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Vision and Learning for Deliberative Monocular Cluttered Flight | cs.RO cs.CV cs.LG | Cameras provide a rich source of information while being passive, cheap and
lightweight for small and medium Unmanned Aerial Vehicles (UAVs). In this work
we present the first implementation of receding horizon control, which is
widely used in ground vehicles, with monocular vision as the only sensing mode
for autonomous UAV flight in dense clutter. We make it feasible on UAVs via a
number of contributions: novel coupling of perception and control via relevant
and diverse, multiple interpretations of the scene around the robot, leveraging
recent advances in machine learning to showcase anytime budgeted cost-sensitive
feature selection, and fast non-linear regression for monocular depth
prediction. We empirically demonstrate the efficacy of our novel pipeline via
real world experiments of more than 2 kms through dense trees with a quadrotor
built from off-the-shelf parts. Moreover our pipeline is designed to combine
information from other modalities like stereo and lidar as well if available.
| Debadeepta Dey, Kumar Shaurya Shankar, Sam Zeng, Rupesh Mehta, M.
Talha Agcayazi, Christopher Eriksen, Shreyansh Daftry, Martial Hebert, and J.
Andrew Bagnell | null | 1411.6326 | null | null |
A Hybrid Solution to improve Iteration Efficiency in the Distributed
Learning | cs.DC cs.LG | Currently, many machine learning algorithms contain lots of iterations. When
it comes to existing large-scale distributed systems, some slave nodes may
break down or have lower efficiency. Therefore traditional machine learning
algorithm may fail because of the instability of distributed system.We presents
a hybrid approach which not only own a high fault-tolerant but also achieve a
balance of performance and efficiency.For each iteration, the result of slow
machines will be abandoned. Then, we discuss the relationship between accuracy
and abandon rate. Next we debate the convergence speed of this process.
Finally, our experiments demonstrate our idea can dramatically reduce
calculation time and be used in many platforms.
| Junxiong Wang, Hongzhi Wang and Chenxu Zhao | null | 1411.6358 | null | null |
Scale-Invariant Convolutional Neural Networks | cs.CV cs.LG cs.NE | Even though convolutional neural networks (CNN) has achieved near-human
performance in various computer vision tasks, its ability to tolerate scale
variations is limited. The popular practise is making the model bigger first,
and then train it with data augmentation using extensive scale-jittering. In
this paper, we propose a scaleinvariant convolutional neural network (SiCNN), a
modeldesigned to incorporate multi-scale feature exaction and classification
into the network structure. SiCNN uses a multi-column architecture, with each
column focusing on a particular scale. Unlike previous multi-column strategies,
these columns share the same set of filter parameters by a scale transformation
among them. This design deals with scale variation without blowing up the model
size. Experimental results show that SiCNN detects features at various scales,
and the classification result exhibits strong robustness against object scale
variations.
| Yichong Xu, Tianjun Xiao, Jiaxing Zhang, Kuiyuan Yang, Zheng Zhang | null | 1411.6369 | null | null |
Big Learning with Bayesian Methods | cs.LG stat.AP stat.CO stat.ME stat.ML | Explosive growth in data and availability of cheap computing resources have
sparked increasing interest in Big learning, an emerging subfield that studies
scalable machine learning algorithms, systems, and applications with Big Data.
Bayesian methods represent one important class of statistic methods for machine
learning, with substantial recent developments on adaptive, flexible and
scalable Bayesian learning. This article provides a survey of the recent
advances in Big learning with Bayesian methods, termed Big Bayesian Learning,
including nonparametric Bayesian methods for adaptively inferring model
complexity, regularized Bayesian inference for improving the flexibility via
posterior regularization, and scalable algorithms and systems based on
stochastic subsampling and distributed computing for dealing with large-scale
applications.
| Jun Zhu, Jianfei Chen, Wenbo Hu, Bo Zhang | null | 1411.6370 | null | null |
Mutual Information-Based Unsupervised Feature Transformation for
Heterogeneous Feature Subset Selection | stat.ML cs.LG | Conventional mutual information (MI) based feature selection (FS) methods are
unable to handle heterogeneous feature subset selection properly because of
data format differences or estimation methods of MI between feature subset and
class label. A way to solve this problem is feature transformation (FT). In
this study, a novel unsupervised feature transformation (UFT) which can
transform non-numerical features into numerical features is developed and
tested. The UFT process is MI-based and independent of class label. MI-based FS
algorithms, such as Parzen window feature selector (PWFS), minimum redundancy
maximum relevance feature selection (mRMR), and normalized MI feature selection
(NMIFS), can all adopt UFT for pre-processing of non-numerical features. Unlike
traditional FT methods, the proposed UFT is unbiased while PWFS is utilized to
its full advantage. Simulations and analyses of large-scale datasets showed
that feature subset selected by the integrated method, UFT-PWFS, outperformed
other FT-FS integrated methods in classification accuracy.
| Min Wei, Tommy W. S. Chow, Rosa H. M. Chan | null | 1411.6400 | null | null |
Distributed Coordinate Descent for L1-regularized Logistic Regression | stat.ML cs.LG | Solving logistic regression with L1-regularization in distributed settings is
an important problem. This problem arises when training dataset is very large
and cannot fit the memory of a single machine. We present d-GLMNET, a new
algorithm solving logistic regression with L1-regularization in the distributed
settings. We empirically show that it is superior over distributed online
learning via truncated gradient.
| Ilya Trofimov, Alexander Genkin | 10.1007/978-3-319-26123-2_24 | 1411.6520 | null | null |
Consistency of Cheeger and Ratio Graph Cuts | stat.ML cs.LG math.ST stat.TH | This paper establishes the consistency of a family of graph-cut-based
algorithms for clustering of data clouds. We consider point clouds obtained as
samples of a ground-truth measure. We investigate approaches to clustering
based on minimizing objective functionals defined on proximity graphs of the
given sample. Our focus is on functionals based on graph cuts like the Cheeger
and ratio cuts. We show that minimizers of the these cuts converge as the
sample size increases to a minimizer of a corresponding continuum cut (which
partitions the ground truth measure). Moreover, we obtain sharp conditions on
how the connectivity radius can be scaled with respect to the number of sample
points for the consistency to hold. We provide results for two-way and for
multiway cuts. Furthermore we provide numerical experiments that illustrate the
results and explore the optimality of scaling in dimension two.
| Nicolas Garcia Trillos, Dejan Slepcev, James von Brecht, Thomas
Laurent and Xavier Bresson | null | 1411.6590 | null | null |
A Latent Source Model for Online Collaborative Filtering | cs.LG cs.IR stat.ML | Despite the prevalence of collaborative filtering in recommendation systems,
there has been little theoretical development on why and how well it works,
especially in the "online" setting, where items are recommended to users over
time. We address this theoretical gap by introducing a model for online
recommendation systems, cast item recommendation under the model as a learning
problem, and analyze the performance of a cosine-similarity collaborative
filtering method. In our model, each of $n$ users either likes or dislikes each
of $m$ items. We assume there to be $k$ types of users, and all the users of a
given type share a common string of probabilities determining the chance of
liking each item. At each time step, we recommend an item to each user, where a
key distinction from related bandit literature is that once a user consumes an
item (e.g., watches a movie), then that item cannot be recommended to the same
user again. The goal is to maximize the number of likable items recommended to
users over time. Our main result establishes that after nearly $\log(km)$
initial learning time steps, a simple collaborative filtering algorithm
achieves essentially optimal performance without knowing $k$. The algorithm has
an exploitation step that uses cosine similarity and two types of exploration
steps, one to explore the space of items (standard in the literature) and the
other to explore similarity between users (novel to this work).
| Guy Bresler, George H. Chen, Devavrat Shah | null | 1411.6591 | null | null |
Noise Benefits in Expectation-Maximization Algorithms | stat.ML cs.LG math.ST stat.TH | This dissertation shows that careful injection of noise into sample data can
substantially speed up Expectation-Maximization algorithms.
Expectation-Maximization algorithms are a class of iterative algorithms for
extracting maximum likelihood estimates from corrupted or incomplete data. The
convergence speed-up is an example of a noise benefit or "stochastic resonance"
in statistical signal processing. The dissertation presents derivations of
sufficient conditions for such noise-benefits and demonstrates the speed-up in
some ubiquitous signal-processing algorithms. These algorithms include
parameter estimation for mixture models, the $k$-means clustering algorithm,
the Baum-Welch algorithm for training hidden Markov models, and backpropagation
for training feedforward artificial neural networks. This dissertation also
analyses the effects of data and model corruption on the more general Bayesian
inference estimation framework. The main finding is a theorem guaranteeing that
uniform approximators for Bayesian model functions produce uniform
approximators for the posterior pdf via Bayes theorem. This result also applies
to hierarchical and multidimensional Bayesian models.
| Osonde Adekorede Osoba | null | 1411.6622 | null | null |
One Vector is Not Enough: Entity-Augmented Distributional Semantics for
Discourse Relations | cs.CL cs.LG | Discourse relations bind smaller linguistic units into coherent texts.
However, automatically identifying discourse relations is difficult, because it
requires understanding the semantics of the linked arguments. A more subtle
challenge is that it is not enough to represent the meaning of each argument of
a discourse relation, because the relation may depend on links between
lower-level components, such as entity mentions. Our solution computes
distributional meaning representations by composition up the syntactic parse
tree. A key difference from previous work on compositional distributional
semantics is that we also compute representations for entity mentions, using a
novel downward compositional pass. Discourse relations are predicted from the
distributional representations of the arguments, and also of their coreferent
entity mentions. The resulting system obtains substantial improvements over the
previous state-of-the-art in predicting implicit discourse relations in the
Penn Discourse Treebank.
| Yangfeng Ji and Jacob Eisenstein | null | 1411.6699 | null | null |
LABR: A Large Scale Arabic Sentiment Analysis Benchmark | cs.CL cs.LG | We introduce LABR, the largest sentiment analysis dataset to-date for the
Arabic language. It consists of over 63,000 book reviews, each rated on a scale
of 1 to 5 stars. We investigate the properties of the dataset, and present its
statistics. We explore using the dataset for two tasks: (1) sentiment polarity
classification; and (2) ratings classification. Moreover, we provide standard
splits of the dataset into training, validation and testing, for both polarity
and ratings classification, in both balanced and unbalanced settings. We extend
our previous work by performing a comprehensive analysis on the dataset. In
particular, we perform an extended survey of the different classifiers
typically used for the sentiment polarity classification problem. We also
construct a sentiment lexicon from the dataset that contains both single and
compound sentiment words and we explore its effectiveness. We make the dataset
and experimental details publicly available.
| Mahmoud Nabil, Mohamed Aly, Amir Atiya | null | 1411.6718 | null | null |
Accelerated Parallel Optimization Methods for Large Scale Machine
Learning | cs.LG | The growing amount of high dimensional data in different machine learning
applications requires more efficient and scalable optimization algorithms. In
this work, we consider combining two techniques, parallelism and Nesterov's
acceleration, to design faster algorithms for L1-regularized loss. We first
simplify BOOM, a variant of gradient descent, and study it in a unified
framework, which allows us to not only propose a refined measurement of
sparsity to improve BOOM, but also show that BOOM is provably slower than
FISTA. Moving on to parallel coordinate descent methods, we then propose an
efficient accelerated version of Shotgun, improving the convergence rate from
$O(1/t)$ to $O(1/t^2)$. Our algorithm enjoys a concise form and analysis
compared to previous work, and also allows one to study several connected work
in a unified way.
| Haipeng Luo, Patrick Haffner and Jean-Francois Paiement | null | 1411.6725 | null | null |
Efficient Algorithms for Bayesian Network Parameter Learning from
Incomplete Data | cs.LG cs.AI | We propose an efficient family of algorithms to learn the parameters of a
Bayesian network from incomplete data. In contrast to textbook approaches such
as EM and the gradient method, our approach is non-iterative, yields closed
form parameter estimates, and eliminates the need for inference in a Bayesian
network. Our approach provides consistent parameter estimates for missing data
problems that are MCAR, MAR, and in some cases, MNAR. Empirically, our approach
is orders of magnitude faster than EM (as our approach requires no inference).
Given sufficient data, we learn parameters that can be orders of magnitude more
accurate.
| Guy Van den Broeck, Karthika Mohan, Arthur Choi, Judea Pearl | null | 1411.7014 | null | null |
Localized Complexities for Transductive Learning | stat.ML cs.LG | We show two novel concentration inequalities for suprema of empirical
processes when sampling without replacement, which both take the variance of
the functions into account. While these inequalities may potentially have broad
applications in learning theory in general, we exemplify their significance by
studying the transductive setting of learning theory. For which we provide the
first excess risk bounds based on the localized complexity of the hypothesis
class, which can yield fast rates of convergence also in the transductive
learning setting. We give a preliminary analysis of the localized complexities
for the prominent case of kernel classes.
| Ilya Tolstikhin and Gilles Blanchard and Marius Kloft | null | 1411.7200 | null | null |
Heuristics for Exact Nonnegative Matrix Factorization | math.OC cs.LG cs.NA stat.ML | The exact nonnegative matrix factorization (exact NMF) problem is the
following: given an $m$-by-$n$ nonnegative matrix $X$ and a factorization rank
$r$, find, if possible, an $m$-by-$r$ nonnegative matrix $W$ and an $r$-by-$n$
nonnegative matrix $H$ such that $X = WH$. In this paper, we propose two
heuristics for exact NMF, one inspired from simulated annealing and the other
from the greedy randomized adaptive search procedure. We show that these two
heuristics are able to compute exact nonnegative factorizations for several
classes of nonnegative matrices (namely, linear Euclidean distance matrices,
slack matrices, unique-disjointness matrices, and randomly generated matrices)
and as such demonstrate their superiority over standard multi-start strategies.
We also consider a hybridization between these two heuristics that allows us to
combine the advantages of both methods. Finally, we discuss the use of these
heuristics to gain insight on the behavior of the nonnegative rank, i.e., the
minimum factorization rank such that an exact NMF exists. In particular, we
disprove a conjecture on the nonnegative rank of a Kronecker product, propose a
new upper bound on the extension complexity of generic $n$-gons and conjecture
the exact value of (i) the extension complexity of regular $n$-gons and (ii)
the nonnegative rank of a submatrix of the slack matrix of the correlation
polytope.
| Arnaud Vandaele and Nicolas Gillis and Fran\c{c}ois Glineur and Daniel
Tuyttens | 10.1007/s10898-015-0350-z | 1411.7245 | null | null |
A Chasm Between Identity and Equivalence Testing with Conditional
Queries | cs.DS cs.CC cs.LG math.PR math.ST stat.TH | A recent model for property testing of probability distributions (Chakraborty
et al., ITCS 2013, Canonne et al., SICOMP 2015) enables tremendous savings in
the sample complexity of testing algorithms, by allowing them to condition the
sampling on subsets of the domain. In particular, Canonne, Ron, and Servedio
(SICOMP 2015) showed that, in this setting, testing identity of an unknown
distribution $D$ (whether $D=D^\ast$ for an explicitly known $D^\ast$) can be
done with a constant number of queries, independent of the support size $n$ --
in contrast to the required $\Omega(\sqrt{n})$ in the standard sampling model.
It was unclear whether the same stark contrast exists for the case of testing
equivalence, where both distributions are unknown. While Canonne et al.
established a $\mathrm{poly}(\log n)$-query upper bound for equivalence
testing, very recently brought down to $\tilde O(\log\log n)$ by Falahatgar et
al. (COLT 2015), whether a dependence on the domain size $n$ is necessary was
still open, and explicitly posed by Fischer at the Bertinoro Workshop on
Sublinear Algorithms (2014). We show that any testing algorithm for equivalence
must make $\Omega(\sqrt{\log\log n})$ queries in the conditional sampling
model. This demonstrates a gap between identity and equivalence testing, absent
in the standard sampling model (where both problems have sampling complexity
$n^{\Theta(1)}$).
We also obtain results on the query complexity of uniformity testing and
support-size estimation with conditional samples. We answer a question of
Chakraborty et al. (ITCS 2013) showing that non-adaptive uniformity testing
indeed requires $\Omega(\log n)$ queries in the conditional model. For the
related problem of support-size estimation, we provide both adaptive and
non-adaptive algorithms, with query complexities $\mathrm{poly}(\log\log n)$
and $\mathrm{poly}(\log n)$, respectively.
| Jayadev Acharya, Cl\'ement L. Canonne, Gautam Kamath | null | 1411.7346 | null | null |
Signal Recovery on Graphs: Variation Minimization | cs.SI cs.LG stat.ML | We consider the problem of signal recovery on graphs as graphs model data
with complex structure as signals on a graph. Graph signal recovery implies
recovery of one or multiple smooth graph signals from noisy, corrupted, or
incomplete measurements. We propose a graph signal model and formulate signal
recovery as a corresponding optimization problem. We provide a general solution
by using the alternating direction methods of multipliers. We next show how
signal inpainting, matrix completion, robust principal component analysis, and
anomaly detection all relate to graph signal recovery, and provide
corresponding specific solutions and theoretical analysis. Finally, we validate
the proposed methods on real-world recovery problems, including online blog
classification, bridge condition identification, temperature estimation,
recommender system, and expert opinion combination of online blog
classification.
| Siheng Chen and Aliaksei Sandryhaila and Jos\'e M. F. Moura and Jelena
Kova\v{c}evi\'c | 10.1109/TSP.2015.2441042 | 1411.7414 | null | null |
Metrics for Probabilistic Geometries | stat.ML cs.LG | We investigate the geometrical structure of probabilistic generative
dimensionality reduction models using the tools of Riemannian geometry. We
explicitly define a distribution over the natural metric given by the models.
We provide the necessary algorithms to compute expected metric tensors where
the distribution over mappings is given by a Gaussian process. We treat the
corresponding latent variable model as a Riemannian manifold and we use the
expectation of the metric under the Gaussian process prior to define
interpolating paths and measure distance between latent points. We show how
distances that respect the expected metric lead to more appropriate generation
of new data.
| Alessandra Tosi, S{\o}ren Hauberg, Alfredo Vellido, Neil D. Lawrence | null | 1411.7432 | null | null |
Pattern Decomposition with Complex Combinatorial Constraints:
Application to Materials Discovery | cs.AI cs.LG stat.ML | Identifying important components or factors in large amounts of noisy data is
a key problem in machine learning and data mining. Motivated by a pattern
decomposition problem in materials discovery, aimed at discovering new
materials for renewable energy, e.g. for fuel and solar cells, we introduce
CombiFD, a framework for factor based pattern decomposition that allows the
incorporation of a-priori knowledge as constraints, including complex
combinatorial constraints. In addition, we propose a new pattern decomposition
algorithm, called AMIQO, based on solving a sequence of (mixed-integer)
quadratic programs. Our approach considerably outperforms the state of the art
on the materials discovery problem, scaling to larger datasets and recovering
more precise and physically meaningful decompositions. We also show the
effectiveness of our approach for enforcing background knowledge on other
application domains.
| Stefano Ermon, Ronan Le Bras, Santosh K. Suram, John M. Gregoire,
Carla Gomes, Bart Selman, Robert B. van Dover | null | 1411.7441 | null | null |
Worst-Case Linear Discriminant Analysis as Scalable Semidefinite
Feasibility Problems | cs.LG | In this paper, we propose an efficient semidefinite programming (SDP)
approach to worst-case linear discriminant analysis (WLDA). Compared with the
traditional LDA, WLDA considers the dimensionality reduction problem from the
worst-case viewpoint, which is in general more robust for classification.
However, the original problem of WLDA is non-convex and difficult to optimize.
In this paper, we reformulate the optimization problem of WLDA into a sequence
of semidefinite feasibility problems. To efficiently solve the semidefinite
feasibility problems, we design a new scalable optimization method with
quasi-Newton methods and eigen-decomposition being the core components. The
proposed method is orders of magnitude faster than standard interior-point
based SDP solvers.
Experiments on a variety of classification problems demonstrate that our
approach achieves better performance than standard LDA. Our method is also much
faster and more scalable than standard interior-point SDP solvers based WLDA.
The computational complexity for an SDP with $m$ constraints and matrices of
size $d$ by $d$ is roughly reduced from $\mathcal{O}(m^3+md^3+m^2d^2)$ to
$\mathcal{O}(d^3)$ ($m>d$ in our case).
| Hui Li, Chunhua Shen, Anton van den Hengel, Qinfeng Shi | 10.1109/TIP.2015.2401511 | 1411.7450 | null | null |
Graph Sensitive Indices for Comparing Clusterings | cs.LG | This report discusses two new indices for comparing clusterings of a set of
points. The motivation for looking at new ways for comparing clusterings stems
from the fact that the existing clustering indices are based on set cardinality
alone and do not consider the positions of data points. The new indices,
namely, the Random Walk index (RWI) and Variation of Information with Neighbors
(VIN), are both inspired by the clustering metric Variation of Information
(VI). VI possesses some interesting theoretical properties which are also
desirable in a metric for comparing clusterings. We define our indices and
discuss some of their explored properties which appear relevant for a
clustering index. We also include the results of these indices on clusterings
of some example data sets.
| Zaeem Hussain and Marina Meila | null | 1411.7582 | null | null |
Learning Stochastic Recurrent Networks | stat.ML cs.LG | Leveraging advances in variational inference, we propose to enhance recurrent
neural networks with latent variables, resulting in Stochastic Recurrent
Networks (STORNs). The model i) can be trained with stochastic gradient
methods, ii) allows structured and multi-modal conditionals at each time step,
iii) features a reliable estimator of the marginal likelihood and iv) is a
generalisation of deterministic recurrent neural networks. We evaluate the
method on four polyphonic musical data sets and motion capture data.
| Justin Bayer and Christian Osendorfer | null | 1411.7610 | null | null |
On the Expressive Efficiency of Sum Product Networks | cs.LG stat.ML | Sum Product Networks (SPNs) are a recently developed class of deep generative
models which compute their associated unnormalized density functions using a
special type of arithmetic circuit. When certain sufficient conditions, called
the decomposability and completeness conditions (or "D&C" conditions), are
imposed on the structure of these circuits, marginal densities and other useful
quantities, which are typically intractable for other deep generative models,
can be computed by what amounts to a single evaluation of the network (which is
a property known as "validity"). However, the effect that the D&C conditions
have on the capabilities of D&C SPNs is not well understood.
In this work we analyze the D&C conditions, expose the various connections
that D&C SPNs have with multilinear arithmetic circuits, and consider the
question of how well they can capture various distributions as a function of
their size and depth. Among our various contributions is a result which
establishes the existence of a relatively simple distribution with fully
tractable marginal densities which cannot be efficiently captured by D&C SPNs
of any depth, but which can be efficiently captured by various other deep
generative models. We also show that with each additional layer of depth
permitted, the set of distributions which can be efficiently captured by D&C
SPNs grows in size. This kind of "depth hierarchy" property has been widely
conjectured to hold for various deep models, but has never been proven for any
of them. Some of our other contributions include a new characterization of the
D&C conditions as sufficient and necessary ones for a slightly strengthened
notion of validity, and various state-machine characterizations of the types of
computations that can be performed efficiently by D&C SPNs.
| James Martens, Venkatesh Medabalimi | null | 1411.7717 | null | null |
Classification with Noisy Labels by Importance Reweighting | stat.ML cs.LG | In this paper, we study a classification problem in which sample labels are
randomly corrupted. In this scenario, there is an unobservable sample with
noise-free labels. However, before being observed, the true labels are
independently flipped with a probability $\rho\in[0,0.5)$, and the random label
noise can be class-conditional. Here, we address two fundamental problems
raised by this scenario. The first is how to best use the abundant surrogate
loss functions designed for the traditional classification problem when there
is label noise. We prove that any surrogate loss function can be used for
classification with noisy labels by using importance reweighting, with
consistency assurance that the label noise does not ultimately hinder the
search for the optimal classifier of the noise-free sample. The other is the
open problem of how to obtain the noise rate $\rho$. We show that the rate is
upper bounded by the conditional probability $P(y|x)$ of the noisy sample.
Consequently, the rate can be estimated, because the upper bound can be easily
reached in classification problems. Experimental results on synthetic and real
datasets confirm the efficiency of our methods.
| Tongliang Liu and Dacheng Tao | 10.1109/TPAMI.2015.2456899 | 1411.7718 | null | null |
From neural PCA to deep unsupervised learning | stat.ML cs.LG cs.NE | A network supporting deep unsupervised learning is presented. The network is
an autoencoder with lateral shortcut connections from the encoder to decoder at
each level of the hierarchy. The lateral shortcut connections allow the higher
levels of the hierarchy to focus on abstract invariant features. While standard
autoencoders are analogous to latent variable models with a single layer of
stochastic variables, the proposed network is analogous to hierarchical latent
variables models. Learning combines denoising autoencoder and denoising sources
separation frameworks. Each layer of the network contributes to the cost
function a term which measures the distance of the representations produced by
the encoder and the decoder. Since training signals originate from all levels
of the network, all layers can learn efficiently even in deep networks. The
speedup offered by cost terms from higher levels of the hierarchy and the
ability to learn invariant features are demonstrated in experiments.
| Harri Valpola | null | 1411.7783 | null | null |
Learning with Algebraic Invariances, and the Invariant Kernel Trick | stat.ML cs.LG math.ST stat.TH | When solving data analysis problems it is important to integrate prior
knowledge and/or structural invariances. This paper contributes by a novel
framework for incorporating algebraic invariance structure into kernels. In
particular, we show that algebraic properties such as sign symmetries in data,
phase independence, scaling etc. can be included easily by essentially
performing the kernel trick twice. We demonstrate the usefulness of our theory
in simulations on selected applications such as sign-invariant spectral
clustering and underdetermined ICA.
| Franz J. Kir\'aly, Andreas Ziehe, Klaus-Robert M\"uller | null | 1411.7817 | null | null |
Predicting clicks in online display advertising with latent features and
side-information | stat.ML cs.LG stat.AP | We review a method for click-through rate prediction based on the work of
Menon et al. [11], which combines collaborative filtering and matrix
factorization with a side-information model and fuses the outputs to proper
probabilities in [0,1]. In addition we provide details, both for the modeling
as well as the experimental part, that are not found elsewhere. We rigorously
test the performance on several test data sets from consecutive days in a
click-through rate prediction setup, in a manner which reflects a real-world
pipeline. Our results confirm that performance can be increased using latent
features, albeit the differences in the measures are small but significant.
| Bjarne {\O}rum Fruergaard | null | 1411.7924 | null | null |
Bus Travel Time Predictions Using Additive Models | cs.LG stat.AP | Many factors can affect the predictability of public bus services such as
traffic, weather and local events. Other aspects, such as day of week or hour
of day, may influence bus travel times as well, either directly or in
conjunction with other variables. However, the exact nature of such
relationships between travel times and predictor variables is, in most
situations, not known. In this paper we develop a framework that allows for
flexible modeling of bus travel times through the use of Additive Models. In
particular, we model travel times as a sum of linear as well as nonlinear terms
that are modeled as smooth functions of predictor variables. The proposed class
of models provides a principled statistical framework that is highly flexible
in terms of model building. The experimental results demonstrate uniformly
superior performance of our best model as compared to previous prediction
methods when applied to a very large GPS data set obtained from buses operating
in the city of Rio de Janeiro.
| Matthias Kormaksson, Luciano Barbosa, Marcos R. Vieira, Bianca
Zadrozny | 10.1109/ICDM.2014.107 | 1411.7973 | null | null |
Guaranteed Matrix Completion via Non-convex Factorization | cs.LG | Matrix factorization is a popular approach for large-scale matrix completion.
The optimization formulation based on matrix factorization can be solved very
efficiently by standard algorithms in practice. However, due to the
non-convexity caused by the factorization model, there is a limited theoretical
understanding of this formulation. In this paper, we establish a theoretical
guarantee for the factorization formulation to correctly recover the underlying
low-rank matrix. In particular, we show that under similar conditions to those
in previous works, many standard optimization algorithms converge to the global
optima of a factorization formulation, and recover the true low-rank matrix. We
study the local geometry of a properly regularized factorization formulation
and prove that any stationary point in a certain local region is globally
optimal. A major difference of our work from the existing results is that we do
not need resampling in either the algorithm or its analysis. Compared to other
works on nonconvex optimization, one extra difficulty lies in analyzing
nonconvex constrained optimization when the constraint (or the corresponding
regularizer) is not "consistent" with the gradient direction. One technical
contribution is the perturbation analysis for non-symmetric matrix
factorization.
| Ruoyu Sun, Zhi-Quan Luo | 10.1109/TIT.2016.2598574 | 1411.8003 | null | null |
Multiple Instance Reinforcement Learning for Efficient Weakly-Supervised
Detection in Images | cs.CV cs.LG | State-of-the-art visual recognition and detection systems increasingly rely
on large amounts of training data and complex classifiers. Therefore it becomes
increasingly expensive both to manually annotate datasets and to keep running
times at levels acceptable for practical applications. In this paper, we
propose two solutions to address these issues. First, we introduce a weakly
supervised, segmentation-based approach to learn accurate detectors and image
classifiers from weak supervisory signals that provide only approximate
constraints on target localization. We illustrate our system on the problem of
action detection in static images (Pascal VOC Actions 2012), using human visual
search patterns as our training signal. Second, inspired from the
saccade-and-fixate operating principle of the human visual system, we use
reinforcement learning techniques to train efficient search models for
detection. Our sequential method is weakly supervised and general (it does not
require eye movements), finds optimal search strategies for any given detection
confidence function and achieves performance similar to exhaustive sliding
window search at a fraction of its computational cost.
| Stefan Mathe, Cristian Sminchisescu | null | 1412.0100 | null | null |
Constant Step Size Least-Mean-Square: Bias-Variance Trade-offs and
Optimal Sampling Distributions | cs.LG math.OC stat.ML | We consider the least-squares regression problem and provide a detailed
asymptotic analysis of the performance of averaged constant-step-size
stochastic gradient descent (a.k.a. least-mean-squares). In the strongly-convex
case, we provide an asymptotic expansion up to explicit exponentially decaying
terms. Our analysis leads to new insights into stochastic approximation
algorithms: (a) it gives a tighter bound on the allowed step-size; (b) the
generalization error may be divided into a variance term which is decaying as
O(1/n), independently of the step-size $\gamma$, and a bias term that decays as
O(1/$\gamma$ 2 n 2); (c) when allowing non-uniform sampling, the choice of a
good sampling density depends on whether the variance or bias terms dominate.
In particular, when the variance term dominates, optimal sampling densities do
not lead to much gain, while when the bias term dominates, we can choose larger
step-sizes that leads to significant improvements.
| Alexandre D\'efossez (LIENS, INRIA Paris - Rocquencourt), Francis Bach
(LIENS, INRIA Paris - Rocquencourt) | null | 1412.0156 | null | null |
Empirical Q-Value Iteration | math.OC cs.LG | We propose a new simple and natural algorithm for learning the optimal
Q-value function of a discounted-cost Markov Decision Process (MDP) when the
transition kernels are unknown. Unlike the classical learning algorithms for
MDPs, such as Q-learning and actor-critic algorithms, this algorithm doesn't
depend on a stochastic approximation-based method. We show that our algorithm,
which we call the empirical Q-value iteration (EQVI) algorithm, converges to
the optimal Q-value function. We also give a rate of convergence or a
non-asymptotic sample complexity bound, and also show that an asynchronous (or
online) version of the algorithm will also work. Preliminary experimental
results suggest a faster rate of convergence to a ball park estimate for our
algorithm compared to stochastic approximation-based algorithms.
| Dileep Kalathil, Vivek S. Borkar, Rahul Jain | null | 1412.0180 | null | null |
The Loss Surfaces of Multilayer Networks | cs.LG | We study the connection between the highly non-convex loss function of a
simple model of the fully-connected feed-forward neural network and the
Hamiltonian of the spherical spin-glass model under the assumptions of: i)
variable independence, ii) redundancy in network parametrization, and iii)
uniformity. These assumptions enable us to explain the complexity of the fully
decoupled neural network through the prism of the results from random matrix
theory. We show that for large-size decoupled networks the lowest critical
values of the random loss function form a layered structure and they are
located in a well-defined band lower-bounded by the global minimum. The number
of local minima outside that band diminishes exponentially with the size of the
network. We empirically verify that the mathematical model exhibits similar
behavior as the computer simulations, despite the presence of high dependencies
in real networks. We conjecture that both simulated annealing and SGD converge
to the band of low critical points, and that all critical points found there
are local minima of high quality measured by the test error. This emphasizes a
major difference between large- and small-size networks where for the latter
poor quality local minima have non-zero probability of being recovered.
Finally, we prove that recovering the global minimum becomes harder as the
network size increases and that it is in practice irrelevant as global minimum
often leads to overfitting.
| Anna Choromanska, Mikael Henaff, Michael Mathieu, G\'erard Ben Arous,
Yann LeCun | null | 1412.0233 | null | null |
An Infra-Structure for Performance Estimation and Experimental
Comparison of Predictive Models in R | cs.MS cs.LG cs.SE stat.CO | This document describes an infra-structure provided by the R package
performanceEstimation that allows to estimate the predictive performance of
different approaches (workflows) to predictive tasks. The infra-structure is
generic in the sense that it can be used to estimate the values of any
performance metrics, for any workflow on different predictive tasks, namely,
classification, regression and time series tasks. The package also includes
several standard workflows that allow users to easily set up their experiments
limiting the amount of work and information they need to provide. The overall
goal of the infra-structure provided by our package is to facilitate the task
of estimating the predictive performance of different modeling approaches to
predictive tasks in the R environment.
| Luis Torgo | null | 1412.0436 | null | null |
Low-Rank Approximation and Completion of Positive Tensors | math.ST cs.LG stat.TH | Unlike the matrix case, computing low-rank approximations of tensors is
NP-hard and numerically ill-posed in general. Even the best rank-1
approximation of a tensor is NP-hard. In this paper, we use convex optimization
to develop polynomial-time algorithms for low-rank approximation and completion
of positive tensors. Our approach is to use algebraic topology to define a new
(numerically well-posed) decomposition for positive tensors, which we show is
equivalent to the standard tensor decomposition in important cases. Though
computing this decomposition is a nonconvex optimization problem, we prove it
can be exactly reformulated as a convex optimization problem. This allows us to
construct polynomial-time randomized algorithms for computing this
decomposition and for solving low-rank tensor approximation problems. Among the
consequences is that best rank-1 approximations of positive tensors can be
computed in polynomial time. Our framework is next extended to the tensor
completion problem, where noisy entries of a tensor are observed and then used
to estimate missing entries. We provide a polynomial-time algorithm that for
specific cases requires a polynomial (in tensor order) number of measurements,
in contrast to existing approaches that require an exponential number of
measurements. These algorithms are extended to exploit sparsity in the tensor
to reduce the number of measurements needed. We conclude by providing a novel
interpretation of statistical regression problems with categorical variables as
tensor completion problems, and numerical examples with synthetic data and data
from a bioengineered metabolic network show the improved performance of our
approach on this problem.
| Anil Aswani | null | 1412.0620 | null | null |
Effective Use of Word Order for Text Categorization with Convolutional
Neural Networks | cs.CL cs.LG stat.ML | Convolutional neural network (CNN) is a neural network that can make use of
the internal structure of data such as the 2D structure of image data. This
paper studies CNN on text categorization to exploit the 1D structure (namely,
word order) of text data for accurate prediction. Instead of using
low-dimensional word vectors as input as is often done, we directly apply CNN
to high-dimensional text data, which leads to directly learning embedding of
small text regions for use in classification. In addition to a straightforward
adaptation of CNN from image to text, a simple but new variation which employs
bag-of-word conversion in the convolution layer is proposed. An extension to
combine multiple convolution layers is also explored for higher accuracy. The
experiments demonstrate the effectiveness of our approach in comparison with
state-of-the-art methods.
| Rie Johnson and Tong Zhang | null | 1412.1058 | null | null |
Learning interpretable models of phenotypes from whole genome sequences
with the Set Covering Machine | q-bio.GN cs.CE cs.LG stat.ML | The increased affordability of whole genome sequencing has motivated its use
for phenotypic studies. We address the problem of learning interpretable models
for discrete phenotypes from whole genomes. We propose a general approach that
relies on the Set Covering Machine and a k-mer representation of the genomes.
We show results for the problem of predicting the resistance of Pseudomonas
Aeruginosa, an important human pathogen, against 4 antibiotics. Our results
demonstrate that extremely sparse models which are biologically relevant can be
learnt using this approach.
| Alexandre Drouin, S\'ebastien Gigu\`ere, Vladana Sagatovich, Maxime
D\'eraspe, Fran\c{c}ois Laviolette, Mario Marchand, Jacques Corbeil | null | 1412.1074 | null | null |
Easy Hyperparameter Search Using Optunity | cs.LG | Optunity is a free software package dedicated to hyperparameter optimization.
It contains various types of solvers, ranging from undirected methods to direct
search, particle swarm and evolutionary optimization. The design focuses on
ease of use, flexibility, code clarity and interoperability with existing
software in all machine learning environments. Optunity is written in Python
and contains interfaces to environments such as R and MATLAB. Optunity uses a
BSD license and is freely available online at http://www.optunity.net.
| Marc Claesen, Jaak Simm, Dusan Popovic, Yves Moreau, Bart De Moor | null | 1412.1114 | null | null |
Highly comparative fetal heart rate analysis | cs.LG cs.AI q-bio.QM | A database of fetal heart rate (FHR) time series measured from 7221 patients
during labor is analyzed with the aim of learning the types of features of
these recordings that are informative of low cord pH. Our 'highly comparative'
analysis involves extracting over 9000 time-series analysis features from each
FHR time series, including measures of autocorrelation, entropy, distribution,
and various model fits. This diverse collection of features was developed in
previous work, and is publicly available. We describe five features that most
accurately classify a balanced training set of 59 'low pH' and 59 'normal pH'
FHR recordings. We then describe five of the features with the strongest linear
correlation to cord pH across the full dataset of FHR time series. The features
identified in this work may be used as part of a system for guiding
intervention during labor in future. This work successfully demonstrates the
utility of comparing across a large, interdisciplinary literature on
time-series analysis to automatically contribute new scientific results for
specific biomedical signal processing challenges.
| B. D. Fulcher, A. E. Georgieva, C. W. G. Redman, Nick S. Jones | 10.1109/EMBC.2012.6346629 | 1412.1138 | null | null |
New insights and perspectives on the natural gradient method | cs.LG stat.ML | Natural gradient descent is an optimization method traditionally motivated
from the perspective of information geometry, and works well for many
applications as an alternative to stochastic gradient descent. In this paper we
critically analyze this method and its properties, and show how it can be
viewed as a type of 2nd-order optimization method, with the Fisher information
matrix acting as a substitute for the Hessian. In many important cases, the
Fisher information matrix is shown to be equivalent to the Generalized
Gauss-Newton matrix, which both approximates the Hessian, but also has certain
properties that favor its use over the Hessian. This perspective turns out to
have significant implications for the design of a practical and robust natural
gradient optimizer, as it motivates the use of techniques like trust regions
and Tikhonov regularization. Additionally, we make a series of contributions to
the understanding of natural gradient and 2nd-order methods, including: a
thorough analysis of the convergence speed of stochastic natural gradient
descent (and more general stochastic 2nd-order methods) as applied to convex
quadratics, a critical examination of the oft-used "empirical" approximation of
the Fisher matrix, and an analysis of the (approximate) parameterization
invariance property possessed by natural gradient methods (which we show also
holds for certain other curvature, but notably not the Hessian).
| James Martens | null | 1412.1193 | null | null |
Deep Distributed Random Samplings for Supervised Learning: An
Alternative to Random Forests? | cs.LG stat.ML | In (\cite{zhang2014nonlinear,zhang2014nonlinear2}), we have viewed machine
learning as a coding and dimensionality reduction problem, and further proposed
a simple unsupervised dimensionality reduction method, entitled deep
distributed random samplings (DDRS). In this paper, we further extend it to
supervised learning incrementally. The key idea here is to incorporate label
information into the coding process by reformulating that each center in DDRS
has multiple output units indicating which class the center belongs to. The
supervised learning method seems somewhat similar with random forests
(\cite{breiman2001random}), here we emphasize their differences as follows. (i)
Each layer of our method considers the relationship between part of the data
points in training data with all training data points, while random forests
focus on building each decision tree on only part of training data points
independently. (ii) Our method builds gradually-narrowed network by sampling
less and less data points, while random forests builds gradually-narrowed
network by merging subclasses. (iii) Our method is trained more straightforward
from bottom layer to top layer, while random forests build each tree from top
layer to bottom layer by splitting. (iv) Our method encodes output targets
implicitly in sparse codes, while random forests encode output targets by
remembering the class attributes of the activated nodes. Therefore, our method
is a simpler, more straightforward, and maybe a better alternative choice,
though both methods use two very basic elements---randomization and nearest
neighbor optimization---as the core. This preprint is used to protect the
incremental idea from (\cite{zhang2014nonlinear,zhang2014nonlinear2}). Full
empirical evaluation will be announced carefully later.
| Xiao-Lei Zhang | null | 1412.1271 | null | null |
Curriculum Learning of Multiple Tasks | stat.ML cs.LG | Sharing information between multiple tasks enables algorithms to achieve good
generalization performance even from small amounts of training data. However,
in a realistic scenario of multi-task learning not all tasks are equally
related to each other, hence it could be advantageous to transfer information
only between the most related tasks. In this work we propose an approach that
processes multiple tasks in a sequence with sharing between subsequent tasks
instead of solving all tasks jointly. Subsequently, we address the question of
curriculum learning of tasks, i.e. finding the best order of tasks to be
learned. Our approach is based on a generalization bound criterion for choosing
the task order that optimizes the average expected classification performance
over all tasks. Our experimental results show that learning multiple related
tasks sequentially can be more effective than learning them jointly, the order
in which tasks are being solved affects the overall performance, and that our
model is able to automatically discover the favourable order of tasks.
| Anastasia Pentina and Viktoriia Sharmanska and Christoph H. Lampert | null | 1412.1353 | null | null |
Structure learning of antiferromagnetic Ising models | stat.ML cs.IT cs.LG math.IT | In this paper we investigate the computational complexity of learning the
graph structure underlying a discrete undirected graphical model from i.i.d.
samples. We first observe that the notoriously difficult problem of learning
parities with noise can be captured as a special case of learning graphical
models. This leads to an unconditional computational lower bound of $\Omega
(p^{d/2})$ for learning general graphical models on $p$ nodes of maximum degree
$d$, for the class of so-called statistical algorithms recently introduced by
Feldman et al (2013). The lower bound suggests that the $O(p^d)$ runtime
required to exhaustively search over neighborhoods cannot be significantly
improved without restricting the class of models.
Aside from structural assumptions on the graph such as it being a tree,
hypertree, tree-like, etc., many recent papers on structure learning assume
that the model has the correlation decay property. Indeed, focusing on
ferromagnetic Ising models, Bento and Montanari (2009) showed that all known
low-complexity algorithms fail to learn simple graphs when the interaction
strength exceeds a number related to the correlation decay threshold. Our
second set of results gives a class of repelling (antiferromagnetic) models
that have the opposite behavior: very strong interaction allows efficient
learning in time $O(p^2)$. We provide an algorithm whose performance
interpolates between $O(p^2)$ and $O(p^{d+2})$ depending on the strength of the
repulsion.
| Guy Bresler, David Gamarnik, and Devavrat Shah | null | 1412.1443 | null | null |
Skip-gram Language Modeling Using Sparse Non-negative Matrix Probability
Estimation | cs.LG cs.CL | We present a novel family of language model (LM) estimation techniques named
Sparse Non-negative Matrix (SNM) estimation. A first set of experiments
empirically evaluating it on the One Billion Word Benchmark shows that SNM
$n$-gram LMs perform almost as well as the well-established Kneser-Ney (KN)
models. When using skip-gram features the models are able to match the
state-of-the-art recurrent neural network (RNN) LMs; combining the two modeling
techniques yields the best known result on the benchmark. The computational
advantages of SNM over both maximum entropy and RNN LM estimation are probably
its main strength, promising an approach that has the same flexibility in
combining arbitrary features effectively and yet should scale to very large
amounts of data as gracefully as $n$-gram LMs do.
| Noam Shazeer, Joris Pelemans, Ciprian Chelba | null | 1412.1454 | null | null |
On the String Kernel Pre-Image Problem with Applications in Drug
Discovery | cs.LG cs.CE | The pre-image problem has to be solved during inference by most structured
output predictors. For string kernels, this problem corresponds to finding the
string associated to a given input. An algorithm capable of solving or finding
good approximations to this problem would have many applications in
computational biology and other fields. This work uses a recent result on
combinatorial optimization of linear predictors based on string kernels to
develop, for the pre-image, a low complexity upper bound valid for many string
kernels. This upper bound is used with success in a branch and bound searching
algorithm. Applications and results in the discovery of druggable peptides are
presented and discussed.
| S\'ebastien Gigu\`ere, Am\'elie Rolland, Fran\c{c}ois Laviolette and
Mario Marchand | null | 1412.1463 | null | null |
Information Exchange and Learning Dynamics over Weakly-Connected
Adaptive Networks | cs.MA cs.IT cs.LG math.IT | The paper examines the learning mechanism of adaptive agents over
weakly-connected graphs and reveals an interesting behavior on how information
flows through such topologies. The results clarify how asymmetries in the
exchange of data can mask local information at certain agents and make them
totally dependent on other agents. A leader-follower relationship develops with
the performance of some agents being fully determined by the performance of
other agents that are outside their domain of influence. This scenario can
arise, for example, due to intruder attacks by malicious agents or as the
result of failures by some critical links. The findings in this work help
explain why strong-connectivity of the network topology, adaptation of the
combination weights, and clustering of agents are important ingredients to
equalize the learning abilities of all agents against such disturbances. The
results also clarify how weak-connectivity can be helpful in reducing the
effect of outlier data on learning performance.
| Bicheng Ying and Ali H. Sayed | null | 1412.1523 | null | null |
Metric Learning Driven Multi-Task Structured Output Optimization for
Robust Keypoint Tracking | cs.CV cs.LG | As an important and challenging problem in computer vision and graphics,
keypoint-based object tracking is typically formulated in a spatio-temporal
statistical learning framework. However, most existing keypoint trackers are
incapable of effectively modeling and balancing the following three aspects in
a simultaneous manner: temporal model coherence across frames, spatial model
consistency within frames, and discriminative feature construction. To address
this issue, we propose a robust keypoint tracker based on spatio-temporal
multi-task structured output optimization driven by discriminative metric
learning. Consequently, temporal model coherence is characterized by multi-task
structured keypoint model learning over several adjacent frames, while spatial
model consistency is modeled by solving a geometric verification based
structured learning problem. Discriminative feature construction is enabled by
metric learning to ensure the intra-class compactness and inter-class
separability. Finally, the above three modules are simultaneously optimized in
a joint learning scheme. Experimental results have demonstrated the
effectiveness of our tracker.
| Liming Zhao, Xi Li, Jun Xiao, Fei Wu, Yueting Zhuang | null | 1412.1574 | null | null |
LightLDA: Big Topic Models on Modest Compute Clusters | stat.ML cs.DC cs.IR cs.LG | When building large-scale machine learning (ML) programs, such as big topic
models or deep neural nets, one usually assumes such tasks can only be
attempted with industrial-sized clusters with thousands of nodes, which are out
of reach for most practitioners or academic researchers. We consider this
challenge in the context of topic modeling on web-scale corpora, and show that
with a modest cluster of as few as 8 machines, we can train a topic model with
1 million topics and a 1-million-word vocabulary (for a total of 1 trillion
parameters), on a document collection with 200 billion tokens -- a scale not
yet reported even with thousands of machines. Our major contributions include:
1) a new, highly efficient O(1) Metropolis-Hastings sampling algorithm, whose
running cost is (surprisingly) agnostic of model size, and empirically
converges nearly an order of magnitude faster than current state-of-the-art
Gibbs samplers; 2) a structure-aware model-parallel scheme, which leverages
dependencies within the topic model, yielding a sampling strategy that is
frugal on machine memory and network communication; 3) a differential
data-structure for model storage, which uses separate data structures for high-
and low-frequency words to allow extremely large models to fit in memory, while
maintaining high inference speed; and 4) a bounded asynchronous data-parallel
scheme, which allows efficient distributed processing of massive data via a
parameter server. Our distribution strategy is an instance of the
model-and-data-parallel programming model underlying the Petuum framework for
general distributed ML, and was implemented on top of the Petuum open-source
system. We provide experimental evidence showing how this development puts
massive models within reach on a small cluster while still enjoying
proportional time cost reductions with increasing cluster size, in comparison
with alternative options.
| Jinhui Yuan, Fei Gao, Qirong Ho, Wei Dai, Jinliang Wei, Xun Zheng,
Eric P. Xing, Tie-Yan Liu, Wei-Ying Ma | null | 1412.1576 | null | null |
The entropic barrier: a simple and optimal universal self-concordant
barrier | math.OC cs.IT cs.LG math.IT | We prove that the Cram\'er transform of the uniform measure on a convex body
in $\mathbb{R}^n$ is a $(1+o(1)) n$-self-concordant barrier, improving a
seminal result of Nesterov and Nemirovski. This gives the first explicit
construction of a universal barrier for convex bodies with optimal
self-concordance parameter. The proof is based on basic geometry of log-concave
distributions, and elementary duality in exponential families.
| S\'ebastien Bubeck and Ronen Eldan | null | 1412.1587 | null | null |
End-to-end Continuous Speech Recognition using Attention-based Recurrent
NN: First Results | cs.NE cs.LG stat.ML | We replace the Hidden Markov Model (HMM) which is traditionally used in in
continuous speech recognition with a bi-directional recurrent neural network
encoder coupled to a recurrent neural network decoder that directly emits a
stream of phonemes. The alignment between the input and output sequences is
established using an attention mechanism: the decoder emits each symbol based
on a context created with a subset of input symbols elected by the attention
mechanism. We report initial results demonstrating that this new approach
achieves phoneme error rates that are comparable to the state-of-the-art
HMM-based decoders, on the TIMIT dataset.
| Jan Chorowski, Dzmitry Bahdanau, Kyunghyun Cho, Yoshua Bengio | null | 1412.1602 | null | null |
Fast Rates by Transferring from Auxiliary Hypotheses | cs.LG | In this work we consider the learning setting where, in addition to the
training set, the learner receives a collection of auxiliary hypotheses
originating from other tasks. We focus on a broad class of ERM-based linear
algorithms that can be instantiated with any non-negative smooth loss function
and any strongly convex regularizer. We establish generalization and excess
risk bounds, showing that, if the algorithm is fed with a good combination of
source hypotheses, generalization happens at the fast rate $\mathcal{O}(1/m)$
instead of the usual $\mathcal{O}(1/\sqrt{m})$. On the other hand, if the
source hypotheses combination is a misfit for the target task, we recover the
usual learning rate. As a byproduct of our study, we also prove a new bound on
the Rademacher complexity of the smooth loss class under weaker assumptions
compared to previous works.
| Ilja Kuzborskij, Francesco Orabona | 10.1007/s10994-016-5594-4 | 1412.1619 | null | null |
Fisher Kernel for Deep Neural Activations | cs.CV cs.LG cs.NE | Compared to image representation based on low-level local descriptors, deep
neural activations of Convolutional Neural Networks (CNNs) are richer in
mid-level representation, but poorer in geometric invariance properties. In
this paper, we present a straightforward framework for better image
representation by combining the two approaches. To take advantages of both
representations, we propose an efficient method to extract a fair amount of
multi-scale dense local activations from a pre-trained CNN. We then aggregate
the activations by Fisher kernel framework, which has been modified with a
simple scale-wise normalization essential to make it suitable for CNN
activations. Replacing the direct use of a single activation vector with our
representation demonstrates significant performance improvements: +17.76 (Acc.)
on MIT Indoor 67 and +7.18 (mAP) on PASCAL VOC 2007. The results suggest that
our proposal can be used as a primary image representation for better
performances in visual recognition tasks.
| Donggeun Yoo, Sunggyun Park, Joon-Young Lee, In So Kweon | null | 1412.1628 | null | null |
Image Data Compression for Covariance and Histogram Descriptors | stat.ML cs.CV cs.LG | Covariance and histogram image descriptors provide an effective way to
capture information about images. Both excel when used in combination with
special purpose distance metrics. For covariance descriptors these metrics
measure the distance along the non-Euclidean Riemannian manifold of symmetric
positive definite matrices. For histogram descriptors the Earth Mover's
distance measures the optimal transport between two histograms. Although more
precise, these distance metrics are very expensive to compute, making them
impractical in many applications, even for data sets of only a few thousand
examples. In this paper we present two methods to compress the size of
covariance and histogram datasets with only marginal increases in test error
for k-nearest neighbor classification. Specifically, we show that we can reduce
data sets to 16% and in some cases as little as 2% of their original size,
while approximately matching the test error of kNN classification on the full
training set. In fact, because the compressed set is learned in a supervised
fashion, it sometimes even outperforms the full data set, while requiring only
a fraction of the space and drastically reducing test-time computation.
| Matt J. Kusner, Nicholas I. Kolkin, Stephen Tyree, Kilian Q.
Weinberger | null | 1412.1740 | null | null |
Primal-Dual Algorithms for Non-negative Matrix Factorization with the
Kullback-Leibler Divergence | cs.LG math.OC | Non-negative matrix factorization (NMF) approximates a given matrix as a
product of two non-negative matrices. Multiplicative algorithms deliver
reliable results, but they show slow convergence for high-dimensional data and
may be stuck away from local minima. Gradient descent methods have better
behavior, but only apply to smooth losses such as the least-squares loss. In
this article, we propose a first-order primal-dual algorithm for non-negative
decomposition problems (where one factor is fixed) with the KL divergence,
based on the Chambolle-Pock algorithm. All required computations may be
obtained in closed form and we provide an efficient heuristic way to select
step-sizes. By using alternating optimization, our algorithm readily extends to
NMF and, on synthetic examples, face recognition or music source separation
datasets, it is either faster than existing algorithms, or leads to improved
local optima, or both.
| Felipe Yanez (LIENS, INRIA Paris - Rocquencourt), Francis Bach (LIENS,
INRIA Paris - Rocquencourt) | null | 1412.1788 | null | null |
Integer-Programming Ensemble of Temporal-Relations Classifiers | cs.CL cs.LG math.OC | The extraction and understanding of temporal events and their relations are
major challenges in natural language processing. Processing text on a
sentence-by-sentence or expression-by-expression basis often fails, in part due
to the challenge of capturing the global consistency of the text. We present an
ensemble method, which reconciles the outputs of multiple classifiers of
temporal expressions across the text using integer programming. Computational
experiments show that the ensemble improves upon the best individual results
from two recent challenges, SemEval-2013 TempEval-3 (Temporal Annotation) and
SemEval-2016 Task 12 (Clinical TempEval).
| Catherine Kerr, Terri Hoare, Paula Carroll, Jakub Marecek | 10.1007/s10618-019-00671-x | 1412.1866 | null | null |
A parallel sampling based clustering | cs.LG | The problem of automatically clustering data is an age old problem. People
have created numerous algorithms to tackle this problem. The execution time of
any of this algorithm grows with the number of input points and the number of
cluster centers required. To reduce the number of input points we could average
the points locally and use the means or the local centers as the input for
clustering. However since the required number of local centers is very high,
running the clustering algorithm on the entire dataset to obtain these
representational points is very time consuming. To remedy this problem, in this
paper we are proposing two subclustering schemes where by we subdivide the
dataset into smaller sets and run the clustering algorithm on the smaller
datasets to obtain the required number of datapoints to run our clustering
algorithm with. As we are subdividing the given dataset, we could run
clustering algorithm on each smaller piece of the dataset in parallel. We found
that both parallel and serial execution of this method to be much faster than
the original clustering algorithm and error in running the clustering algorithm
on a reduced set to be very less.
| Aditya AV Sastry and Kalyan Netti | null | 1412.1947 | null | null |
Learning Multi-target Tracking with Quadratic Object Interactions | cs.CV cs.LG | We describe a model for multi-target tracking based on associating
collections of candidate detections across frames of a video. In order to model
pairwise interactions between different tracks, such as suppression of
overlapping tracks and contextual cues about co-occurence of different objects,
we augment a standard min-cost flow objective with quadratic terms between
detection variables. We learn the parameters of this model using structured
prediction and a loss function which approximates the multi-target tracking
accuracy. We evaluate two different approaches to finding an optimal set of
tracks under model objective based on an LP relaxation and a novel greedy
extension to dynamic programming that handles pairwise interactions. We find
the greedy algorithm achieves equivalent performance to the LP relaxation while
being 2-7x faster than a commercial solver. The resulting model with learned
parameters outperforms existing methods across several categories on the KITTI
tracking benchmark.
| Shaofei Wang and Charless C. Fowlkes | null | 1412.2066 | null | null |
Consistent optimization of AMS by logistic loss minimization | cs.LG | In this paper, we theoretically justify an approach popular among
participants of the Higgs Boson Machine Learning Challenge to optimize
approximate median significance (AMS). The approach is based on the following
two-stage procedure. First, a real-valued function is learned by minimizing a
surrogate loss for binary classification, such as logistic loss, on the
training sample. Then, a threshold is tuned on a separate validation sample, by
direct optimization of AMS. We show that the regret of the resulting
(thresholded) classifier measured with respect to the squared AMS, is
upperbounded by the regret of the underlying real-valued function measured with
respect to the logistic loss. Hence, we prove that minimizing logistic
surrogate is a consistent method of optimizing AMS.
| Wojciech Kot{\l}owski | null | 1412.2106 | null | null |
Consistent Collective Matrix Completion under Joint Low Rank Structure | stat.ML cs.LG | We address the collective matrix completion problem of jointly recovering a
collection of matrices with shared structure from partial (and potentially
noisy) observations. To ensure well--posedness of the problem, we impose a
joint low rank structure, wherein each component matrix is low rank and the
latent space of the low rank factors corresponding to each entity is shared
across the entire collection. We first develop a rigorous algebra for
representing and manipulating collective--matrix structure, and identify
sufficient conditions for consistent estimation of collective matrices. We then
propose a tractable convex estimator for solving the collective matrix
completion problem, and provide the first non--trivial theoretical guarantees
for consistency of collective matrix completion. We show that under reasonable
assumptions stated in Section 3.1, with high probability, the proposed
estimator exactly recovers the true matrices whenever sample complexity
requirements dictated by Theorem 1 are met. The sample complexity requirement
derived in the paper are optimum up to logarithmic factors, and significantly
improve upon the requirements obtained by trivial extensions of standard matrix
completion. Finally, we propose a scalable approximate algorithm to solve the
proposed convex program, and corroborate our results through simulated
experiments.
| Suriya Gunasekar, Makoto Yamada, Dawei Yin, Yi Chang | null | 1412.2113 | null | null |
Relations among Some Low Rank Subspace Recovery Models | cs.LG math.OC | Recovering intrinsic low dimensional subspaces from data distributed on them
is a key preprocessing step to many applications. In recent years, there has
been a lot of work that models subspace recovery as low rank minimization
problems. We find that some representative models, such as Robust Principal
Component Analysis (R-PCA), Robust Low Rank Representation (R-LRR), and Robust
Latent Low Rank Representation (R-LatLRR), are actually deeply connected. More
specifically, we discover that once a solution to one of the models is
obtained, we can obtain the solutions to other models in closed-form
formulations. Since R-PCA is the simplest, our discovery makes it the center of
low rank subspace recovery models. Our work has two important implications.
First, R-PCA has a solid theoretical foundation. Under certain conditions, we
could find better solutions to these low rank models at overwhelming
probabilities, although these models are non-convex. Second, we can obtain
significantly faster algorithms for these models by solving R-PCA first. The
computation cost can be further cut by applying low complexity randomized
algorithms, e.g., our novel $\ell_{2,1}$ filtering algorithm, to R-PCA.
Experiments verify the advantages of our algorithms over other state-of-the-art
ones that are based on the alternating direction method.
| Hongyang Zhang, Zhouchen Lin, Chao Zhang, Junbin Gao | null | 1412.2196 | null | null |
Generalized Singular Value Thresholding | cs.CV cs.LG cs.NA math.NA | This work studies the Generalized Singular Value Thresholding (GSVT) operator
${\text{Prox}}_{g}^{{\sigma}}(\cdot)$, \begin{equation*}
{\text{Prox}}_{g}^{{\sigma}}(B)=\arg\min\limits_{X}\sum_{i=1}^{m}g(\sigma_{i}(X))
+ \frac{1}{2}||X-B||_{F}^{2}, \end{equation*} associated with a nonconvex
function $g$ defined on the singular values of $X$. We prove that GSVT can be
obtained by performing the proximal operator of $g$ (denoted as
$\text{Prox}_g(\cdot)$) on the singular values since $\text{Prox}_g(\cdot)$ is
monotone when $g$ is lower bounded. If the nonconvex $g$ satisfies some
conditions (many popular nonconvex surrogate functions, e.g., $\ell_p$-norm,
$0<p<1$, of $\ell_0$-norm are special cases), a general solver to find
$\text{Prox}_g(b)$ is proposed for any $b\geq0$. GSVT greatly generalizes the
known Singular Value Thresholding (SVT) which is a basic subroutine in many
convex low rank minimization methods. We are able to solve the nonconvex low
rank minimization problem by using GSVT in place of SVT.
| Canyi Lu, Changbo Zhu, Chunyan Xu, Shuicheng Yan, Zhouchen Lin | null | 1412.2231 | null | null |
Theano-based Large-Scale Visual Recognition with Multiple GPUs | cs.LG | In this report, we describe a Theano-based AlexNet (Krizhevsky et al., 2012)
implementation and its naive data parallelism on multiple GPUs. Our performance
on 2 GPUs is comparable with the state-of-art Caffe library (Jia et al., 2014)
run on 1 GPU. To the best of our knowledge, this is the first open-source
Python-based AlexNet implementation to-date.
| Weiguang Ding, Ruoyan Wang, Fei Mao, Graham Taylor | null | 1412.2302 | null | null |
Visual Causal Feature Learning | stat.ML cs.AI cs.CV cs.LG | We provide a rigorous definition of the visual cause of a behavior that is
broadly applicable to the visually driven behavior in humans, animals, neurons,
robots and other perceiving systems. Our framework generalizes standard
accounts of causal learning to settings in which the causal variables need to
be constructed from micro-variables. We prove the Causal Coarsening Theorem,
which allows us to gain causal knowledge from observational data with minimal
experimental effort. The theorem provides a connection to standard inference
techniques in machine learning that identify features of an image that
correlate with, but may not cause, the target behavior. Finally, we propose an
active learning scheme to learn a manipulator function that performs optimal
manipulations on the image to automatically identify the visual cause of a
target behavior. We illustrate our inference and learning algorithms in
experiments based on both synthetic and real data.
| Krzysztof Chalupka and Pietro Perona and Frederick Eberhardt | null | 1412.2309 | null | null |
$\ell_p$ Testing and Learning of Discrete Distributions | cs.DS cs.LG math.ST stat.TH | The classic problems of testing uniformity of and learning a discrete
distribution, given access to independent samples from it, are examined under
general $\ell_p$ metrics. The intuitions and results often contrast with the
classic $\ell_1$ case. For $p > 1$, we can learn and test with a number of
samples that is independent of the support size of the distribution: With an
$\ell_p$ tolerance $\epsilon$, $O(\max\{ \sqrt{1/\epsilon^q}, 1/\epsilon^2 \})$
samples suffice for testing uniformity and $O(\max\{ 1/\epsilon^q,
1/\epsilon^2\})$ samples suffice for learning, where $q=p/(p-1)$ is the
conjugate of $p$. As this parallels the intuition that $O(\sqrt{n})$ and $O(n)$
samples suffice for the $\ell_1$ case, it seems that $1/\epsilon^q$ acts as an
upper bound on the "apparent" support size.
For some $\ell_p$ metrics, uniformity testing becomes easier over larger
supports: a 6-sided die requires fewer trials to test for fairness than a
2-sided coin, and a card-shuffler requires fewer trials than the die. In fact,
this inverse dependence on support size holds if and only if $p > \frac{4}{3}$.
The uniformity testing algorithm simply thresholds the number of "collisions"
or "coincidences" and has an optimal sample complexity up to constant factors
for all $1 \leq p \leq 2$. Another algorithm gives order-optimal sample
complexity for $\ell_{\infty}$ uniformity testing. Meanwhile, the most natural
learning algorithm is shown to have order-optimal sample complexity for all
$\ell_p$ metrics.
The author thanks Cl\'{e}ment Canonne for discussions and contributions to
this work.
| Bo Waggoner | 10.1145/2688073.2688095 | 1412.2314 | null | null |
Dimensionality Reduction with Subspace Structure Preservation | cs.LG stat.ML | Modeling data as being sampled from a union of independent subspaces has been
widely applied to a number of real world applications. However, dimensionality
reduction approaches that theoretically preserve this independence assumption
have not been well studied. Our key contribution is to show that $2K$
projection vectors are sufficient for the independence preservation of any $K$
class data sampled from a union of independent subspaces. It is this
non-trivial observation that we use for designing our dimensionality reduction
technique. In this paper, we propose a novel dimensionality reduction algorithm
that theoretically preserves this structure for a given dataset. We support our
theoretical analysis with empirical results on both synthetic and real world
data achieving \textit{state-of-the-art} results compared to popular
dimensionality reduction techniques.
| Devansh Arpit, Ifeoma Nwogu, Venu Govindaraju | null | 1412.2404 | null | null |
MLitB: Machine Learning in the Browser | cs.DC cs.LG stat.ML | With few exceptions, the field of Machine Learning (ML) research has largely
ignored the browser as a computational engine. Beyond an educational resource
for ML, the browser has vast potential to not only improve the state-of-the-art
in ML research, but also, inexpensively and on a massive scale, to bring
sophisticated ML learning and prediction to the public at large. This paper
introduces MLitB, a prototype ML framework written entirely in JavaScript,
capable of performing large-scale distributed computing with heterogeneous
classes of devices. The development of MLitB has been driven by several
underlying objectives whose aim is to make ML learning and usage ubiquitous (by
using ubiquitous compute devices), cheap and effortlessly distributed, and
collaborative. This is achieved by allowing every internet capable device to
run training algorithms and predictive models with no software installation and
by saving models in universally readable formats. Our prototype library is
capable of training deep neural networks with synchronized, distributed
stochastic gradient descent. MLitB offers several important opportunities for
novel ML research, including: development of distributed learning algorithms,
advancement of web GPU algorithms, novel field and mobile applications, privacy
preserving computing, and green grid-computing. MLitB is available as open
source software.
| Edward Meeds and Remco Hendriks and Said Al Faraby and Magiel Bruntink
and Max Welling | null | 1412.2432 | null | null |
Weighted Polynomial Approximations: Limits for Learning and
Pseudorandomness | cs.CC cs.LG | Polynomial approximations to boolean functions have led to many positive
results in computer science. In particular, polynomial approximations to the
sign function underly algorithms for agnostically learning halfspaces, as well
as pseudorandom generators for halfspaces. In this work, we investigate the
limits of these techniques by proving inapproximability results for the sign
function.
Firstly, the polynomial regression algorithm of Kalai et al. (SIAM J. Comput.
2008) shows that halfspaces can be learned with respect to log-concave
distributions on $\mathbb{R}^n$ in the challenging agnostic learning model. The
power of this algorithm relies on the fact that under log-concave
distributions, halfspaces can be approximated arbitrarily well by low-degree
polynomials. We ask whether this technique can be extended beyond log-concave
distributions, and establish a negative result. We show that polynomials of any
degree cannot approximate the sign function to within arbitrarily low error for
a large class of non-log-concave distributions on the real line, including
those with densities proportional to $\exp(-|x|^{0.99})$.
Secondly, we investigate the derandomization of Chernoff-type concentration
inequalities. Chernoff-type tail bounds on sums of independent random variables
have pervasive applications in theoretical computer science. Schmidt et al.
(SIAM J. Discrete Math. 1995) showed that these inequalities can be established
for sums of random variables with only $O(\log(1/\delta))$-wise independence,
for a tail probability of $\delta$. We show that their results are tight up to
constant factors.
These results rely on techniques from weighted approximation theory, which
studies how well functions on the real line can be approximated by polynomials
under various distributions. We believe that these techniques will have further
applications in other areas of computer science.
| Mark Bun and Thomas Steinke | null | 1412.2457 | null | null |
Accurate Streaming Support Vector Machines | cs.LG | A widely-used tool for binary classification is the Support Vector Machine
(SVM), a supervised learning technique that finds the "maximum margin" linear
separator between the two classes. While SVMs have been well studied in the
batch (offline) setting, there is considerably less work on the streaming
(online) setting, which requires only a single pass over the data using
sub-linear space. Existing streaming algorithms are not yet competitive with
the batch implementation. In this paper, we use the formulation of the SVM as a
minimum enclosing ball (MEB) problem to provide a streaming SVM algorithm based
off of the blurred ball cover originally proposed by Agarwal and Sharathkumar.
Our implementation consistently outperforms existing streaming SVM approaches
and provides higher accuracies than libSVM on several datasets, thus making it
competitive with the standard SVM batch implementation.
| Vikram Nathan, Sharath Raghvendra | null | 1412.2485 | null | null |
A New Approach of Learning Hierarchy Construction Based on Fuzzy Logic | cs.CY cs.AI cs.LG | In recent years, adaptive learning systems rely increasingly on learning
hierarchy to customize the educational logic developed in their courses. Most
approaches do not consider that the relationships of prerequisites between the
skills are fuzzy relationships. In this article, we describe a new approach of
a practical application of fuzzy logic techniques to the construction of
learning hierarchies. For this, we use a learning hierarchy predefined by one
or more experts of a specific field. However, the relationships of
prerequisites between the skills in the learning hierarchy are not definitive
and they are fuzzy relationships. Indeed, we measure relevance degree of all
relationships existing in this learning hierarchy and we try to answer to the
following question: Is the relationships of prerequisites predefined in initial
learning hierarchy are correctly established or not?
| Ali Aajli, Karim Afdel | null | 1412.2689 | null | null |
Provable Methods for Training Neural Networks with Sparse Connectivity | cs.LG cs.NE stat.ML | We provide novel guaranteed approaches for training feedforward neural
networks with sparse connectivity. We leverage on the techniques developed
previously for learning linear networks and show that they can also be
effectively adopted to learn non-linear networks. We operate on the moments
involving label and the score function of the input, and show that their
factorization provably yields the weight matrix of the first layer of a deep
network under mild conditions. In practice, the output of our method can be
employed as effective initializers for gradient descent.
| Hanie Sedghi and Anima Anandkumar | null | 1412.2693 | null | null |
Unsupervised Induction of Semantic Roles within a Reconstruction-Error
Minimization Framework | cs.CL cs.AI cs.LG stat.ML | We introduce a new approach to unsupervised estimation of feature-rich
semantic role labeling models. Our model consists of two components: (1) an
encoding component: a semantic role labeling model which predicts roles given a
rich set of syntactic and lexical features; (2) a reconstruction component: a
tensor factorization model which relies on roles to predict argument fillers.
When the components are estimated jointly to minimize errors in argument
reconstruction, the induced roles largely correspond to roles defined in
annotated resources. Our method performs on par with most accurate role
induction methods on English and German, even though, unlike these previous
approaches, we do not incorporate any prior linguistic knowledge about the
languages.
| Ivan Titov and Ehsan Khoddam | null | 1412.2812 | null | null |
Circumventing the Curse of Dimensionality in Prediction: Causal
Rate-Distortion for Infinite-Order Markov Processes | cond-mat.stat-mech cs.LG nlin.CD q-bio.NC stat.ML | Predictive rate-distortion analysis suffers from the curse of dimensionality:
clustering arbitrarily long pasts to retain information about arbitrarily long
futures requires resources that typically grow exponentially with length. The
challenge is compounded for infinite-order Markov processes, since conditioning
on finite sequences cannot capture all of their past dependencies. Spectral
arguments show that algorithms which cluster finite-length sequences fail
dramatically when the underlying process has long-range temporal correlations
and can fail even for processes generated by finite-memory hidden Markov
models. We circumvent the curse of dimensionality in rate-distortion analysis
of infinite-order processes by casting predictive rate-distortion objective
functions in terms of the forward- and reverse-time causal states of
computational mechanics. Examples demonstrate that the resulting causal
rate-distortion theory substantially improves current predictive
rate-distortion analyses.
| Sarah Marzen and James P. Crutchfield | null | 1412.2859 | null | null |
Score Function Features for Discriminative Learning: Matrix and Tensor
Framework | cs.LG stat.ML | Feature learning forms the cornerstone for tackling challenging learning
problems in domains such as speech, computer vision and natural language
processing. In this paper, we consider a novel class of matrix and
tensor-valued features, which can be pre-trained using unlabeled samples. We
present efficient algorithms for extracting discriminative information, given
these pre-trained features and labeled samples for any related task. Our class
of features are based on higher-order score functions, which capture local
variations in the probability density function of the input. We establish a
theoretical framework to characterize the nature of discriminative information
that can be extracted from score-function features, when used in conjunction
with labeled samples. We employ efficient spectral decomposition algorithms (on
matrices and tensors) for extracting discriminative components. The advantage
of employing tensor-valued features is that we can extract richer
discriminative information in the form of an overcomplete representations.
Thus, we present a novel framework for employing generative models of the input
for discriminative learning.
| Majid Janzamin, Hanie Sedghi, Anima Anandkumar | null | 1412.2863 | null | null |
Bayesian Fisher's Discriminant for Functional Data | cs.LG stat.ML | We propose a Bayesian framework of Gaussian process in order to extend
Fisher's discriminant to classify functional data such as spectra and images.
The probability structure for our extended Fisher's discriminant is explicitly
formulated, and we utilize the smoothness assumptions of functional data as
prior probabilities. Existing methods which directly employ the smoothness
assumption of functional data can be shown as special cases within this
framework given corresponding priors while their estimates of the unknowns are
one-step approximations to the proposed MAP estimates. Empirical results on
various simulation studies and different real applications show that the
proposed method significantly outperforms the other Fisher's discriminant
methods for functional data.
| Yao-Hsiang Yang, Lu-Hung Chen, Chieh-Chih Wang, and Chu-Song Chen | null | 1412.2929 | null | null |
Max vs Min: Tensor Decomposition and ICA with nearly Linear Sample
Complexity | cs.DS cs.LG stat.ML | We present a simple, general technique for reducing the sample complexity of
matrix and tensor decomposition algorithms applied to distributions. We use the
technique to give a polynomial-time algorithm for standard ICA with sample
complexity nearly linear in the dimension, thereby improving substantially on
previous bounds. The analysis is based on properties of random polynomials,
namely the spacings of an ensemble of polynomials. Our technique also applies
to other applications of tensor decompositions, including spherical Gaussian
mixture models.
| Santosh S. Vempala and Ying Xiao | null | 1412.2954 | null | null |
Provable Tensor Methods for Learning Mixtures of Generalized Linear
Models | cs.LG stat.ML | We consider the problem of learning mixtures of generalized linear models
(GLM) which arise in classification and regression problems. Typical learning
approaches such as expectation maximization (EM) or variational Bayes can get
stuck in spurious local optima. In contrast, we present a tensor decomposition
method which is guaranteed to correctly recover the parameters. The key insight
is to employ certain feature transformations of the input, which depend on the
input generative model. Specifically, we employ score function tensors of the
input and compute their cross-correlation with the response variable. We
establish that the decomposition of this tensor consistently recovers the
parameters, under mild non-degeneracy conditions. We demonstrate that the
computational and sample complexity of our method is a low order polynomial of
the input and the latent dimensions.
| Hanie Sedghi, Majid Janzamin, Anima Anandkumar | null | 1412.3046 | null | null |
Hierarchical Mixture-of-Experts Model for Large-Scale Gaussian Process
Regression | stat.ML cs.AI cs.LG stat.CO | We propose a practical and scalable Gaussian process model for large-scale
nonlinear probabilistic regression. Our mixture-of-experts model is
conceptually simple and hierarchically recombines computations for an overall
approximation of a full Gaussian process. Closed-form and distributed
computations allow for efficient and massive parallelisation while keeping the
memory consumption small. Given sufficient computing resources, our model can
handle arbitrarily large data sets, without explicit sparse approximations. We
provide strong experimental evidence that our model can be applied to large
data sets of sizes far beyond millions. Hence, our model has the potential to
lay the foundation for general large-scale Gaussian process research.
| Jun Wei Ng and Marc Peter Deisenroth | null | 1412.3078 | null | null |
Semi-Supervised Learning with Heterophily | cs.LG cs.DB | We derive a family of linear inference algorithms that generalize existing
graph-based label propagation algorithms by allowing them to propagate
generalized assumptions about "attraction" or "compatibility" between classes
of neighboring nodes (in particular those that involve heterophily between
nodes where "opposites attract"). We thus call this formulation Semi-Supervised
Learning with Heterophily (SSLH) and show how it generalizes and improves upon
a recently proposed approach called Linearized Belief Propagation (LinBP).
Importantly, our framework allows us to reduce the problem of estimating the
relative compatibility between nodes from partially labeled graph to a simple
optimization problem. The result is a very fast algorithm that -- despite its
simplicity -- is surprisingly effective: we can classify unlabeled nodes within
the same graph in the same time as LinBP but with a superior accuracy and
despite our algorithm not knowing the compatibilities.
| Wolfgang Gatterbauer | null | 1412.3100 | null | null |
Multimodal Transfer Deep Learning with Applications in Audio-Visual
Recognition | cs.NE cs.LG | We propose a transfer deep learning (TDL) framework that can transfer the
knowledge obtained from a single-modal neural network to a network with a
different modality. Specifically, we show that we can leverage speech data to
fine-tune the network trained for video recognition, given an initial set of
audio-video parallel dataset within the same semantics. Our approach first
learns the analogy-preserving embeddings between the abstract representations
learned from intermediate layers of each network, allowing for semantics-level
transfer between the source and target modalities. We then apply our neural
network operation that fine-tunes the target network with the additional
knowledge transferred from the source network, while keeping the topology of
the target network unchanged. While we present an audio-visual recognition task
as an application of our approach, our framework is flexible and thus can work
with any multimodal dataset, or with any already-existing deep networks that
share the common underlying semantics. In this work in progress report, we aim
to provide comprehensive results of different configurations of the proposed
approach on two widely used audio-visual datasets, and we discuss potential
applications of the proposed approach.
| Seungwhan Moon and Suyoun Kim and Haohan Wang | null | 1412.3121 | null | null |
Generalised Entropy MDPs and Minimax Regret | cs.LG stat.ML | Bayesian methods suffer from the problem of how to specify prior beliefs. One
interesting idea is to consider worst-case priors. This requires solving a
stochastic zero-sum game. In this paper, we extend well-known results from
bandit theory in order to discover minimax-Bayes policies and discuss when they
are practical.
| Emmanouil G. Androulakis, Christos Dimitrakakis | null | 1412.3276 | null | null |
Web image annotation by diffusion maps manifold learning algorithm | cs.CV cs.IR cs.LG | Automatic image annotation is one of the most challenging problems in machine
vision areas. The goal of this task is to predict number of keywords
automatically for images captured in real data. Many methods are based on
visual features in order to calculate similarities between image samples. But
the computation cost of these approaches is very high. These methods require
many training samples to be stored in memory. To lessen this burden, a number
of techniques have been developed to reduce the number of features in a
dataset. Manifold learning is a popular approach to nonlinear dimensionality
reduction. In this paper, we investigate Diffusion maps manifold learning
method for web image auto-annotation task. Diffusion maps manifold learning
method is used to reduce the dimension of some visual features. Extensive
experiments and analysis on NUS-WIDE-LITE web image dataset with different
visual features show how this manifold learning dimensionality reduction method
can be applied effectively to image annotation.
| Neda Pourali | 10.5121/ijfcst.2014.4606 | 1412.3352 | null | null |
Sequential Labeling with online Deep Learning | cs.LG | Deep learning has attracted great attention recently and yielded the state of
the art performance in dimension reduction and classification problems.
However, it cannot effectively handle the structured output prediction, e.g.
sequential labeling. In this paper, we propose a deep learning structure, which
can learn discriminative features for sequential labeling problems. More
specifically, we add the inter-relationship between labels in our deep learning
structure, in order to incorporate the context information from the sequential
data. Thus, our model is more powerful than linear Conditional Random Fields
(CRFs) because the objective function learns latent non-linear features so that
target labeling can be better predicted. We pretrain the deep structure with
stacked restricted Boltzmann machines (RBMs) for feature learning and optimize
our objective function with online learning algorithm, a mixture of perceptron
training and stochastic gradient descent. We test our model on different
challenge tasks, and show that our model outperforms significantly over the
completive baselines.
| Gang Chen, Ran Xu and Sargur Srihari | null | 1412.3397 | null | null |
Teaching Deep Convolutional Neural Networks to Play Go | cs.AI cs.LG cs.NE | Mastering the game of Go has remained a long standing challenge to the field
of AI. Modern computer Go systems rely on processing millions of possible
future positions to play well, but intuitively a stronger and more 'humanlike'
way to play the game would be to rely on pattern recognition abilities rather
then brute force computation. Following this sentiment, we train deep
convolutional neural networks to play Go by training them to predict the moves
made by expert Go players. To solve this problem we introduce a number of novel
techniques, including a method of tying weights in the network to 'hard code'
symmetries that are expect to exist in the target function, and demonstrate in
an ablation study they considerably improve performance. Our final networks are
able to achieve move prediction accuracies of 41.1% and 44.4% on two different
Go datasets, surpassing previous state of the art on this task by significant
margins. Additionally, while previous move prediction programs have not yielded
strong Go playing programs, we show that the networks trained in this work
acquired high levels of skill. Our convolutional neural networks can
consistently defeat the well known Go program GNU Go, indicating it is state of
the art among programs that do not use Monte Carlo Tree Search. It is also able
to win some games against state of the art Go playing program Fuego while using
a fraction of the play time. This success at playing Go indicates high level
principles of the game were learned.
| Christopher Clark and Amos Storkey | null | 1412.3409 | null | null |
GP-select: Accelerating EM using adaptive subspace preselection | stat.ML cs.LG | We propose a nonparametric procedure to achieve fast inference in generative
graphical models when the number of latent states is very large. The approach
is based on iterative latent variable preselection, where we alternate between
learning a 'selection function' to reveal the relevant latent variables, and
use this to obtain a compact approximation of the posterior distribution for
EM; this can make inference possible where the number of possible latent states
is e.g. exponential in the number of latent variables, whereas an exact
approach would be computationally unfeasible. We learn the selection function
entirely from the observed data and current EM state via Gaussian process
regression. This is by contrast with earlier approaches, where selection
functions were manually-designed for each problem setting. We show that our
approach performs as well as these bespoke selection functions on a wide
variety of inference problems: in particular, for the challenging case of a
hierarchical model for object localization with occlusion, we achieve results
that match a customized state-of-the-art selection method, at a far lower
computational cost.
| Jacquelyn A. Shelton, Jan Gasthaus, Zhenwen Dai, Joerg Luecke, Arthur
Gretton | 10.1162/neco_a_00982 | 1412.3411 | null | null |
Quantum Deep Learning | quant-ph cs.LG cs.NE | In recent years, deep learning has had a profound impact on machine learning
and artificial intelligence. At the same time, algorithms for quantum computers
have been shown to efficiently solve some problems that are intractable on
conventional, classical computers. We show that quantum computing not only
reduces the time required to train a deep restricted Boltzmann machine, but
also provides a richer and more comprehensive framework for deep learning than
classical computing and leads to significant improvements in the optimization
of the underlying objective function. Our quantum methods also permit efficient
training of full Boltzmann machines and multi-layer, fully connected models and
do not have well known classical counterparts.
| Nathan Wiebe, Ashish Kapoor, Krysta M. Svore | null | 1412.3489 | null | null |
Empirical Evaluation of Gated Recurrent Neural Networks on Sequence
Modeling | cs.NE cs.LG | In this paper we compare different types of recurrent units in recurrent
neural networks (RNNs). Especially, we focus on more sophisticated units that
implement a gating mechanism, such as a long short-term memory (LSTM) unit and
a recently proposed gated recurrent unit (GRU). We evaluate these recurrent
units on the tasks of polyphonic music modeling and speech signal modeling. Our
experiments revealed that these advanced recurrent units are indeed better than
more traditional recurrent units such as tanh units. Also, we found GRU to be
comparable to LSTM.
| Junyoung Chung and Caglar Gulcehre and KyungHyun Cho and Yoshua Bengio | null | 1412.3555 | null | null |
Simulating a perceptron on a quantum computer | quant-ph cs.LG cs.NE | Perceptrons are the basic computational unit of artificial neural networks,
as they model the activation mechanism of an output neuron due to incoming
signals from its neighbours. As linear classifiers, they play an important role
in the foundations of machine learning. In the context of the emerging field of
quantum machine learning, several attempts have been made to develop a
corresponding unit using quantum information theory. Based on the quantum phase
estimation algorithm, this paper introduces a quantum perceptron model
imitating the step-activation function of a classical perceptron. This scheme
requires resources in $\mathcal{O}(n)$ (where $n$ is the size of the input) and
promises efficient applications for more complex structures such as trainable
quantum neural networks.
| Maria Schuld, Ilya Sinayskiy and Francesco Petruccione | 10.1016/j.physleta.2014.11.061 | 1412.3635 | null | null |
Object Recognition Using Deep Neural Networks: A Survey | cs.CV cs.LG cs.NE | Recognition of objects using Deep Neural Networks is an active area of
research and many breakthroughs have been made in the last few years. The paper
attempts to indicate how far this field has progressed. The paper briefly
describes the history of research in Neural Networks and describe several of
the recent advances in this field. The performances of recently developed
Neural Network Algorithm over benchmark datasets have been tabulated. Finally,
some the applications of this field have been provided.
| Soren Goyal, Paul Benjamin | null | 1412.3684 | null | null |
A Topic Modeling Approach to Ranking | cs.LG stat.ML | We propose a topic modeling approach to the prediction of preferences in
pairwise comparisons. We develop a new generative model for pairwise
comparisons that accounts for multiple shared latent rankings that are
prevalent in a population of users. This new model also captures inconsistent
user behavior in a natural way. We show how the estimation of latent rankings
in the new generative model can be formally reduced to the estimation of topics
in a statistically equivalent topic modeling problem. We leverage recent
advances in the topic modeling literature to develop an algorithm that can
learn shared latent rankings with provable consistency as well as sample and
computational complexity guarantees. We demonstrate that the new approach is
empirically competitive with the current state-of-the-art approaches in
predicting preferences on some semi-synthetic and real world datasets.
| Weicong Ding, Prakash Ishwar, Venkatesh Saligrama | null | 1412.3705 | null | null |
Compact Compositional Models | cs.CV cs.LG stat.ML | Learning compact and interpretable representations is a very natural task,
which has not been solved satisfactorily even for simple binary datasets. In
this paper, we review various ways of composing experts for binary data and
argue that competitive forms of interaction are best suited to learn
low-dimensional representations. We propose a new composition rule that
discourages experts from focusing on similar structures and that penalizes
opposing votes strongly so that abstaining from voting becomes more attractive.
We also introduce a novel sequential initialization procedure, which is based
on a process of oversimplification and correction. Experiments show that with
our approach very intuitive models can be learned.
| Marc Goessling and Yali Amit | null | 1412.3708 | null | null |
Feature Weight Tuning for Recursive Neural Networks | cs.NE cs.AI cs.CL cs.LG | This paper addresses how a recursive neural network model can automatically
leave out useless information and emphasize important evidence, in other words,
to perform "weight tuning" for higher-level representation acquisition. We
propose two models, Weighted Neural Network (WNN) and Binary-Expectation Neural
Network (BENN), which automatically control how much one specific unit
contributes to the higher-level representation. The proposed model can be
viewed as incorporating a more powerful compositional function for embedding
acquisition in recursive neural networks. Experimental results demonstrate the
significant improvement over standard neural models.
| Jiwei Li | null | 1412.3714 | null | null |
Distinguishing cause from effect using observational data: methods and
benchmarks | cs.LG cs.AI stat.ML stat.OT | The discovery of causal relationships from purely observational data is a
fundamental problem in science. The most elementary form of such a causal
discovery problem is to decide whether X causes Y or, alternatively, Y causes
X, given joint observations of two variables X, Y. An example is to decide
whether altitude causes temperature, or vice versa, given only joint
measurements of both variables. Even under the simplifying assumptions of no
confounding, no feedback loops, and no selection bias, such bivariate causal
discovery problems are challenging. Nevertheless, several approaches for
addressing those problems have been proposed in recent years. We review two
families of such methods: Additive Noise Methods (ANM) and Information
Geometric Causal Inference (IGCI). We present the benchmark CauseEffectPairs
that consists of data for 100 different cause-effect pairs selected from 37
datasets from various domains (e.g., meteorology, biology, medicine,
engineering, economy, etc.) and motivate our decisions regarding the "ground
truth" causal directions of all pairs. We evaluate the performance of several
bivariate causal discovery methods on these real-world benchmark data and in
addition on artificially simulated data. Our empirical results on real-world
data indicate that certain methods are indeed able to distinguish cause from
effect using only purely observational data, although more benchmark data would
be needed to obtain statistically significant conclusions. One of the best
performing methods overall is the additive-noise method originally proposed by
Hoyer et al. (2009), which obtains an accuracy of 63+-10 % and an AUC of
0.74+-0.05 on the real-world benchmark. As the main theoretical contribution of
this work we prove the consistency of that method.
| Joris M. Mooij, Jonas Peters, Dominik Janzing, Jakob Zscheischler,
Bernhard Sch\"olkopf | null | 1412.3773 | null | null |
Machine Learning for Neuroimaging with Scikit-Learn | cs.LG cs.CV stat.ML | Statistical machine learning methods are increasingly used for neuroimaging
data analysis. Their main virtue is their ability to model high-dimensional
datasets, e.g. multivariate analysis of activation images or resting-state time
series. Supervised learning is typically used in decoding or encoding settings
to relate brain images to behavioral or clinical observations, while
unsupervised learning can uncover hidden structures in sets of images (e.g.
resting state functional MRI) or find sub-populations in large cohorts. By
considering different functional neuroimaging applications, we illustrate how
scikit-learn, a Python machine learning library, can be used to perform some
key analysis steps. Scikit-learn contains a very large set of statistical
learning algorithms, both supervised and unsupervised, and its application to
neuroimaging data provides a versatile tool to study the brain.
| Alexandre Abraham (NEUROSPIN, INRIA Saclay - Ile de France), Fabian
Pedregosa (INRIA Saclay - Ile de France), Michael Eickenberg (LNAO, INRIA
Saclay - Ile de France), Philippe Gervais (NEUROSPIN, INRIA Saclay - Ile de
France, LNAO), Andreas Muller, Jean Kossaifi, Alexandre Gramfort (NEUROSPIN,
LTCI), Bertrand Thirion (NEUROSPIN, INRIA Saclay - Ile de France), G\"ael
Varoquaux (NEUROSPIN, INRIA Saclay - Ile de France, LNAO) | null | 1412.3919 | null | null |
Size sensitive packing number for Hamming cube and its consequences | cs.DM cs.CG cs.LG math.CO | We prove a size-sensitive version of Haussler's Packing
lemma~\cite{Haussler92spherepacking} for set-systems with bounded primal
shatter dimension, which have an additional {\em size-sensitive property}. This
answers a question asked by Ezra~\cite{Ezra-sizesendisc-soda-14}. We also
partially address another point raised by Ezra regarding overcounting of sets
in her chaining procedure. As a consequence of these improvements, we get an
improvement on the size-sensitive discrepancy bounds for set systems with the
above property. Improved bounds on the discrepancy for these special set
systems also imply an improvement in the sizes of {\em relative $(\varepsilon,
\delta)$-approximations} and $(\nu, \alpha)$-samples.
| Kunal Dutta, Arijit Ghosh | null | 1412.3922 | null | null |
Sparsity and adaptivity for the blind separation of partially correlated
sources | stat.AP cs.LG stat.ML | Blind source separation (BSS) is a very popular technique to analyze
multichannel data. In this context, the data are modeled as the linear
combination of sources to be retrieved. For that purpose, standard BSS methods
all rely on some discrimination principle, whether it is statistical
independence or morphological diversity, to distinguish between the sources.
However, dealing with real-world data reveals that such assumptions are rarely
valid in practice: the signals of interest are more likely partially
correlated, which generally hampers the performances of standard BSS methods.
In this article, we introduce a novel sparsity-enforcing BSS method coined
Adaptive Morphological Component Analysis (AMCA), which is designed to retrieve
sparse and partially correlated sources. More precisely, it makes profit of an
adaptive re-weighting scheme to favor/penalize samples based on their level of
correlation. Extensive numerical experiments have been carried out which show
that the proposed method is robust to the partial correlation of sources while
standard BSS techniques fail. The AMCA algorithm is evaluated in the field of
astrophysics for the separation of physical components from microwave data.
| Jerome Bobin and Jeremy Rapin and Anthony Larue and Jean-Luc Starck | 10.1109/TSP.2015.2391071 | 1412.4005 | null | null |
Dynamic Screening: Accelerating First-Order Algorithms for the Lasso and
Group-Lasso | stat.ML cs.LG | Recent computational strategies based on screening tests have been proposed
to accelerate algorithms addressing penalized sparse regression problems such
as the Lasso. Such approaches build upon the idea that it is worth dedicating
some small computational effort to locate inactive atoms and remove them from
the dictionary in a preprocessing stage so that the regression algorithm
working with a smaller dictionary will then converge faster to the solution of
the initial problem. We believe that there is an even more efficient way to
screen the dictionary and obtain a greater acceleration: inside each iteration
of the regression algorithm, one may take advantage of the algorithm
computations to obtain a new screening test for free with increasing screening
effects along the iterations. The dictionary is henceforth dynamically screened
instead of being screened statically, once and for all, before the first
iteration. We formalize this dynamic screening principle in a general
algorithmic scheme and apply it by embedding inside a number of first-order
algorithms adapted existing screening tests to solve the Lasso or new screening
tests to solve the Group-Lasso. Computational gains are assessed in a large set
of experiments on synthetic data as well as real-world sounds and images. They
show both the screening efficiency and the gain in terms running times.
| Antoine Bonnefoy, Valentin Emiya, Liva Ralaivola, R\'emi Gribonval
(INRIA - IRISA) | 10.1109/TSP.2015.2447503 | 1412.4080 | null | null |
The Statistics of Streaming Sparse Regression | math.ST cs.LG stat.ML stat.TH | We present a sparse analogue to stochastic gradient descent that is
guaranteed to perform well under similar conditions to the lasso. In the linear
regression setup with irrepresentable noise features, our algorithm recovers
the support set of the optimal parameter vector with high probability, and
achieves a statistically quasi-optimal rate of convergence of Op(k log(d)/T),
where k is the sparsity of the solution, d is the number of features, and T is
the number of training examples. Meanwhile, our algorithm does not require any
more computational resources than stochastic gradient descent. In our
experiments, we find that our method substantially out-performs existing
streaming algorithms on both real and simulated data.
| Jacob Steinhardt, Stefan Wager, and Percy Liang | null | 1412.4182 | null | null |
An Evaluation of Support Vector Machines as a Pattern Recognition Tool | cs.LG | The purpose of this report is in examining the generalization performance of
Support Vector Machines (SVM) as a tool for pattern recognition and object
classification. The work is motivated by the growing popularity of the method
that is claimed to guarantee a good generalization performance for the task in
hand. The method is implemented in MATLAB. SVMs based on various kernels are
tested for classifying data from various domains.
| Eugene Borovikov | null | 1412.4186 | null | null |
Unsupervised Domain Adaptation with Feature Embeddings | cs.CL cs.LG | Representation learning is the dominant technique for unsupervised domain
adaptation, but existing approaches often require the specification of "pivot
features" that generalize across domains, which are selected by task-specific
heuristics. We show that a novel but simple feature embedding approach provides
better performance, by exploiting the feature template structure common in NLP
problems.
| Yi Yang and Jacob Eisenstein | null | 1412.4385 | null | null |
Domain-Adversarial Neural Networks | stat.ML cs.LG cs.NE | We introduce a new representation learning algorithm suited to the context of
domain adaptation, in which data at training and test time come from similar
but different distributions. Our algorithm is directly inspired by theory on
domain adaptation suggesting that, for effective domain transfer to be
achieved, predictions must be made based on a data representation that cannot
discriminate between the training (source) and test (target) domains. We
propose a training objective that implements this idea in the context of a
neural network, whose hidden layer is trained to be predictive of the
classification task, but uninformative as to the domain of the input. Our
experiments on a sentiment analysis classification benchmark, where the target
domain data available at training time is unlabeled, show that our neural
network for domain adaption algorithm has better performance than either a
standard neural network or an SVM, even if trained on input features extracted
with the state-of-the-art marginalized stacked denoising autoencoders of Chen
et al. (2012).
| Hana Ajakan, Pascal Germain, Hugo Larochelle, Fran\c{c}ois Laviolette,
Mario Marchand | null | 1412.4446 | null | null |
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