is a crucial, but under-explored, area of online
algorithms. This paper studies a class of online optimization problems where we
have external noisy predictions available. We propose a stochastic prediction
error model that generalizes prior models in the learning and stochastic
control communities, incorporates correlation among prediction errors, and
captures the fact that predictions improve as time passes. We prove that
achieving sublinear regret and constant competitive ratio for online algorithms
requires the use of an unbounded prediction window in adversarial settings, but
that under more realistic stochastic prediction error models it is possible to
use Averaging Fixed Horizon Control (AFHC) to simultaneously achieve sublinear
regret and constant competitive ratio in expectation using only a
constant-sized prediction window. Furthermore, we show that the performance of
AFHC is tightly concentrated around its mean.
| Niangjun Chen, Anish Agarwal, Adam Wierman, Siddharth Barman and
Lachlan L. H. Andrew | null | 1504.06681 | null | null |
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