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Effective Data Mining Technique for Classification Cancers via Mutations
in Gene using Neural Network | cs.LG | The prediction plays the important role in detecting efficient protection and
therapy of cancer. The prediction of mutations in gene needs a diagnostic and
classification, which is based on the whole database (big dataset), to reach
sufficient accuracy results. Since the tumor suppressor P53 is approximately
about fifty percentage of all human tumors because mutations that occur in the
TP53 gene into the cells. So, this paper is applied on tumor p53, where the
problem is there are several primitive databases (excel database) contain
datasets of TP53 gene with its tumor protein p53, these databases are rich
datasets that cover all mutations and cause diseases (cancers). But these Data
Bases cannot reach to predict and diagnosis cancers, i.e. the big datasets have
not efficient Data Mining method, which can predict, diagnosis the mutation,
and classify the cancer of patient. The goal of this paper to reach a Data
Mining technique, that employs neural network, which bases on the big datasets.
Also, offers friendly predictions, flexible, and effective classified cancers,
in order to overcome the previous techniques drawbacks. This proposed technique
is done by using two approaches, first, bioinformatics techniques by using
BLAST, CLUSTALW, etc, in order to know if there are malignant mutations or not.
The second, data mining by using neural network; it is selected (12) out of
(53) TP53 gene database fields. To clarify, one of these 12 fields (gene
location field) did not exists in TP53 gene database; therefore, it is added to
the database of TP53 gene in training and testing back propagation algorithm,
in order to classify specifically the types of cancers. Feed Forward Back
Propagation supports this Data Mining method with data training rate (1) and
Mean Square Error (MSE) (0.00000000000001). This effective technique allows in
a quick, accurate and easy way to classify the type of cancer.
| Ayad Ghany Ismaeel, Dina Yousif Mikhail | 10.14569/IJACSA.2016.070710 | 1608.02888 | null | null |
Syntactically Informed Text Compression with Recurrent Neural Networks | cs.LG cs.CL cs.IT math.IT | We present a self-contained system for constructing natural language models
for use in text compression. Our system improves upon previous neural network
based models by utilizing recent advances in syntactic parsing -- Google's
SyntaxNet -- to augment character-level recurrent neural networks. RNNs have
proven exceptional in modeling sequence data such as text, as their
architecture allows for modeling of long-term contextual information.
| David Cox | null | 1608.02893 | null | null |
Neuroevolution-Based Inverse Reinforcement Learning | cs.NE cs.AI cs.LG | The problem of Learning from Demonstration is targeted at learning to perform
tasks based on observed examples. One approach to Learning from Demonstration
is Inverse Reinforcement Learning, in which actions are observed to infer
rewards. This work combines a feature based state evaluation approach to
Inverse Reinforcement Learning with neuroevolution, a paradigm for modifying
neural networks based on their performance on a given task. Neural networks are
used to learn from a demonstrated expert policy and are evolved to generate a
policy similar to the demonstration. The algorithm is discussed and evaluated
against competitive feature-based Inverse Reinforcement Learning approaches. At
the cost of execution time, neural networks allow for non-linear combinations
of features in state evaluations. These valuations may correspond to state
value or state reward. This results in better correspondence to observed
examples as opposed to using linear combinations. This work also extends
existing work on Bayesian Non-Parametric Feature Construction for Inverse
Reinforcement Learning by using non-linear combinations of intermediate data to
improve performance. The algorithm is observed to be specifically suitable for
a linearly solvable non-deterministic Markov Decision Processes in which
multiple rewards are sparsely scattered in state space. A conclusive
performance hierarchy between evaluated algorithms is presented.
| Karan K. Budhraja and Tim Oates | null | 1608.02971 | null | null |
Towards cross-lingual distributed representations without parallel text
trained with adversarial autoencoders | cs.CL cs.LG cs.NE | Current approaches to learning vector representations of text that are
compatible between different languages usually require some amount of parallel
text, aligned at word, sentence or at least document level. We hypothesize
however, that different natural languages share enough semantic structure that
it should be possible, in principle, to learn compatible vector representations
just by analyzing the monolingual distribution of words.
In order to evaluate this hypothesis, we propose a scheme to map word vectors
trained on a source language to vectors semantically compatible with word
vectors trained on a target language using an adversarial autoencoder.
We present preliminary qualitative results and discuss possible future
developments of this technique, such as applications to cross-lingual sentence
representations.
| Antonio Valerio Miceli Barone | null | 1608.02996 | null | null |
Mining Fashion Outfit Composition Using An End-to-End Deep Learning
Approach on Set Data | cs.MM cs.LG | Composing fashion outfits involves deep understanding of fashion standards
while incorporating creativity for choosing multiple fashion items (e.g.,
Jewelry, Bag, Pants, Dress). In fashion websites, popular or high-quality
fashion outfits are usually designed by fashion experts and followed by large
audiences. In this paper, we propose a machine learning system to compose
fashion outfits automatically. The core of the proposed automatic composition
system is to score fashion outfit candidates based on the appearances and
meta-data. We propose to leverage outfit popularity on fashion oriented
websites to supervise the scoring component. The scoring component is a
multi-modal multi-instance deep learning system that evaluates instance
aesthetics and set compatibility simultaneously. In order to train and evaluate
the proposed composition system, we have collected a large scale fashion outfit
dataset with 195K outfits and 368K fashion items from Polyvore. Although the
fashion outfit scoring and composition is rather challenging, we have achieved
an AUC of 85% for the scoring component, and an accuracy of 77% for a
constrained composition task.
| Yuncheng Li, LiangLiang Cao, Jiang Zhu, Jiebo Luo | 10.1109/TMM.2017.2690144 | 1608.03016 | null | null |
Stochastic Rank-1 Bandits | cs.LG stat.ML | We propose stochastic rank-$1$ bandits, a class of online learning problems
where at each step a learning agent chooses a pair of row and column arms, and
receives the product of their values as a reward. The main challenge of the
problem is that the individual values of the row and column are unobserved. We
assume that these values are stochastic and drawn independently. We propose a
computationally-efficient algorithm for solving our problem, which we call
Rank1Elim. We derive a $O((K + L) (1 / \Delta) \log n)$ upper bound on its
$n$-step regret, where $K$ is the number of rows, $L$ is the number of columns,
and $\Delta$ is the minimum of the row and column gaps; under the assumption
that the mean row and column rewards are bounded away from zero. To the best of
our knowledge, we present the first bandit algorithm that finds the maximum
entry of a rank-$1$ matrix whose regret is linear in $K + L$, $1 / \Delta$, and
$\log n$. We also derive a nearly matching lower bound. Finally, we evaluate
Rank1Elim empirically on multiple problems. We observe that it leverages the
structure of our problems and can learn near-optimal solutions even if our
modeling assumptions are mildly violated.
| Sumeet Katariya, Branislav Kveton, Csaba Szepesvari, Claire Vernade,
and Zheng Wen | null | 1608.03023 | null | null |
Estimation from Indirect Supervision with Linear Moments | stat.ML cs.LG | In structured prediction problems where we have indirect supervision of the
output, maximum marginal likelihood faces two computational obstacles:
non-convexity of the objective and intractability of even a single gradient
computation. In this paper, we bypass both obstacles for a class of what we
call linear indirectly-supervised problems. Our approach is simple: we solve a
linear system to estimate sufficient statistics of the model, which we then use
to estimate parameters via convex optimization. We analyze the statistical
properties of our approach and show empirically that it is effective in two
settings: learning with local privacy constraints and learning from low-cost
count-based annotations.
| Aditi Raghunathan, Roy Frostig, John Duchi, Percy Liang | null | 1608.031 | null | null |
Combination of LMS Adaptive Filters with Coefficients Feedback | math.OC cs.IT cs.LG math.IT | Parallel combinations of adaptive filters have been effectively used to
improve the performance of adaptive algorithms and address well-known
trade-offs, such as convergence rate vs. steady-state error. Nevertheless,
typical combinations suffer from a convergence stagnation issue due to the fact
that the component filters run independently. Solutions to this issue usually
involve conditional transfers of coefficients between filters, which although
effective, are hard to generalize to combinations with more filters or when
there is no clearly faster adaptive filter. In this work, a more natural
solution is proposed by cyclically feeding back the combined coefficient vector
to all component filters. Besides coping with convergence stagnation, this new
topology improves tracking and supervisor stability, and bridges an important
conceptual gap between combinations of adaptive filters and variable step size
schemes. We analyze the steady-state, tracking, and transient performance of
this topology for LMS component filters and supervisors with generic activation
functions. Numerical examples are used to illustrate how coefficients feedback
can improve the performance of parallel combinations at a small computational
overhead.
| Luiz F. O. Chamon and Cassio G. Lopes | null | 1608.03248 | null | null |
Deep vs. shallow networks : An approximation theory perspective | cs.LG math.FA | The paper briefy reviews several recent results on hierarchical architectures
for learning from examples, that may formally explain the conditions under
which Deep Convolutional Neural Networks perform much better in function
approximation problems than shallow, one-hidden layer architectures. The paper
announces new results for a non-smooth activation function - the ReLU function
- used in present-day neural networks, as well as for the Gaussian networks. We
propose a new definition of relative dimension to encapsulate different notions
of sparsity of a function class that can possibly be exploited by deep networks
but not by shallow ones to drastically reduce the complexity required for
approximation and learning.
| Hrushikesh Mhaskar and Tomaso Poggio | null | 1608.03287 | null | null |
Temporal Learning and Sequence Modeling for a Job Recommender System | cs.LG stat.ML | We present our solution to the job recommendation task for RecSys Challenge
2016. The main contribution of our work is to combine temporal learning with
sequence modeling to capture complex user-item activity patterns to improve job
recommendations. First, we propose a time-based ranking model applied to
historical observations and a hybrid matrix factorization over time re-weighted
interactions. Second, we exploit sequence properties in user-items activities
and develop a RNN-based recommendation model. Our solution achieved 5$^{th}$
place in the challenge among more than 100 participants. Notably, the strong
performance of our RNN approach shows a promising new direction in employing
sequence modeling for recommendation systems.
| Kuan Liu, Xing Shi, Anoop Kumar, Linhong Zhu, Prem Natarajan | 10.1145/2987538.2987540 | 1608.03333 | null | null |
Distributed learning with regularized least squares | cs.LG stat.ML | We study distributed learning with the least squares regularization scheme in
a reproducing kernel Hilbert space (RKHS). By a divide-and-conquer approach,
the algorithm partitions a data set into disjoint data subsets, applies the
least squares regularization scheme to each data subset to produce an output
function, and then takes an average of the individual output functions as a
final global estimator or predictor. We show with error bounds in expectation
in both the $L^2$-metric and RKHS-metric that the global output function of
this distributed learning is a good approximation to the algorithm processing
the whole data in one single machine. Our error bounds are sharp and stated in
a general setting without any eigenfunction assumption. The analysis is
achieved by a novel second order decomposition of operator differences in our
integral operator approach. Even for the classical least squares regularization
scheme in the RKHS associated with a general kernel, we give the best learning
rate in the literature.
| Shao-Bo Lin, Xin Guo, Ding-Xuan Zhou | null | 1608.03339 | null | null |
Multi-source Hierarchical Prediction Consolidation | cs.DB cs.LG | In big data applications such as healthcare data mining, due to privacy
concerns, it is necessary to collect predictions from multiple information
sources for the same instance, with raw features being discarded or withheld
when aggregating multiple predictions. Besides, crowd-sourced labels need to be
aggregated to estimate the ground truth of the data. Because of the imperfect
predictive models or human crowdsourcing workers, noisy and conflicting
information is ubiquitous and inevitable. Although state-of-the-art aggregation
methods have been proposed to handle label spaces with flat structures, as the
label space is becoming more and more complicated, aggregation under a label
hierarchical structure becomes necessary but has been largely ignored. These
label hierarchies can be quite informative as they are usually created by
domain experts to make sense of highly complex label correlations for many
real-world cases like protein functionality interactions or disease
relationships.
We propose a novel multi-source hierarchical prediction consolidation method
to effectively exploits the complicated hierarchical label structures to
resolve the noisy and conflicting information that inherently originates from
multiple imperfect sources. We formulate the problem as an optimization problem
with a closed-form solution. The proposed method captures the smoothness
overall information sources as well as penalizing any consolidation result that
violates the constraints derived from the label hierarchy. The hierarchical
instance similarity, as well as the consolidation result, are inferred in a
totally unsupervised, iterative fashion. Experimental results on both synthetic
and real-world datasets show the effectiveness of the proposed method over
existing alternatives.
| Chenwei Zhang, Sihong Xie, Yaliang Li, Jing Gao, Wei Fan, Philip S. Yu | null | 1608.03344 | null | null |
Semi-Supervised Prediction of Gene Regulatory Networks Using Machine
Learning Algorithms | cs.LG q-bio.QM stat.ML | Use of computational methods to predict gene regulatory networks (GRNs) from
gene expression data is a challenging task. Many studies have been conducted
using unsupervised methods to fulfill the task; however, such methods usually
yield low prediction accuracies due to the lack of training data. In this
article, we propose semi-supervised methods for GRN prediction by utilizing two
machine learning algorithms, namely support vector machines (SVM) and random
forests (RF). The semi-supervised methods make use of unlabeled data for
training. We investigate inductive and transductive learning approaches, both
of which adopt an iterative procedure to obtain reliable negative training data
from the unlabeled data. We then apply our semi-supervised methods to gene
expression data of Escherichia coli and Saccharomyces cerevisiae, and evaluate
the performance of our methods using the expression data. Our analysis
indicated that the transductive learning approach outperformed the inductive
learning approach for both organisms. However, there was no conclusive
difference identified in the performance of SVM and RF. Experimental results
also showed that the proposed semi-supervised methods performed better than
existing supervised methods for both organisms.
| Nihir Patel and Jason T. L. Wang | null | 1608.0353 | null | null |
Sequence Graph Transform (SGT): A Feature Embedding Function for
Sequence Data Mining | stat.ML cs.LG | Sequence feature embedding is a challenging task due to the unstructuredness
of sequence, i.e., arbitrary strings of arbitrary length. Existing methods are
efficient in extracting short-term dependencies but typically suffer from
computation issues for the long-term. Sequence Graph Transform (SGT), a feature
embedding function, that can extract a varying amount of short- to long-term
dependencies without increasing the computation is proposed. SGT's properties
are analytically proved for interpretation under normal and uniform
distribution assumptions. SGT features yield significantly superior results in
sequence clustering and classification with higher accuracy and lower
computation as compared to the existing methods, including the state-of-the-art
sequence/string Kernels and LSTM.
| Chitta Ranjan, Samaneh Ebrahimi and Kamran Paynabar | null | 1608.03533 | null | null |
On Context-Dependent Clustering of Bandits | cs.LG cs.AI cs.IR stat.ML | We investigate a novel cluster-of-bandit algorithm CAB for collaborative
recommendation tasks that implements the underlying feedback sharing mechanism
by estimating the neighborhood of users in a context-dependent manner. CAB
makes sharp departures from the state of the art by incorporating collaborative
effects into inference as well as learning processes in a manner that
seamlessly interleaving explore-exploit tradeoffs and collaborative steps. We
prove regret bounds under various assumptions on the data, which exhibit a
crisp dependence on the expected number of clusters over the users, a natural
measure of the statistical difficulty of the learning task. Experiments on
production and real-world datasets show that CAB offers significantly increased
prediction performance against a representative pool of state-of-the-art
methods.
| Claudio Gentile, Shuai Li, Purushottam Kar, Alexandros Karatzoglou,
Evans Etrue, Giovanni Zappella | null | 1608.03544 | null | null |
Warm Starting Bayesian Optimization | stat.ML cs.LG stat.AP | We develop a framework for warm-starting Bayesian optimization, that reduces
the solution time required to solve an optimization problem that is one in a
sequence of related problems. This is useful when optimizing the output of a
stochastic simulator that fails to provide derivative information, for which
Bayesian optimization methods are well-suited. Solving sequences of related
optimization problems arises when making several business decisions using one
optimization model and input data collected over different time periods or
markets. While many gradient-based methods can be warm started by initiating
optimization at the solution to the previous problem, this warm start approach
does not apply to Bayesian optimization methods, which carry a full metamodel
of the objective function from iteration to iteration. Our approach builds a
joint statistical model of the entire collection of related objective
functions, and uses a value of information calculation to recommend points to
evaluate.
| Matthias Poloczek, Jialei Wang, and Peter I. Frazier | null | 1608.03585 | null | null |
Faster Training of Very Deep Networks Via p-Norm Gates | stat.ML cs.LG cs.NE | A major contributing factor to the recent advances in deep neural networks is
structural units that let sensory information and gradients to propagate
easily. Gating is one such structure that acts as a flow control. Gates are
employed in many recent state-of-the-art recurrent models such as LSTM and GRU,
and feedforward models such as Residual Nets and Highway Networks. This enables
learning in very deep networks with hundred layers and helps achieve
record-breaking results in vision (e.g., ImageNet with Residual Nets) and NLP
(e.g., machine translation with GRU). However, there is limited work in
analysing the role of gating in the learning process. In this paper, we propose
a flexible $p$-norm gating scheme, which allows user-controllable flow and as a
consequence, improve the learning speed. This scheme subsumes other existing
gating schemes, including those in GRU, Highway Networks and Residual Nets as
special cases. Experiments on large sequence and vector datasets demonstrate
that the proposed gating scheme helps improve the learning speed significantly
without extra overhead.
| Trang Pham, Truyen Tran, Dinh Phung, Svetha Venkatesh | null | 1608.03639 | null | null |
Chi-squared Amplification: Identifying Hidden Hubs | cs.LG cs.DS stat.ML | We consider the following general hidden hubs model: an $n \times n$ random
matrix $A$ with a subset $S$ of $k$ special rows (hubs): entries in rows
outside $S$ are generated from the probability distribution $p_0 \sim
N(0,\sigma_0^2)$; for each row in $S$, some $k$ of its entries are generated
from $p_1 \sim N(0,\sigma_1^2)$, $\sigma_1>\sigma_0$, and the rest of the
entries from $p_0$. The problem is to identify the high-degree hubs
efficiently. This model includes and significantly generalizes the planted
Gaussian Submatrix Model, where the special entries are all in a $k \times k$
submatrix. There are two well-known barriers: if $k\geq c\sqrt{n\ln n}$, just
the row sums are sufficient to find $S$ in the general model. For the submatrix
problem, this can be improved by a $\sqrt{\ln n}$ factor to $k \ge c\sqrt{n}$
by spectral methods or combinatorial methods. In the variant with $p_0=\pm 1$
(with probability $1/2$ each) and $p_1\equiv 1$, neither barrier has been
broken.
We give a polynomial-time algorithm to identify all the hidden hubs with high
probability for $k \ge n^{0.5-\delta}$ for some $\delta >0$, when
$\sigma_1^2>2\sigma_0^2$. The algorithm extends to the setting where planted
entries might have different variances each at least as large as $\sigma_1^2$.
We also show a nearly matching lower bound: for $\sigma_1^2 \le 2\sigma_0^2$,
there is no polynomial-time Statistical Query algorithm for distinguishing
between a matrix whose entries are all from $N(0,\sigma_0^2)$ and a matrix with
$k=n^{0.5-\delta}$ hidden hubs for any $\delta >0$. The lower bound as well as
the algorithm are related to whether the chi-squared distance of the two
distributions diverges. At the critical value $\sigma_1^2=2\sigma_0^2$, we show
that the general hidden hubs problem can be solved for $k\geq c\sqrt n(\ln
n)^{1/4}$, improving on the naive row sum-based method.
| Ravi Kannan and Santosh Vempala | null | 1608.03643 | null | null |
Deep Motif Dashboard: Visualizing and Understanding Genomic Sequences
Using Deep Neural Networks | cs.LG cs.CV cs.NE | Deep neural network (DNN) models have recently obtained state-of-the-art
prediction accuracy for the transcription factor binding (TFBS) site
classification task. However, it remains unclear how these approaches identify
meaningful DNA sequence signals and give insights as to why TFs bind to certain
locations. In this paper, we propose a toolkit called the Deep Motif Dashboard
(DeMo Dashboard) which provides a suite of visualization strategies to extract
motifs, or sequence patterns from deep neural network models for TFBS
classification. We demonstrate how to visualize and understand three important
DNN models: convolutional, recurrent, and convolutional-recurrent networks. Our
first visualization method is finding a test sequence's saliency map which uses
first-order derivatives to describe the importance of each nucleotide in making
the final prediction. Second, considering recurrent models make predictions in
a temporal manner (from one end of a TFBS sequence to the other), we introduce
temporal output scores, indicating the prediction score of a model over time
for a sequential input. Lastly, a class-specific visualization strategy finds
the optimal input sequence for a given TFBS positive class via stochastic
gradient optimization. Our experimental results indicate that a
convolutional-recurrent architecture performs the best among the three
architectures. The visualization techniques indicate that CNN-RNN makes
predictions by modeling both motifs as well as dependencies among them.
| Jack Lanchantin, Ritambhara Singh, Beilun Wang, and Yanjun Qi | null | 1608.03644 | null | null |
Learning with Value-Ramp | cs.LG | We study a learning principle based on the intuition of forming ramps. The
agent tries to follow an increasing sequence of values until the agent meets a
peak of reward. The resulting Value-Ramp algorithm is natural, easy to
configure, and has a robust implementation with natural numbers.
| Tom J. Ameloot and Jan Van den Bussche | null | 1608.03647 | null | null |
Learning Structured Sparsity in Deep Neural Networks | cs.NE cs.LG stat.ML | High demand for computation resources severely hinders deployment of
large-scale Deep Neural Networks (DNN) in resource constrained devices. In this
work, we propose a Structured Sparsity Learning (SSL) method to regularize the
structures (i.e., filters, channels, filter shapes, and layer depth) of DNNs.
SSL can: (1) learn a compact structure from a bigger DNN to reduce computation
cost; (2) obtain a hardware-friendly structured sparsity of DNN to efficiently
accelerate the DNNs evaluation. Experimental results show that SSL achieves on
average 5.1x and 3.1x speedups of convolutional layer computation of AlexNet
against CPU and GPU, respectively, with off-the-shelf libraries. These speedups
are about twice speedups of non-structured sparsity; (3) regularize the DNN
structure to improve classification accuracy. The results show that for
CIFAR-10, regularization on layer depth can reduce 20 layers of a Deep Residual
Network (ResNet) to 18 layers while improve the accuracy from 91.25% to 92.60%,
which is still slightly higher than that of original ResNet with 32 layers. For
AlexNet, structure regularization by SSL also reduces the error by around ~1%.
Open source code is in https://github.com/wenwei202/caffe/tree/scnn
| Wei Wen, Chunpeng Wu, Yandan Wang, Yiran Chen, Hai Li | null | 1608.03665 | null | null |
Density Matching Reward Learning | cs.RO cs.LG | In this paper, we focus on the problem of inferring the underlying reward
function of an expert given demonstrations, which is often referred to as
inverse reinforcement learning (IRL). In particular, we propose a model-free
density-based IRL algorithm, named density matching reward learning (DMRL),
which does not require model dynamics. The performance of DMRL is analyzed
theoretically and the sample complexity is derived. Furthermore, the proposed
DMRL is extended to handle nonlinear IRL problems by assuming that the reward
function is in the reproducing kernel Hilbert space (RKHS) and kernel DMRL
(KDMRL) is proposed. The parameters for KDMRL can be computed analytically,
which greatly reduces the computation time. The performance of KDMRL is
extensively evaluated in two sets of experiments: grid world and track driving
experiments. In grid world experiments, the proposed KDMRL method is compared
with both model-based and model-free IRL methods and shows superior performance
on a nonlinear reward setting and competitive performance on a linear reward
setting in terms of expected value differences. Then we move on to more
realistic experiments of learning different driving styles for autonomous
navigation in complex and dynamic tracks using KDMRL and receding horizon
control.
| Sungjoon Choi, Kyungjae Lee, Andy Park, Songhwai Oh | null | 1608.03694 | null | null |
Unsupervised feature learning from finite data by message passing:
discontinuous versus continuous phase transition | cond-mat.dis-nn cond-mat.stat-mech cs.LG q-bio.NC | Unsupervised neural network learning extracts hidden features from unlabeled
training data. This is used as a pretraining step for further supervised
learning in deep networks. Hence, understanding unsupervised learning is of
fundamental importance. Here, we study the unsupervised learning from a finite
number of data, based on the restricted Boltzmann machine learning. Our study
inspires an efficient message passing algorithm to infer the hidden feature,
and estimate the entropy of candidate features consistent with the data. Our
analysis reveals that the learning requires only a few data if the feature is
salient and extensively many if the feature is weak. Moreover, the entropy of
candidate features monotonically decreases with data size and becomes negative
(i.e., entropy crisis) before the message passing becomes unstable, suggesting
a discontinuous phase transition. In terms of convergence time of the message
passing algorithm, the unsupervised learning exhibits an easy-hard-easy
phenomenon as the training data size increases. All these properties are
reproduced in an approximate Hopfield model, with an exception that the entropy
crisis is absent, and only continuous phase transition is observed. This key
difference is also confirmed in a handwritten digits dataset. This study
deepens our understanding of unsupervised learning from a finite number of
data, and may provide insights into its role in training deep networks.
| Haiping Huang and Taro Toyoizumi | 10.1103/PhysRevE.94.062310 | 1608.03714 | null | null |
Applying Deep Learning to Basketball Trajectories | cs.NE cs.CV cs.LG | One of the emerging trends for sports analytics is the growing use of player
and ball tracking data. A parallel development is deep learning predictive
approaches that use vast quantities of data with less reliance on feature
engineering. This paper applies recurrent neural networks in the form of
sequence modeling to predict whether a three-point shot is successful. The
models are capable of learning the trajectory of a basketball without any
knowledge of physics. For comparison, a baseline static machine learning model
with a full set of features, such as angle and velocity, in addition to the
positional data is also tested. Using a dataset of over 20,000 three pointers
from NBA SportVu data, the models based simply on sequential positional data
outperform a static feature rich machine learning model in predicting whether a
three-point shot is successful. This suggests deep learning models may offer an
improvement to traditional feature based machine learning methods for tracking
data.
| Rajiv Shah and Rob Romijnders | null | 1608.03793 | null | null |
Content-based image retrieval tutorial | stat.ML cs.IR cs.LG | This paper functions as a tutorial for individuals interested to enter the
field of information retrieval but wouldn't know where to begin from. It
describes two fundamental yet efficient image retrieval techniques, the first
being k - nearest neighbors (knn) and the second support vector machines(svm).
The goal is to provide the reader with both the theoretical and practical
aspects in order to acquire a better understanding. Along with this tutorial we
have also developed the equivalent software1 using the MATLAB environment in
order to illustrate the techniques, so that the reader can have a hands-on
experience.
| Joani Mitro | null | 1608.03811 | null | null |
Distributed Optimization for Client-Server Architecture with Negative
Gradient Weights | cs.DC cs.LG math.OC | Availability of both massive datasets and computing resources have made
machine learning and predictive analytics extremely pervasive. In this work we
present a synchronous algorithm and architecture for distributed optimization
motivated by privacy requirements posed by applications in machine learning. We
present an algorithm for the recently proposed multi-parameter-server
architecture. We consider a group of parameter servers that learn a model based
on randomized gradients received from clients. Clients are computational
entities with private datasets (inducing a private objective function), that
evaluate and upload randomized gradients to the parameter servers. The
parameter servers perform model updates based on received gradients and share
the model parameters with other servers. We prove that the proposed algorithm
can optimize the overall objective function for a very general architecture
involving $C$ clients connected to $S$ parameter servers in an arbitrary time
varying topology and the parameter servers forming a connected network.
| Shripad Gade and Nitin H. Vaidya | null | 1608.03866 | null | null |
Rapid Classification of Crisis-Related Data on Social Networks using
Convolutional Neural Networks | cs.CL cs.LG cs.SI | The role of social media, in particular microblogging platforms such as
Twitter, as a conduit for actionable and tactical information during disasters
is increasingly acknowledged. However, time-critical analysis of big crisis
data on social media streams brings challenges to machine learning techniques,
especially the ones that use supervised learning. The Scarcity of labeled data,
particularly in the early hours of a crisis, delays the machine learning
process. The current state-of-the-art classification methods require a
significant amount of labeled data specific to a particular event for training
plus a lot of feature engineering to achieve best results. In this work, we
introduce neural network based classification methods for binary and
multi-class tweet classification task. We show that neural network based models
do not require any feature engineering and perform better than state-of-the-art
methods. In the early hours of a disaster when no labeled data is available,
our proposed method makes the best use of the out-of-event data and achieves
good results.
| Dat Tien Nguyen, Kamela Ali Al Mannai, Shafiq Joty, Hassan Sajjad,
Muhammad Imran, Prasenjit Mitra | null | 1608.03902 | null | null |
Improved Dynamic Regret for Non-degenerate Functions | cs.LG | Recently, there has been a growing research interest in the analysis of
dynamic regret, which measures the performance of an online learner against a
sequence of local minimizers. By exploiting the strong convexity, previous
studies have shown that the dynamic regret can be upper bounded by the
path-length of the comparator sequence. In this paper, we illustrate that the
dynamic regret can be further improved by allowing the learner to query the
gradient of the function multiple times, and meanwhile the strong convexity can
be weakened to other non-degenerate conditions. Specifically, we introduce the
squared path-length, which could be much smaller than the path-length, as a new
regularity of the comparator sequence. When multiple gradients are accessible
to the learner, we first demonstrate that the dynamic regret of strongly convex
functions can be upper bounded by the minimum of the path-length and the
squared path-length. We then extend our theoretical guarantee to functions that
are semi-strongly convex or self-concordant. To the best of our knowledge, this
is the first time that semi-strong convexity and self-concordance are utilized
to tighten the dynamic regret.
| Lijun Zhang, Tianbao Yang, Jinfeng Yi, Rong Jin, Zhi-Hua Zhou | null | 1608.03933 | null | null |
Recurrent Fully Convolutional Neural Networks for Multi-slice MRI
Cardiac Segmentation | stat.ML cs.CV cs.LG | In cardiac magnetic resonance imaging, fully-automatic segmentation of the
heart enables precise structural and functional measurements to be taken, e.g.
from short-axis MR images of the left-ventricle. In this work we propose a
recurrent fully-convolutional network (RFCN) that learns image representations
from the full stack of 2D slices and has the ability to leverage inter-slice
spatial dependences through internal memory units. RFCN combines anatomical
detection and segmentation into a single architecture that is trained
end-to-end thus significantly reducing computational time, simplifying the
segmentation pipeline, and potentially enabling real-time applications. We
report on an investigation of RFCN using two datasets, including the publicly
available MICCAI 2009 Challenge dataset. Comparisons have been carried out
between fully convolutional networks and deep restricted Boltzmann machines,
including a recurrent version that leverages inter-slice spatial correlation.
Our studies suggest that RFCN produces state-of-the-art results and can
substantially improve the delineation of contours near the apex of the heart.
| Rudra P K Poudel and Pablo Lamata and Giovanni Montana | null | 1608.03974 | null | null |
SGDR: Stochastic Gradient Descent with Warm Restarts | cs.LG cs.NE math.OC | Restart techniques are common in gradient-free optimization to deal with
multimodal functions. Partial warm restarts are also gaining popularity in
gradient-based optimization to improve the rate of convergence in accelerated
gradient schemes to deal with ill-conditioned functions. In this paper, we
propose a simple warm restart technique for stochastic gradient descent to
improve its anytime performance when training deep neural networks. We
empirically study its performance on the CIFAR-10 and CIFAR-100 datasets, where
we demonstrate new state-of-the-art results at 3.14% and 16.21%, respectively.
We also demonstrate its advantages on a dataset of EEG recordings and on a
downsampled version of the ImageNet dataset. Our source code is available at
https://github.com/loshchil/SGDR
| Ilya Loshchilov and Frank Hutter | null | 1608.03983 | null | null |
An approach to dealing with missing values in heterogeneous data using
k-nearest neighbors | cs.LG cs.IR stat.ML | Techniques such as clusterization, neural networks and decision making
usually rely on algorithms that are not well suited to deal with missing
values. However, real world data frequently contains such cases. The simplest
solution is to either substitute them by a best guess value or completely
disregard the missing values. Unfortunately, both approaches can lead to biased
results. In this paper, we propose a technique for dealing with missing values
in heterogeneous data using imputation based on the k-nearest neighbors
algorithm. It can handle real (which we refer to as crisp henceforward),
interval and fuzzy data. The effectiveness of the algorithm is tested on
several datasets and the numerical results are promising.
| Davi E. N. Frossard, Igor O. Nunes, Renato A. Krohling | null | 1608.04037 | null | null |
Stacked Approximated Regression Machine: A Simple Deep Learning Approach | cs.LG cs.CV | With the agreement of my coauthors, I Zhangyang Wang would like to withdraw
the manuscript "Stacked Approximated Regression Machine: A Simple Deep Learning
Approach". Some experimental procedures were not included in the manuscript,
which makes a part of important claims not meaningful. In the relevant
research, I was solely responsible for carrying out the experiments; the other
coauthors joined in the discussions leading to the main algorithm.
Please see the updated text for more details.
| Zhangyang Wang, Shiyu Chang, Qing Ling, Shuai Huang, Xia Hu, Honghui
Shi, Thomas S. Huang | null | 1608.04062 | null | null |
Bayesian Model Selection Methods for Mutual and Symmetric $k$-Nearest
Neighbor Classification | cs.LG stat.ML | The $k$-nearest neighbor classification method ($k$-NNC) is one of the
simplest nonparametric classification methods. The mutual $k$-NN classification
method (M$k$NNC) is a variant of $k$-NNC based on mutual neighborship. We
propose another variant of $k$-NNC, the symmetric $k$-NN classification method
(S$k$NNC) based on both mutual neighborship and one-sided neighborship. The
performance of M$k$NNC and S$k$NNC depends on the parameter $k$ as the one of
$k$-NNC does. We propose the ways how M$k$NN and S$k$NN classification can be
performed based on Bayesian mutual and symmetric $k$-NN regression methods with
the selection schemes for the parameter $k$. Bayesian mutual and symmetric
$k$-NN regression methods are based on Gaussian process models, and it turns
out that they can do M$k$NN and S$k$NN classification with new encodings of
target values (class labels). The simulation results show that the proposed
methods are better than or comparable to $k$-NNC, M$k$NNC and S$k$NNC with the
parameter $k$ selected by the leave-one-out cross validation method not only
for an artificial data set but also for real world data sets.
| Hyun-Chul Kim | null | 1608.04063 | null | null |
Generative Knowledge Transfer for Neural Language Models | cs.LG | In this paper, we propose a generative knowledge transfer technique that
trains an RNN based language model (student network) using text and output
probabilities generated from a previously trained RNN (teacher network). The
text generation can be conducted by either the teacher or the student network.
We can also improve the performance by taking the ensemble of soft labels
obtained from multiple teacher networks. This method can be used for privacy
conscious language model adaptation because no user data is directly used for
training. Especially, when the soft labels of multiple devices are aggregated
via a trusted third party, we can expect very strong privacy protection.
| Sungho Shin, Kyuyeon Hwang, and Wonyong Sung | null | 1608.04077 | null | null |
Dynamic Hand Gesture Recognition for Wearable Devices with Low
Complexity Recurrent Neural Networks | cs.CV cs.LG | Gesture recognition is a very essential technology for many wearable devices.
While previous algorithms are mostly based on statistical methods including the
hidden Markov model, we develop two dynamic hand gesture recognition techniques
using low complexity recurrent neural network (RNN) algorithms. One is based on
video signal and employs a combined structure of a convolutional neural network
(CNN) and an RNN. The other uses accelerometer data and only requires an RNN.
Fixed-point optimization that quantizes most of the weights into two bits is
conducted to optimize the amount of memory size for weight storage and reduce
the power consumption in hardware and software based implementations.
| Sungho Shin and Wonyong Sung | null | 1608.0408 | null | null |
Power Data Classification: A Hybrid of a Novel Local Time Warping and
LSTM | cs.NE cs.LG | In this paper, for the purpose of data centre energy consumption monitoring
and analysis, we propose to detect the running programs in a server by
classifying the observed power consumption series. Time series classification
problem has been extensively studied with various distance measurements
developed; also recently the deep learning based sequence models have been
proved to be promising. In this paper, we propose a novel distance measurement
and build a time series classification algorithm hybridizing nearest neighbour
and long short term memory (LSTM) neural network. More specifically, first we
propose a new distance measurement termed as Local Time Warping (LTW), which
utilizes a user-specified set for local warping, and is designed to be
non-commutative and non-dynamic programming. Second we hybridize the 1NN-LTW
and LSTM together. In particular, we combine the prediction probability vector
of 1NN-LTW and LSTM to determine the label of the test cases. Finally, using
the power consumption data from a real data center, we show that the proposed
LTW can improve the classification accuracy of DTW from about 84% to 90%. Our
experimental results prove that the proposed LTW is competitive on our data set
compared with existed DTW variants and its non-commutative feature is indeed
beneficial. We also test a linear version of LTW and it can significantly
outperform existed linear runtime lower bound methods like LB_Keogh.
Furthermore, with the hybrid algorithm, for the power series classification
task we achieve an accuracy up to about 93%. Our research can inspire more
studies on time series distance measurement and the hybrid of the deep learning
models with other traditional models.
| Yuanlong Li, Han Hu, Yonggang Wen, Jun Zhang | null | 1608.04171 | null | null |
Using Machine Learning to Decide When to Precondition Cylindrical
Algebraic Decomposition With Groebner Bases | cs.SC cs.LG | Cylindrical Algebraic Decomposition (CAD) is a key tool in computational
algebraic geometry, particularly for quantifier elimination over real-closed
fields. However, it can be expensive, with worst case complexity doubly
exponential in the size of the input. Hence it is important to formulate the
problem in the best manner for the CAD algorithm. One possibility is to
precondition the input polynomials using Groebner Basis (GB) theory. Previous
experiments have shown that while this can often be very beneficial to the CAD
algorithm, for some problems it can significantly worsen the CAD performance.
In the present paper we investigate whether machine learning, specifically a
support vector machine (SVM), may be used to identify those CAD problems which
benefit from GB preconditioning. We run experiments with over 1000 problems
(many times larger than previous studies) and find that the machine learned
choice does better than the human-made heuristic.
| Zongyan Huang, Matthew England, James H. Davenport and Lawrence C.
Paulson | 10.1109/SYNASC.2016.020 | 1608.04219 | null | null |
Generative and Discriminative Voxel Modeling with Convolutional Neural
Networks | cs.CV cs.HC cs.LG stat.ML | When working with three-dimensional data, choice of representation is key. We
explore voxel-based models, and present evidence for the viability of
voxellated representations in applications including shape modeling and object
classification. Our key contributions are methods for training voxel-based
variational autoencoders, a user interface for exploring the latent space
learned by the autoencoder, and a deep convolutional neural network
architecture for object classification. We address challenges unique to
voxel-based representations, and empirically evaluate our models on the
ModelNet benchmark, where we demonstrate a 51.5% relative improvement in the
state of the art for object classification.
| Andrew Brock, Theodore Lim, J.M. Ritchie, Nick Weston | null | 1608.04236 | null | null |
The Bayesian Low-Rank Determinantal Point Process Mixture Model | stat.ML cs.LG | Determinantal point processes (DPPs) are an elegant model for encoding
probabilities over subsets, such as shopping baskets, of a ground set, such as
an item catalog. They are useful for a number of machine learning tasks,
including product recommendation. DPPs are parametrized by a positive
semi-definite kernel matrix. Recent work has shown that using a low-rank
factorization of this kernel provides remarkable scalability improvements that
open the door to training on large-scale datasets and computing online
recommendations, both of which are infeasible with standard DPP models that use
a full-rank kernel. In this paper we present a low-rank DPP mixture model that
allows us to represent the latent structure present in observed subsets as a
mixture of a number of component low-rank DPPs, where each component DPP is
responsible for representing a portion of the observed data. The mixture model
allows us to effectively address the capacity constraints of the low-rank DPP
model. We present an efficient and scalable Markov Chain Monte Carlo (MCMC)
learning algorithm for our model that uses Gibbs sampling and stochastic
gradient Hamiltonian Monte Carlo (SGHMC). Using an evaluation on several
real-world product recommendation datasets, we show that our low-rank DPP
mixture model provides substantially better predictive performance than is
possible with a single low-rank or full-rank DPP, and significantly better
performance than several other competing recommendation methods in many cases.
| Mike Gartrell, Ulrich Paquet, Noam Koenigstein | null | 1608.04245 | null | null |
Correlated-PCA: Principal Components' Analysis when Data and Noise are
Correlated | cs.LG cs.IT math.IT | Given a matrix of observed data, Principal Components Analysis (PCA) computes
a small number of orthogonal directions that contain most of its variability.
Provably accurate solutions for PCA have been in use for a long time. However,
to the best of our knowledge, all existing theoretical guarantees for it assume
that the data and the corrupting noise are mutually independent, or at least
uncorrelated. This is valid in practice often, but not always. In this paper,
we study the PCA problem in the setting where the data and noise can be
correlated. Such noise is often also referred to as "data-dependent noise". We
obtain a correctness result for the standard eigenvalue decomposition (EVD)
based solution to PCA under simple assumptions on the data-noise correlation.
We also develop and analyze a generalization of EVD, cluster-EVD, that improves
upon EVD in certain regimes.
| Namrata Vaswani, Han Guo | null | 1608.0432 | null | null |
Consistency constraints for overlapping data clustering | cs.LG stat.ML | We examine overlapping clustering schemes with functorial constraints, in the
spirit of Carlsson--Memoli. This avoids issues arising from the chaining
required by partition-based methods. Our principal result shows that any
clustering functor is naturally constrained to refine single-linkage clusters
and be refined by maximal-linkage clusters. We work in the context of metric
spaces with non-expansive maps, which is appropriate for modeling data
processing which does not increase information content.
| Jared Culbertson, Dan P. Guralnik, Jakob Hansen, Peter F. Stiller | null | 1608.04331 | null | null |
Anomaly detection and classification for streaming data using PDEs | cs.LG cs.CV cs.DB | Nondominated sorting, also called Pareto Depth Analysis (PDA), is widely used
in multi-objective optimization and has recently found important applications
in multi-criteria anomaly detection. Recently, a partial differential equation
(PDE) continuum limit was discovered for nondominated sorting leading to a very
fast approximate sorting algorithm called PDE-based ranking. We propose in this
paper a fast real-time streaming version of the PDA algorithm for anomaly
detection that exploits the computational advantages of PDE continuum limits.
Furthermore, we derive new PDE continuum limits for sorting points within their
nondominated layers and show how the new PDEs can be used to classify anomalies
based on which criterion was more significantly violated. We also prove
statistical convergence rates for PDE-based ranking, and present the results of
numerical experiments with both synthetic and real data.
| Bilal Abbasi, Jeff Calder, Adam M. Oberman | 10.1137/17M1121184 | 1608.04348 | null | null |
Deep Convolutional Neural Networks and Data Augmentation for
Environmental Sound Classification | cs.SD cs.CV cs.LG cs.NE | The ability of deep convolutional neural networks (CNN) to learn
discriminative spectro-temporal patterns makes them well suited to
environmental sound classification. However, the relative scarcity of labeled
data has impeded the exploitation of this family of high-capacity models. This
study has two primary contributions: first, we propose a deep convolutional
neural network architecture for environmental sound classification. Second, we
propose the use of audio data augmentation for overcoming the problem of data
scarcity and explore the influence of different augmentations on the
performance of the proposed CNN architecture. Combined with data augmentation,
the proposed model produces state-of-the-art results for environmental sound
classification. We show that the improved performance stems from the
combination of a deep, high-capacity model and an augmented training set: this
combination outperforms both the proposed CNN without augmentation and a
"shallow" dictionary learning model with augmentation. Finally, we examine the
influence of each augmentation on the model's classification accuracy for each
class, and observe that the accuracy for each class is influenced differently
by each augmentation, suggesting that the performance of the model could be
improved further by applying class-conditional data augmentation.
| Justin Salamon and Juan Pablo Bello | 10.1109/LSP.2017.2657381 | 1608.04363 | null | null |
Generalization of ERM in Stochastic Convex Optimization: The Dimension
Strikes Back | cs.LG stat.ML | In stochastic convex optimization the goal is to minimize a convex function
$F(x) \doteq {\mathbf E}_{{\mathbf f}\sim D}[{\mathbf f}(x)]$ over a convex set
$\cal K \subset {\mathbb R}^d$ where $D$ is some unknown distribution and each
$f(\cdot)$ in the support of $D$ is convex over $\cal K$. The optimization is
commonly based on i.i.d.~samples $f^1,f^2,\ldots,f^n$ from $D$. A standard
approach to such problems is empirical risk minimization (ERM) that optimizes
$F_S(x) \doteq \frac{1}{n}\sum_{i\leq n} f^i(x)$. Here we consider the question
of how many samples are necessary for ERM to succeed and the closely related
question of uniform convergence of $F_S$ to $F$ over $\cal K$. We demonstrate
that in the standard $\ell_p/\ell_q$ setting of Lipschitz-bounded functions
over a $\cal K$ of bounded radius, ERM requires sample size that scales
linearly with the dimension $d$. This nearly matches standard upper bounds and
improves on $\Omega(\log d)$ dependence proved for $\ell_2/\ell_2$ setting by
Shalev-Shwartz et al. (2009). In stark contrast, these problems can be solved
using dimension-independent number of samples for $\ell_2/\ell_2$ setting and
$\log d$ dependence for $\ell_1/\ell_\infty$ setting using other approaches. We
further show that our lower bound applies even if the functions in the support
of $D$ are smooth and efficiently computable and even if an $\ell_1$
regularization term is added. Finally, we demonstrate that for a more general
class of bounded-range (but not Lipschitz-bounded) stochastic convex programs
an infinite gap appears already in dimension 2.
| Vitaly Feldman | null | 1608.04414 | null | null |
Regularization for Unsupervised Deep Neural Nets | cs.LG cs.NE | Unsupervised neural networks, such as restricted Boltzmann machines (RBMs)
and deep belief networks (DBNs), are powerful tools for feature selection and
pattern recognition tasks. We demonstrate that overfitting occurs in such
models just as in deep feedforward neural networks, and discuss possible
regularization methods to reduce overfitting. We also propose a "partial"
approach to improve the efficiency of Dropout/DropConnect in this scenario, and
discuss the theoretical justification of these methods from model convergence
and likelihood bounds. Finally, we compare the performance of these methods
based on their likelihood and classification error rates for various pattern
recognition data sets.
| Baiyang Wang, Diego Klabjan | null | 1608.04426 | null | null |
TerpreT: A Probabilistic Programming Language for Program Induction | cs.LG cs.AI cs.NE | We study machine learning formulations of inductive program synthesis; given
input-output examples, we try to synthesize source code that maps inputs to
corresponding outputs. Our aims are to develop new machine learning approaches
based on neural networks and graphical models, and to understand the
capabilities of machine learning techniques relative to traditional
alternatives, such as those based on constraint solving from the programming
languages community.
Our key contribution is the proposal of TerpreT, a domain-specific language
for expressing program synthesis problems. TerpreT is similar to a
probabilistic programming language: a model is composed of a specification of a
program representation (declarations of random variables) and an interpreter
describing how programs map inputs to outputs (a model connecting unknowns to
observations). The inference task is to observe a set of input-output examples
and infer the underlying program. TerpreT has two main benefits. First, it
enables rapid exploration of a range of domains, program representations, and
interpreter models. Second, it separates the model specification from the
inference algorithm, allowing like-to-like comparisons between different
approaches to inference. From a single TerpreT specification we automatically
perform inference using four different back-ends. These are based on gradient
descent, linear program (LP) relaxations for graphical models, discrete
satisfiability solving, and the Sketch program synthesis system.
We illustrate the value of TerpreT by developing several interpreter models
and performing an empirical comparison between alternative inference
algorithms. Our key empirical finding is that constraint solvers dominate the
gradient descent and LP-based formulations. We conclude with suggestions for
the machine learning community to make progress on program synthesis.
| Alexander L. Gaunt, Marc Brockschmidt, Rishabh Singh, Nate Kushman,
Pushmeet Kohli, Jonathan Taylor, Daniel Tarlow | null | 1608.04428 | null | null |
Unbiased Learning-to-Rank with Biased Feedback | cs.IR cs.LG | Implicit feedback (e.g., clicks, dwell times, etc.) is an abundant source of
data in human-interactive systems. While implicit feedback has many advantages
(e.g., it is inexpensive to collect, user centric, and timely), its inherent
biases are a key obstacle to its effective use. For example, position bias in
search rankings strongly influences how many clicks a result receives, so that
directly using click data as a training signal in Learning-to-Rank (LTR)
methods yields sub-optimal results. To overcome this bias problem, we present a
counterfactual inference framework that provides the theoretical basis for
unbiased LTR via Empirical Risk Minimization despite biased data. Using this
framework, we derive a Propensity-Weighted Ranking SVM for discriminative
learning from implicit feedback, where click models take the role of the
propensity estimator. In contrast to most conventional approaches to de-bias
the data using click models, this allows training of ranking functions even in
settings where queries do not repeat. Beyond the theoretical support, we show
empirically that the proposed learning method is highly effective in dealing
with biases, that it is robust to noise and propensity model misspecification,
and that it scales efficiently. We also demonstrate the real-world
applicability of our approach on an operational search engine, where it
substantially improves retrieval performance.
| Thorsten Joachims, Adith Swaminathan, Tobias Schnabel | null | 1608.04468 | null | null |
Stein Variational Gradient Descent: A General Purpose Bayesian Inference
Algorithm | stat.ML cs.LG | We propose a general purpose variational inference algorithm that forms a
natural counterpart of gradient descent for optimization. Our method
iteratively transports a set of particles to match the target distribution, by
applying a form of functional gradient descent that minimizes the KL
divergence. Empirical studies are performed on various real world models and
datasets, on which our method is competitive with existing state-of-the-art
methods. The derivation of our method is based on a new theoretical result that
connects the derivative of KL divergence under smooth transforms with Stein's
identity and a recently proposed kernelized Stein discrepancy, which is of
independent interest.
| Qiang Liu and Dilin Wang | null | 1608.04471 | null | null |
A Geometrical Approach to Topic Model Estimation | stat.ME cs.LG stat.ML | In the probabilistic topic models, the quantity of interest---a low-rank
matrix consisting of topic vectors---is hidden in the text corpus matrix,
masked by noise, and the Singular Value Decomposition (SVD) is a potentially
useful tool for learning such a low-rank matrix. However, the connection
between this low-rank matrix and the singular vectors of the text corpus matrix
are usually complicated and hard to spell out, so how to use SVD for learning
topic models faces challenges. In this paper, we overcome the challenge by
revealing a surprising insight: there is a low-dimensional simplex structure
which can be viewed as a bridge between the low-rank matrix of interest and the
SVD of the text corpus matrix, and allows us to conveniently reconstruct the
former using the latter. Such an insight motivates a new SVD approach to
learning topic models, which we analyze with delicate random matrix theory and
derive the rate of convergence. We support our methods and theory numerically,
using both simulated data and real data.
| Zheng Tracy Ke | null | 1608.04478 | null | null |
Dynamic Network Surgery for Efficient DNNs | cs.NE cs.CV cs.LG | Deep learning has become a ubiquitous technology to improve machine
intelligence. However, most of the existing deep models are structurally very
complex, making them difficult to be deployed on the mobile platforms with
limited computational power. In this paper, we propose a novel network
compression method called dynamic network surgery, which can remarkably reduce
the network complexity by making on-the-fly connection pruning. Unlike the
previous methods which accomplish this task in a greedy way, we properly
incorporate connection splicing into the whole process to avoid incorrect
pruning and make it as a continual network maintenance. The effectiveness of
our method is proved with experiments. Without any accuracy loss, our method
can efficiently compress the number of parameters in LeNet-5 and AlexNet by a
factor of $\bm{108}\times$ and $\bm{17.7}\times$ respectively, proving that it
outperforms the recent pruning method by considerable margins. Code and some
models are available at https://github.com/yiwenguo/Dynamic-Network-Surgery.
| Yiwen Guo, Anbang Yao, Yurong Chen | null | 1608.04493 | null | null |
Fast Calculation of the Knowledge Gradient for Optimization of
Deterministic Engineering Simulations | cs.CE cs.LG stat.ML | A novel efficient method for computing the Knowledge-Gradient policy for
Continuous Parameters (KGCP) for deterministic optimization is derived. The
differences with Expected Improvement (EI), a popular choice for Bayesian
optimization of deterministic engineering simulations, are explored. Both
policies and the Upper Confidence Bound (UCB) policy are compared on a number
of benchmark functions including a problem from structural dynamics. It is
empirically shown that KGCP has similar performance as the EI policy for many
problems, but has better convergence properties for complex (multi-modal)
optimization problems as it emphasizes more on exploration when the model is
confident about the shape of optimal regions. In addition, the relationship
between Maximum Likelihood Estimation (MLE) and slice sampling for estimation
of the hyperparameters of the underlying models, and the complexity of the
problem at hand, is studied.
| Joachim van der Herten and Ivo Couckuyt and Dirk Deschrijver and Tom
Dhaene | null | 1608.0455 | null | null |
A novel transfer learning method based on common space mapping and
weighted domain matching | cs.LG stat.ML | In this paper, we propose a novel learning framework for the problem of
domain transfer learning. We map the data of two domains to one single common
space, and learn a classifier in this common space. Then we adapt the common
classifier to the two domains by adding two adaptive functions to it
respectively. In the common space, the target domain data points are weighted
and matched to the target domain in term of distributions. The weighting terms
of source domain data points and the target domain classification responses are
also regularized by the local reconstruction coefficients. The novel transfer
learning framework is evaluated over some benchmark cross-domain data sets, and
it outperforms the existing state-of-the-art transfer learning methods.
| Ru-Ze Liang, Wei Xie, Weizhi Li, Hongqi Wang, Jim Jing-Yan Wang, Lisa
Taylor | null | 1608.04581 | null | null |
Conformalized density- and distance-based anomaly detection in
time-series data | stat.AP cs.LG stat.ML | Anomalies (unusual patterns) in time-series data give essential, and often
actionable information in critical situations. Examples can be found in such
fields as healthcare, intrusion detection, finance, security and flight safety.
In this paper we propose new conformalized density- and distance-based anomaly
detection algorithms for a one-dimensional time-series data. The algorithms use
a combination of a feature extraction method, an approach to assess a score
whether a new observation differs significantly from a previously observed
data, and a probabilistic interpretation of this score based on the conformal
paradigm.
| Evgeny Burnaev and Vladislav Ishimtsev | null | 1608.04585 | null | null |
Training Echo State Networks with Regularization through Dimensionality
Reduction | cs.NE cs.LG | In this paper we introduce a new framework to train an Echo State Network to
predict real valued time-series. The method consists in projecting the output
of the internal layer of the network on a space with lower dimensionality,
before training the output layer to learn the target task. Notably, we enforce
a regularization constraint that leads to better generalization capabilities.
We evaluate the performances of our approach on several benchmark tests, using
different techniques to train the readout of the network, achieving superior
predictive performance when using the proposed framework. Finally, we provide
an insight on the effectiveness of the implemented mechanics through a
visualization of the trajectory in the phase space and relying on the
methodologies of nonlinear time-series analysis. By applying our method on well
known chaotic systems, we provide evidence that the lower dimensional embedding
retains the dynamical properties of the underlying system better than the
full-dimensional internal states of the network.
| Sigurd L{\o}kse, Filippo Maria Bianchi and Robert Jenssen | 10.1007/s12559-017-9450-z | 1608.04622 | null | null |
Linear Convergence of Gradient and Proximal-Gradient Methods Under the
Polyak-\L{}ojasiewicz Condition | cs.LG math.OC stat.CO stat.ML | In 1963, Polyak proposed a simple condition that is sufficient to show a
global linear convergence rate for gradient descent. This condition is a
special case of the \L{}ojasiewicz inequality proposed in the same year, and it
does not require strong convexity (or even convexity). In this work, we show
that this much-older Polyak-\L{}ojasiewicz (PL) inequality is actually weaker
than the main conditions that have been explored to show linear convergence
rates without strong convexity over the last 25 years. We also use the PL
inequality to give new analyses of randomized and greedy coordinate descent
methods, sign-based gradient descent methods, and stochastic gradient methods
in the classic setting (with decreasing or constant step-sizes) as well as the
variance-reduced setting. We further propose a generalization that applies to
proximal-gradient methods for non-smooth optimization, leading to simple proofs
of linear convergence of these methods. Along the way, we give simple
convergence results for a wide variety of problems in machine learning: least
squares, logistic regression, boosting, resilient backpropagation,
L1-regularization, support vector machines, stochastic dual coordinate ascent,
and stochastic variance-reduced gradient methods.
| Hamed Karimi, Julie Nutini and Mark Schmidt | null | 1608.04636 | null | null |
Enabling Factor Analysis on Thousand-Subject Neuroimaging Datasets | stat.ML cs.DC cs.LG | The scale of functional magnetic resonance image data is rapidly increasing
as large multi-subject datasets are becoming widely available and
high-resolution scanners are adopted. The inherent low-dimensionality of the
information in this data has led neuroscientists to consider factor analysis
methods to extract and analyze the underlying brain activity. In this work, we
consider two recent multi-subject factor analysis methods: the Shared Response
Model and Hierarchical Topographic Factor Analysis. We perform analytical,
algorithmic, and code optimization to enable multi-node parallel
implementations to scale. Single-node improvements result in 99x and 1812x
speedups on these two methods, and enables the processing of larger datasets.
Our distributed implementations show strong scaling of 3.3x and 5.5x
respectively with 20 nodes on real datasets. We also demonstrate weak scaling
on a synthetic dataset with 1024 subjects, on up to 1024 nodes and 32,768
cores.
| Michael J. Anderson, Mihai Capot\u{a}, Javier S. Turek, Xia Zhu,
Theodore L. Willke, Yida Wang, Po-Hsuan Chen, Jeremy R. Manning, Peter J.
Ramadge, Kenneth A. Norman | 10.1109/BigData.2016.7840719 | 1608.04647 | null | null |
Shape Constrained Tensor Decompositions using Sparse Representations in
Over-Complete Libraries | stat.ML cs.LG stat.ME | We consider $N$-way data arrays and low-rank tensor factorizations where the
time mode is coded as a sparse linear combination of temporal elements from an
over-complete library. Our method, Shape Constrained Tensor Decomposition
(SCTD) is based upon the CANDECOMP/PARAFAC (CP) decomposition which produces
$r$-rank approximations of data tensors via outer products of vectors in each
dimension of the data. By constraining the vector in the temporal dimension to
known analytic forms which are selected from a large set of candidate
functions, more readily interpretable decompositions are achieved and analytic
time dependencies discovered. The SCTD method circumvents traditional {\em
flattening} techniques where an $N$-way array is reshaped into a matrix in
order to perform a singular value decomposition. A clear advantage of the SCTD
algorithm is its ability to extract transient and intermittent phenomena which
is often difficult for SVD-based methods. We motivate the SCTD method using
several intuitively appealing results before applying it on a number of
high-dimensional, real-world data sets in order to illustrate the efficiency of
the algorithm in extracting interpretable spatio-temporal modes. With the rise
of data-driven discovery methods, the decomposition proposed provides a viable
technique for analyzing multitudes of data in a more comprehensible fashion.
| Bethany Lusch, Eric C. Chi, J. Nathan Kutz | null | 1608.04674 | null | null |
A Shallow High-Order Parametric Approach to Data Visualization and
Compression | cs.AI cs.LG stat.ML | Explicit high-order feature interactions efficiently capture essential
structural knowledge about the data of interest and have been used for
constructing generative models. We present a supervised discriminative
High-Order Parametric Embedding (HOPE) approach to data visualization and
compression. Compared to deep embedding models with complicated deep
architectures, HOPE generates more effective high-order feature mapping through
an embarrassingly simple shallow model. Furthermore, two approaches to
generating a small number of exemplars conveying high-order interactions to
represent large-scale data sets are proposed. These exemplars in combination
with the feature mapping learned by HOPE effectively capture essential data
variations. Moreover, through HOPE, these exemplars are employed to increase
the computational efficiency of kNN classification for fast information
retrieval by thousands of times. For classification in two-dimensional
embedding space on MNIST and USPS datasets, our shallow method HOPE with simple
Sigmoid transformations significantly outperforms state-of-the-art supervised
deep embedding models based on deep neural networks, and even achieved
historically low test error rate of 0.65% in two-dimensional space on MNIST,
which demonstrates the representational efficiency and power of supervised
shallow models with high-order feature interactions.
| Martin Renqiang Min, Hongyu Guo, Dongjin Song | null | 1608.04689 | null | null |
A Data-Driven Approach to Estimating the Number of Clusters in
Hierarchical Clustering | q-bio.QM cs.LG stat.ME | We propose two new methods for estimating the number of clusters in a
hierarchical clustering framework in the hopes of creating a fully automated
process with no human intervention. The methods are completely data-driven and
require no input from the researcher, and as such are fully automated. They are
quite easy to implement and not computationally intensive in the least. We
analyze performance on several simulated data sets and the Biobase Gene
Expression Set, comparing our methods to the established Gap statistic and
Elbow methods and outperforming both in multi-cluster scenarios.
| Antoine Zambelli | null | 1608.047 | null | null |
Faster Sublinear Algorithms using Conditional Sampling | cs.DS cs.LG | A conditional sampling oracle for a probability distribution D returns
samples from the conditional distribution of D restricted to a specified subset
of the domain. A recent line of work (Chakraborty et al. 2013 and Cannone et
al. 2014) has shown that having access to such a conditional sampling oracle
requires only polylogarithmic or even constant number of samples to solve
distribution testing problems like identity and uniformity. This significantly
improves over the standard sampling model where polynomially many samples are
necessary.
Inspired by these results, we introduce a computational model based on
conditional sampling to develop sublinear algorithms with exponentially faster
runtimes compared to standard sublinear algorithms. We focus on geometric
optimization problems over points in high dimensional Euclidean space. Access
to these points is provided via a conditional sampling oracle that takes as
input a succinct representation of a subset of the domain and outputs a
uniformly random point in that subset. We study two well studied problems:
k-means clustering and estimating the weight of the minimum spanning tree. In
contrast to prior algorithms for the classic model, our algorithms have time,
space and sample complexity that is polynomial in the dimension and
polylogarithmic in the number of points.
Finally, we comment on the applicability of the model and compare with
existing ones like streaming, parallel and distributed computational models.
| Themistoklis Gouleakis, Christos Tzamos and Manolis Zampetakis | null | 1608.04759 | null | null |
Faster Principal Component Regression and Stable Matrix Chebyshev
Approximation | stat.ML cs.DS cs.LG math.NA math.OC | We solve principal component regression (PCR), up to a multiplicative
accuracy $1+\gamma$, by reducing the problem to $\tilde{O}(\gamma^{-1})$
black-box calls of ridge regression. Therefore, our algorithm does not require
any explicit construction of the top principal components, and is suitable for
large-scale PCR instances. In contrast, previous result requires
$\tilde{O}(\gamma^{-2})$ such black-box calls.
We obtain this result by developing a general stable recurrence formula for
matrix Chebyshev polynomials, and a degree-optimal polynomial approximation to
the matrix sign function. Our techniques may be of independent interests,
especially when designing iterative methods.
| Zeyuan Allen-Zhu and Yuanzhi Li | null | 1608.04773 | null | null |
Application of multiview techniques to NHANES dataset | cs.LG stat.ML | Disease prediction or classification using health datasets involve using
well-known predictors associated with the disease as features for the models.
This study considers multiple data components of an individual's health, using
the relationship between variables to generate features that may improve the
performance of disease classification models. In order to capture information
from different aspects of the data, this project uses a multiview learning
approach, using Canonical Correlation Analysis (CCA), a technique that finds
projections with maximum correlations between two data views. Data categories
collected from the NHANES survey (1999-2014) are used as views to learn the
multiview representations. The usefulness of the representations is
demonstrated by applying them as features in a Diabetes classification task.
| Aileme Omogbai | null | 1608.04783 | null | null |
Modelling Student Behavior using Granular Large Scale Action Data from a
MOOC | cs.CY cs.LG | Digital learning environments generate a precise record of the actions
learners take as they interact with learning materials and complete exercises
towards comprehension. With this high quantity of sequential data comes the
potential to apply time series models to learn about underlying behavioral
patterns and trends that characterize successful learning based on the granular
record of student actions. There exist several methods for looking at
longitudinal, sequential data like those recorded from learning environments.
In the field of language modelling, traditional n-gram techniques and modern
recurrent neural network (RNN) approaches have been applied to algorithmically
find structure in language and predict the next word given the previous words
in the sentence or paragraph as input. In this paper, we draw an analogy to
this work by treating student sequences of resource views and interactions in a
MOOC as the inputs and predicting students' next interaction as outputs. In
this study, we train only on students who received a certificate of completion.
In doing so, the model could potentially be used for recommendation of
sequences eventually leading to success, as opposed to perpetuating
unproductive behavior. Given that the MOOC used in our study had over 3,500
unique resources, predicting the exact resource that a student will interact
with next might appear to be a difficult classification problem. We find that
simply following the syllabus (built-in structure of the course) gives on
average 23% accuracy in making this prediction, followed by the n-gram method
with 70.4%, and RNN based methods with 72.2%. This research lays the ground
work for recommendation in a MOOC and other digital learning environments where
high volumes of sequential data exist.
| Steven Tang, Joshua C. Peterson, Zachary A. Pardos | null | 1608.04789 | null | null |
Scalable Learning of Non-Decomposable Objectives | stat.ML cs.LG | Modern retrieval systems are often driven by an underlying machine learning
model. The goal of such systems is to identify and possibly rank the few most
relevant items for a given query or context. Thus, such systems are typically
evaluated using a ranking-based performance metric such as the area under the
precision-recall curve, the $F_\beta$ score, precision at fixed recall, etc.
Obviously, it is desirable to train such systems to optimize the metric of
interest.
In practice, due to the scalability limitations of existing approaches for
optimizing such objectives, large-scale retrieval systems are instead trained
to maximize classification accuracy, in the hope that performance as measured
via the true objective will also be favorable. In this work we present a
unified framework that, using straightforward building block bounds, allows for
highly scalable optimization of a wide range of ranking-based objectives. We
demonstrate the advantage of our approach on several real-life retrieval
problems that are significantly larger than those considered in the literature,
while achieving substantial improvement in performance over the
accuracy-objective baseline.
| Elad ET. Eban, Mariano Schain, Alan Mackey, Ariel Gordon, Rif A.
Saurous, Gal Elidan | null | 1608.04802 | null | null |
Outlier Detection on Mixed-Type Data: An Energy-based Approach | stat.ML cs.LG | Outlier detection amounts to finding data points that differ significantly
from the norm. Classic outlier detection methods are largely designed for
single data type such as continuous or discrete. However, real world data is
increasingly heterogeneous, where a data point can have both discrete and
continuous attributes. Handling mixed-type data in a disciplined way remains a
great challenge. In this paper, we propose a new unsupervised outlier detection
method for mixed-type data based on Mixed-variate Restricted Boltzmann Machine
(Mv.RBM). The Mv.RBM is a principled probabilistic method that models data
density. We propose to use \emph{free-energy} derived from Mv.RBM as outlier
score to detect outliers as those data points lying in low density regions. The
method is fast to learn and compute, is scalable to massive datasets. At the
same time, the outlier score is identical to data negative log-density up-to an
additive constant. We evaluate the proposed method on synthetic and real-world
datasets and demonstrate that (a) a proper handling mixed-types is necessary in
outlier detection, and (b) free-energy of Mv.RBM is a powerful and efficient
outlier scoring method, which is highly competitive against state-of-the-arts.
| Kien Do, Truyen Tran, Dinh Phung and Svetha Venkatesh | null | 1608.0483 | null | null |
Dynamic Collaborative Filtering with Compound Poisson Factorization | cs.LG cs.AI stat.ML | Model-based collaborative filtering analyzes user-item interactions to infer
latent factors that represent user preferences and item characteristics in
order to predict future interactions. Most collaborative filtering algorithms
assume that these latent factors are static, although it has been shown that
user preferences and item perceptions drift over time. In this paper, we
propose a conjugate and numerically stable dynamic matrix factorization (DCPF)
based on compound Poisson matrix factorization that models the smoothly
drifting latent factors using Gamma-Markov chains. We propose a numerically
stable Gamma chain construction, and then present a stochastic variational
inference approach to estimate the parameters of our model. We apply our model
to time-stamped ratings data sets: Netflix, Yelp, and Last.fm, where DCPF
achieves a higher predictive accuracy than state-of-the-art static and dynamic
factorization models.
| Ghassen Jerfel, Mehmet E. Basbug, Barbara E. Engelhardt | null | 1608.04839 | null | null |
A Convolutional Autoencoder for Multi-Subject fMRI Data Aggregation | stat.ML cs.AI cs.CV cs.LG | Finding the most effective way to aggregate multi-subject fMRI data is a
long-standing and challenging problem. It is of increasing interest in
contemporary fMRI studies of human cognition due to the scarcity of data per
subject and the variability of brain anatomy and functional response across
subjects. Recent work on latent factor models shows promising results in this
task but this approach does not preserve spatial locality in the brain. We
examine two ways to combine the ideas of a factor model and a searchlight based
analysis to aggregate multi-subject fMRI data while preserving spatial
locality. We first do this directly by combining a recent factor method known
as a shared response model with searchlight analysis. Then we design a
multi-view convolutional autoencoder for the same task. Both approaches
preserve spatial locality and have competitive or better performance compared
with standard searchlight analysis and the shared response model applied across
the whole brain. We also report a system design to handle the computational
challenge of training the convolutional autoencoder.
| Po-Hsuan Chen, Xia Zhu, Hejia Zhang, Javier S. Turek, Janice Chen,
Theodore L. Willke, Uri Hasson, Peter J. Ramadge | null | 1608.04846 | null | null |
Hard Clusters Maximize Mutual Information | cs.IT cs.IR cs.LG math.IT | In this paper, we investigate mutual information as a cost function for
clustering, and show in which cases hard, i.e., deterministic, clusters are
optimal. Using convexity properties of mutual information, we show that certain
formulations of the information bottleneck problem are solved by hard clusters.
Similarly, hard clusters are optimal for the information-theoretic
co-clustering problem that deals with simultaneous clustering of two dependent
data sets. If both data sets have to be clustered using the same cluster
assignment, hard clusters are not optimal in general. We point at interesting
and practically relevant special cases of this so-called pairwise clustering
problem, for which we can either prove or have evidence that hard clusters are
optimal. Our results thus show that one can relax the otherwise combinatorial
hard clustering problem to a real-valued optimization problem with the same
global optimum.
| Bernhard C. Geiger, Rana Ali Amjad | null | 1608.04872 | null | null |
Reinforcement Learning algorithms for regret minimization in structured
Markov Decision Processes | cs.LG | A recent goal in the Reinforcement Learning (RL) framework is to choose a
sequence of actions or a policy to maximize the reward collected or minimize
the regret incurred in a finite time horizon. For several RL problems in
operation research and optimal control, the optimal policy of the underlying
Markov Decision Process (MDP) is characterized by a known structure. The
current state of the art algorithms do not utilize this known structure of the
optimal policy while minimizing regret. In this work, we develop new RL
algorithms that exploit the structure of the optimal policy to minimize regret.
Numerical experiments on MDPs with structured optimal policies show that our
algorithms have better performance, are easy to implement, have a smaller
run-time and require less number of random number generations.
| K J Prabuchandran, Tejas Bodas and Theja Tulabandhula | null | 1608.04929 | null | null |
Mollifying Networks | cs.LG cs.NE | The optimization of deep neural networks can be more challenging than
traditional convex optimization problems due to the highly non-convex nature of
the loss function, e.g. it can involve pathological landscapes such as
saddle-surfaces that can be difficult to escape for algorithms based on simple
gradient descent. In this paper, we attack the problem of optimization of
highly non-convex neural networks by starting with a smoothed -- or
\textit{mollified} -- objective function that gradually has a more non-convex
energy landscape during the training. Our proposition is inspired by the recent
studies in continuation methods: similar to curriculum methods, we begin
learning an easier (possibly convex) objective function and let it evolve
during the training, until it eventually goes back to being the original,
difficult to optimize, objective function. The complexity of the mollified
networks is controlled by a single hyperparameter which is annealed during the
training. We show improvements on various difficult optimization tasks and
establish a relationship with recent works on continuation methods for neural
networks and mollifiers.
| Caglar Gulcehre, Marcin Moczulski, Francesco Visin, Yoshua Bengio | null | 1608.0498 | null | null |
An image compression and encryption scheme based on deep learning | cs.CV cs.LG cs.MM | Stacked Auto-Encoder (SAE) is a kind of deep learning algorithm for
unsupervised learning. Which has multi layers that project the vector
representation of input data into a lower vector space. These projection
vectors are dense representations of the input data. As a result, SAE can be
used for image compression. Using chaotic logistic map, the compression ones
can further be encrypted. In this study, an application of image compression
and encryption is suggested using SAE and chaotic logistic map. Experiments
show that this application is feasible and effective. It can be used for image
transmission and image protection on internet simultaneously.
| Fei Hu, Changjiu Pu, Haowei Gao, Mengzi Tang and Li Li | null | 1608.05001 | null | null |
BBQ-Networks: Efficient Exploration in Deep Reinforcement Learning for
Task-Oriented Dialogue Systems | cs.LG cs.NE stat.ML | We present a new algorithm that significantly improves the efficiency of
exploration for deep Q-learning agents in dialogue systems. Our agents explore
via Thompson sampling, drawing Monte Carlo samples from a Bayes-by-Backprop
neural network. Our algorithm learns much faster than common exploration
strategies such as $\epsilon$-greedy, Boltzmann, bootstrapping, and
intrinsic-reward-based ones. Additionally, we show that spiking the replay
buffer with experiences from just a few successful episodes can make Q-learning
feasible when it might otherwise fail.
| Zachary C. Lipton, Xiujun Li, Jianfeng Gao, Lihong Li, Faisal Ahmed,
Li Deng | null | 1608.05081 | null | null |
A Bayesian Network approach to County-Level Corn Yield Prediction using
historical data and expert knowledge | cs.LG stat.AP stat.ML | Crop yield forecasting is the methodology of predicting crop yields prior to
harvest. The availability of accurate yield prediction frameworks have enormous
implications from multiple standpoints, including impact on the crop commodity
futures markets, formulation of agricultural policy, as well as crop insurance
rating. The focus of this work is to construct a corn yield predictor at the
county scale. Corn yield (forecasting) depends on a complex, interconnected set
of variables that include economic, agricultural, management and meteorological
factors. Conventional forecasting is either knowledge-based computer programs
(that simulate plant-weather-soil-management interactions) coupled with
targeted surveys or statistical model based. The former is limited by the need
for painstaking calibration, while the latter is limited to univariate analysis
or similar simplifying assumptions that fail to capture the complex
interdependencies affecting yield. In this paper, we propose a data-driven
approach that is "gray box" i.e. that seamlessly utilizes expert knowledge in
constructing a statistical network model for corn yield forecasting. Our
multivariate gray box model is developed on Bayesian network analysis to build
a Directed Acyclic Graph (DAG) between predictors and yield. Starting from a
complete graph connecting various carefully chosen variables and yield, expert
knowledge is used to prune or strengthen edges connecting variables.
Subsequently the structure (connectivity and edge weights) of the DAG that
maximizes the likelihood of observing the training data is identified via
optimization. We curated an extensive set of historical data (1948-2012) for
each of the 99 counties in Iowa as data to train the model.
| Vikas Chawla, Hsiang Sing Naik, Adedotun Akintayo, Dermot Hayes,
Patrick Schnable, Baskar Ganapathysubramanian, Soumik Sarkar | null | 1608.05127 | null | null |
Conditional Sparse Linear Regression | cs.LG cs.DS stat.ML | Machine learning and statistics typically focus on building models that
capture the vast majority of the data, possibly ignoring a small subset of data
as "noise" or "outliers." By contrast, here we consider the problem of jointly
identifying a significant (but perhaps small) segment of a population in which
there is a highly sparse linear regression fit, together with the coefficients
for the linear fit. We contend that such tasks are of interest both because the
models themselves may be able to achieve better predictions in such special
cases, but also because they may aid our understanding of the data. We give
algorithms for such problems under the sup norm, when this unknown segment of
the population is described by a k-DNF condition and the regression fit is
s-sparse for constant k and s. For the variants of this problem when the
regression fit is not so sparse or using expected error, we also give a
preliminary algorithm and highlight the question as a challenge for future
work.
| Brendan Juba | null | 1608.05152 | null | null |
A Bayesian Nonparametric Approach for Estimating Individualized
Treatment-Response Curves | cs.LG stat.ML | We study the problem of estimating the continuous response over time to
interventions using observational time series---a retrospective dataset where
the policy by which the data are generated is unknown to the learner. We are
motivated by applications where response varies by individuals and therefore,
estimating responses at the individual-level is valuable for personalizing
decision-making. We refer to this as the problem of estimating individualized
treatment response (ITR) curves. In statistics, G-computation formula (Robins,
1986) has been commonly used for estimating treatment responses from
observational data containing sequential treatment assignments. However, past
studies have focused predominantly on obtaining point-in-time estimates at the
population level. We leverage the G-computation formula and develop a novel
Bayesian nonparametric (BNP) method that can flexibly model functional data and
provide posterior inference over the treatment response curves at both the
individual and population level. On a challenging dataset containing time
series from patients admitted to a hospital, we estimate responses to
treatments used in managing kidney function and show that the resulting fits
are more accurate than alternative approaches. Accurate methods for obtaining
ITRs from observational data can dramatically accelerate the pace at which
personalized treatment plans become possible.
| Yanbo Xu, Yanxun Xu and Suchi Saria | null | 1608.05182 | null | null |
Active Learning for Approximation of Expensive Functions with Normal
Distributed Output Uncertainty | cs.LG stat.ML | When approximating a black-box function, sampling with active learning
focussing on regions with non-linear responses tends to improve accuracy. We
present the FLOLA-Voronoi method introduced previously for deterministic
responses, and theoretically derive the impact of output uncertainty. The
algorithm automatically puts more emphasis on exploration to provide more
information to the models.
| Joachim van der Herten and Ivo Couckuyt and Dirk Deschrijver and Tom
Dhaene | null | 1608.05225 | null | null |
Parameter Learning for Log-supermodular Distributions | stat.ML cs.LG | We consider log-supermodular models on binary variables, which are
probabilistic models with negative log-densities which are submodular. These
models provide probabilistic interpretations of common combinatorial
optimization tasks such as image segmentation. In this paper, we focus
primarily on parameter estimation in the models from known upper-bounds on the
intractable log-partition function. We show that the bound based on separable
optimization on the base polytope of the submodular function is always inferior
to a bound based on "perturb-and-MAP" ideas. Then, to learn parameters, given
that our approximation of the log-partition function is an expectation (over
our own randomization), we use a stochastic subgradient technique to maximize a
lower-bound on the log-likelihood. This can also be extended to conditional
maximum likelihood. We illustrate our new results in a set of experiments in
binary image denoising, where we highlight the flexibility of a probabilistic
model to learn with missing data.
| Tatiana Shpakova and Francis Bach | null | 1608.05258 | null | null |
A Tight Convex Upper Bound on the Likelihood of a Finite Mixture | cs.LG stat.ML | The likelihood function of a finite mixture model is a non-convex function
with multiple local maxima and commonly used iterative algorithms such as EM
will converge to different solutions depending on initial conditions. In this
paper we ask: is it possible to assess how far we are from the global maximum
of the likelihood? Since the likelihood of a finite mixture model can grow
unboundedly by centering a Gaussian on a single datapoint and shrinking the
covariance, we constrain the problem by assuming that the parameters of the
individual models are members of a large discrete set (e.g. estimating a
mixture of two Gaussians where the means and variances of both Gaussians are
members of a set of a million possible means and variances). For this setting
we show that a simple upper bound on the likelihood can be computed using
convex optimization and we analyze conditions under which the bound is
guaranteed to be tight. This bound can then be used to assess the quality of
solutions found by EM (where the final result is projected on the discrete set)
or any other mixture estimation algorithm. For any dataset our method allows us
to find a finite mixture model together with a dataset-specific bound on how
far the likelihood of this mixture is from the global optimum of the likelihood
| Elad Mezuman and Yair Weiss | null | 1608.05275 | null | null |
Caveats on Bayesian and hidden-Markov models (v2.8) | cs.LG | This paper describes a number of fundamental and practical problems in the
application of hidden-Markov models and Bayes when applied to cursive-script
recognition. Several problems, however, will have an effect in other
application areas. The most fundamental problem is the propagation of error in
the product of probabilities. This is a common and pervasive problem which
deserves more attention. On the basis of Monte Carlo modeling, tables for the
expected relative error are given. It seems that it is distributed according to
a continuous Poisson distribution over log probabilities. A second essential
problem is related to the appropriateness of the Markov assumption. Basic tests
will reveal whether a problem requires modeling of the stochastics of
seriality, at all. Examples are given of lexical encodings which cover 95-99%
classification accuracy of a lexicon, with removed sequence information, for
several European languages. Finally, a summary of results on a non- Bayes,
non-Markov method in handwriting recognition are presented, with very
acceptable results and minimal modeling or training requirements using
nearest-mean classification.
| Lambert Schomaker | null | 1608.05277 | null | null |
Decoupled Neural Interfaces using Synthetic Gradients | cs.LG | Training directed neural networks typically requires forward-propagating data
through a computation graph, followed by backpropagating error signal, to
produce weight updates. All layers, or more generally, modules, of the network
are therefore locked, in the sense that they must wait for the remainder of the
network to execute forwards and propagate error backwards before they can be
updated. In this work we break this constraint by decoupling modules by
introducing a model of the future computation of the network graph. These
models predict what the result of the modelled subgraph will produce using only
local information. In particular we focus on modelling error gradients: by
using the modelled synthetic gradient in place of true backpropagated error
gradients we decouple subgraphs, and can update them independently and
asynchronously i.e. we realise decoupled neural interfaces. We show results for
feed-forward models, where every layer is trained asynchronously, recurrent
neural networks (RNNs) where predicting one's future gradient extends the time
over which the RNN can effectively model, and also a hierarchical RNN system
with ticking at different timescales. Finally, we demonstrate that in addition
to predicting gradients, the same framework can be used to predict inputs,
resulting in models which are decoupled in both the forward and backwards pass
-- amounting to independent networks which co-learn such that they can be
composed into a single functioning corporation.
| Max Jaderberg, Wojciech Marian Czarnecki, Simon Osindero, Oriol
Vinyals, Alex Graves, David Silver, Koray Kavukcuoglu | null | 1608.05343 | null | null |
Probabilistic Data Analysis with Probabilistic Programming | cs.AI cs.LG stat.ML | Probabilistic techniques are central to data analysis, but different
approaches can be difficult to apply, combine, and compare. This paper
introduces composable generative population models (CGPMs), a computational
abstraction that extends directed graphical models and can be used to describe
and compose a broad class of probabilistic data analysis techniques. Examples
include hierarchical Bayesian models, multivariate kernel methods,
discriminative machine learning, clustering algorithms, dimensionality
reduction, and arbitrary probabilistic programs. We also demonstrate the
integration of CGPMs into BayesDB, a probabilistic programming platform that
can express data analysis tasks using a modeling language and a structured
query language. The practical value is illustrated in two ways. First, CGPMs
are used in an analysis that identifies satellite data records which probably
violate Kepler's Third Law, by composing causal probabilistic programs with
non-parametric Bayes in under 50 lines of probabilistic code. Second, for
several representative data analysis tasks, we report on lines of code and
accuracy measurements of various CGPMs, plus comparisons with standard baseline
solutions from Python and MATLAB libraries.
| Feras Saad, Vikash Mansinghka | null | 1608.05347 | null | null |
Distributed Optimization of Convex Sum of Non-Convex Functions | cs.DC cs.LG math.OC | We present a distributed solution to optimizing a convex function composed of
several non-convex functions. Each non-convex function is privately stored with
an agent while the agents communicate with neighbors to form a network. We show
that coupled consensus and projected gradient descent algorithm proposed in [1]
can optimize convex sum of non-convex functions under an additional assumption
on gradient Lipschitzness. We further discuss the applications of this analysis
in improving privacy in distributed optimization.
| Shripad Gade and Nitin H. Vaidya | null | 1608.05401 | null | null |
Iterative Views Agreement: An Iterative Low-Rank based Structured
Optimization Method to Multi-View Spectral Clustering | cs.LG stat.ML | Multi-view spectral clustering, which aims at yielding an agreement or
consensus data objects grouping across multi-views with their graph laplacian
matrices, is a fundamental clustering problem. Among the existing methods,
Low-Rank Representation (LRR) based method is quite superior in terms of its
effectiveness, intuitiveness and robustness to noise corruptions. However, it
aggressively tries to learn a common low-dimensional subspace for multi-view
data, while inattentively ignoring the local manifold structure in each view,
which is critically important to the spectral clustering; worse still, the
low-rank minimization is enforced to achieve the data correlation consensus
among all views, failing to flexibly preserve the local manifold structure for
each view. In this paper, 1) we propose a multi-graph laplacian regularized LRR
with each graph laplacian corresponding to one view to characterize its local
manifold structure. 2) Instead of directly enforcing the low-rank minimization
among all views for correlation consensus, we separately impose low-rank
constraint on each view, coupled with a mutual structural consensus constraint,
where it is able to not only well preserve the local manifold structure but
also serve as a constraint for that from other views, which iteratively makes
the views more agreeable. Extensive experiments on real-world multi-view data
sets demonstrate its superiority.
| Yang Wang, Wenjie Zhang, Lin Wu, Xuemin Lin, Meng Fang, Shirui Pan | null | 1608.0556 | null | null |
Unsupervised Feature Selection Based on the Morisita Estimator of
Intrinsic Dimension | stat.ML cs.LG | This paper deals with a new filter algorithm for selecting the smallest
subset of features carrying all the information content of a data set (i.e. for
removing redundant features). It is an advanced version of the fractal
dimension reduction technique, and it relies on the recently introduced
Morisita estimator of Intrinsic Dimension (ID). Here, the ID is used to
quantify dependencies between subsets of features, which allows the effective
processing of highly non-linear data. The proposed algorithm is successfully
tested on simulated and real world case studies. Different levels of sample
size and noise are examined along with the variability of the results. In
addition, a comprehensive procedure based on random forests shows that the data
dimensionality is significantly reduced by the algorithm without loss of
relevant information. And finally, comparisons with benchmark feature selection
techniques demonstrate the promising performance of this new filter.
| Jean Golay and Mikhail Kanevski | null | 1608.05581 | null | null |
A Strongly Quasiconvex PAC-Bayesian Bound | cs.LG stat.ML | We propose a new PAC-Bayesian bound and a way of constructing a hypothesis
space, so that the bound is convex in the posterior distribution and also
convex in a trade-off parameter between empirical performance of the posterior
distribution and its complexity. The complexity is measured by the
Kullback-Leibler divergence to a prior. We derive an alternating procedure for
minimizing the bound. We show that the bound can be rewritten as a
one-dimensional function of the trade-off parameter and provide sufficient
conditions under which the function has a single global minimum. When the
conditions are satisfied the alternating minimization is guaranteed to converge
to the global minimum of the bound. We provide experimental results
demonstrating that rigorous minimization of the bound is competitive with
cross-validation in tuning the trade-off between complexity and empirical
performance. In all our experiments the trade-off turned to be quasiconvex even
when the sufficient conditions were violated.
| Niklas Thiemann and Christian Igel and Olivier Wintenberger and
Yevgeny Seldin | null | 1608.0561 | null | null |
Operator-Valued Bochner Theorem, Fourier Feature Maps for
Operator-Valued Kernels, and Vector-Valued Learning | cs.LG | This paper presents a framework for computing random operator-valued feature
maps for operator-valued positive definite kernels. This is a generalization of
the random Fourier features for scalar-valued kernels to the operator-valued
case. Our general setting is that of operator-valued kernels corresponding to
RKHS of functions with values in a Hilbert space. We show that in general, for
a given kernel, there are potentially infinitely many random feature maps,
which can be bounded or unbounded. Most importantly, given a kernel, we present
a general, closed form formula for computing a corresponding probability
measure, which is required for the construction of the Fourier features, and
which, unlike the scalar case, is not uniquely and automatically determined by
the kernel. We also show that, under appropriate conditions, random bounded
feature maps can always be computed. Furthermore, we show the uniform
convergence, under the Hilbert-Schmidt norm, of the resulting approximate
kernel to the exact kernel on any compact subset of Euclidean space. Our
convergence requires differentiable kernels, an improvement over the
twice-differentiability requirement in previous work in the scalar setting. We
then show how operator-valued feature maps and their approximations can be
employed in a general vector-valued learning framework. The mathematical
formulation is illustrated by numerical examples on matrix-valued kernels.
| Ha Quang Minh | null | 1608.05639 | null | null |
RETAIN: An Interpretable Predictive Model for Healthcare using Reverse
Time Attention Mechanism | cs.LG cs.AI cs.NE | Accuracy and interpretability are two dominant features of successful
predictive models. Typically, a choice must be made in favor of complex black
box models such as recurrent neural networks (RNN) for accuracy versus less
accurate but more interpretable traditional models such as logistic regression.
This tradeoff poses challenges in medicine where both accuracy and
interpretability are important. We addressed this challenge by developing the
REverse Time AttentIoN model (RETAIN) for application to Electronic Health
Records (EHR) data. RETAIN achieves high accuracy while remaining clinically
interpretable and is based on a two-level neural attention model that detects
influential past visits and significant clinical variables within those visits
(e.g. key diagnoses). RETAIN mimics physician practice by attending the EHR
data in a reverse time order so that recent clinical visits are likely to
receive higher attention. RETAIN was tested on a large health system EHR
dataset with 14 million visits completed by 263K patients over an 8 year period
and demonstrated predictive accuracy and computational scalability comparable
to state-of-the-art methods such as RNN, and ease of interpretability
comparable to traditional models.
| Edward Choi, Mohammad Taha Bahadori, Joshua A. Kulas, Andy Schuetz,
Walter F. Stewart, Jimeng Sun | null | 1608.05745 | null | null |
Solving a Mixture of Many Random Linear Equations by Tensor
Decomposition and Alternating Minimization | cs.LG cs.IT math.IT math.ST stat.ML stat.TH | We consider the problem of solving mixed random linear equations with $k$
components. This is the noiseless setting of mixed linear regression. The goal
is to estimate multiple linear models from mixed samples in the case where the
labels (which sample corresponds to which model) are not observed. We give a
tractable algorithm for the mixed linear equation problem, and show that under
some technical conditions, our algorithm is guaranteed to solve the problem
exactly with sample complexity linear in the dimension, and polynomial in $k$,
the number of components. Previous approaches have required either exponential
dependence on $k$, or super-linear dependence on the dimension. The proposed
algorithm is a combination of tensor decomposition and alternating
minimization. Our analysis involves proving that the initialization provided by
the tensor method allows alternating minimization, which is equivalent to EM in
our setting, to converge to the global optimum at a linear rate.
| Xinyang Yi, Constantine Caramanis, Sujay Sanghavi | null | 1608.05749 | null | null |
Fast estimation of approximate matrix ranks using spectral densities | cs.NA cs.LG math.NA | In many machine learning and data related applications, it is required to
have the knowledge of approximate ranks of large data matrices at hand. In this
paper, we present two computationally inexpensive techniques to estimate the
approximate ranks of such large matrices. These techniques exploit approximate
spectral densities, popular in physics, which are probability density
distributions that measure the likelihood of finding eigenvalues of the matrix
at a given point on the real line. Integrating the spectral density over an
interval gives the eigenvalue count of the matrix in that interval. Therefore
the rank can be approximated by integrating the spectral density over a
carefully selected interval. Two different approaches are discussed to estimate
the approximate rank, one based on Chebyshev polynomials and the other based on
the Lanczos algorithm. In order to obtain the appropriate interval, it is
necessary to locate a gap between the eigenvalues that correspond to noise and
the relevant eigenvalues that contribute to the matrix rank. A method for
locating this gap and selecting the interval of integration is proposed based
on the plot of the spectral density. Numerical experiments illustrate the
performance of these techniques on matrices from typical applications.
| Shashanka Ubaru, Yousef Saad, Abd-Krim Seghouane | 10.1162/NECO_a_00951 | 1608.05754 | null | null |
Analysis of Bayesian Classification based Approaches for Android Malware
Detection | cs.CR cs.LG | Mobile malware has been growing in scale and complexity spurred by the
unabated uptake of smartphones worldwide. Android is fast becoming the most
popular mobile platform resulting in sharp increase in malware targeting the
platform. Additionally, Android malware is evolving rapidly to evade detection
by traditional signature-based scanning. Despite current detection measures in
place, timely discovery of new malware is still a critical issue. This calls
for novel approaches to mitigate the growing threat of zero-day Android
malware. Hence, in this paper we develop and analyze proactive Machine Learning
approaches based on Bayesian classification aimed at uncovering unknown Android
malware via static analysis. The study, which is based on a large malware
sample set of majority of the existing families, demonstrates detection
capabilities with high accuracy. Empirical results and comparative analysis are
presented offering useful insight towards development of effective
static-analytic Bayesian classification based solutions for detecting unknown
Android malware.
| Suleiman Y. Yerima, Sakir Sezer, Gavin McWilliams | 10.1049/iet-ifs.2013.0095 | 1608.05812 | null | null |
Online Feature Selection with Group Structure Analysis | cs.CV cs.LG stat.ML | Online selection of dynamic features has attracted intensive interest in
recent years. However, existing online feature selection methods evaluate
features individually and ignore the underlying structure of feature stream.
For instance, in image analysis, features are generated in groups which
represent color, texture and other visual information. Simply breaking the
group structure in feature selection may degrade performance. Motivated by this
fact, we formulate the problem as an online group feature selection. The
problem assumes that features are generated individually but there are group
structure in the feature stream. To the best of our knowledge, this is the
first time that the correlation among feature stream has been considered in the
online feature selection process. To solve this problem, we develop a novel
online group feature selection method named OGFS. Our proposed approach
consists of two stages: online intra-group selection and online inter-group
selection. In the intra-group selection, we design a criterion based on
spectral analysis to select discriminative features in each group. In the
inter-group selection, we utilize a linear regression model to select an
optimal subset. This two-stage procedure continues until there are no more
features arriving or some predefined stopping conditions are met. %Our method
has been applied Finally, we apply our method to multiple tasks including image
classification %, face verification and face verification. Extensive empirical
studies performed on real-world and benchmark data sets demonstrate that our
method outperforms other state-of-the-art online feature selection %method
methods.
| Jing Wang and Meng Wang and Peipei Li and Luoqi Liu and Zhongqiu Zhao
and Xuegang Hu and Xindong Wu | 10.1109/TKDE.2015.2441716 | 1608.05889 | null | null |
Probabilistic Knowledge Graph Construction: Compositional and
Incremental Approaches | stat.ML cs.AI cs.LG | Knowledge graph construction consists of two tasks: extracting information
from external resources (knowledge population) and inferring missing
information through a statistical analysis on the extracted information
(knowledge completion). In many cases, insufficient external resources in the
knowledge population hinder the subsequent statistical inference. The gap
between these two processes can be reduced by an incremental population
approach. We propose a new probabilistic knowledge graph factorisation method
that benefits from the path structure of existing knowledge (e.g. syllogism)
and enables a common modelling approach to be used for both incremental
population and knowledge completion tasks. More specifically, the probabilistic
formulation allows us to develop an incremental population algorithm that
trades off exploitation-exploration. Experiments on three benchmark datasets
show that the balanced exploitation-exploration helps the incremental
population, and the additional path structure helps to predict missing
information in knowledge completion.
| Dongwoo Kim, Lexing Xie, Cheng Soon Ong | 10.1145/2983323.2983677 | 1608.05921 | null | null |
Distributed Representations for Biological Sequence Analysis | cs.LG q-bio.QM | Biological sequence comparison is a key step in inferring the relatedness of
various organisms and the functional similarity of their components. Thanks to
the Next Generation Sequencing efforts, an abundance of sequence data is now
available to be processed for a range of bioinformatics applications. Embedding
a biological sequence over a nucleotide or amino acid alphabet in a lower
dimensional vector space makes the data more amenable for use by current
machine learning tools, provided the quality of embedding is high and it
captures the most meaningful information of the original sequences. Motivated
by recent advances in the text document embedding literature, we present a new
method, called seq2vec, to represent a complete biological sequence in an
Euclidean space. The new representation has the potential to capture the
contextual information of the original sequence necessary for sequence
comparison tasks. We test our embeddings with protein sequence classification
and retrieval tasks and demonstrate encouraging outcomes.
| Dhananjay Kimothi, Akshay Soni, Pravesh Biyani, James M. Hogan | null | 1608.05949 | null | null |
Inverting Variational Autoencoders for Improved Generative Accuracy | cs.LG stat.ML | Recent advances in semi-supervised learning with deep generative models have
shown promise in generalizing from small labeled datasets
($\mathbf{x},\mathbf{y}$) to large unlabeled ones ($\mathbf{x}$). In the case
where the codomain has known structure, a large unfeatured dataset
($\mathbf{y}$) is potentially available. We develop a parameter-efficient, deep
semi-supervised generative model for the purpose of exploiting this untapped
data source. Empirical results show improved performance in disentangling
latent variable semantics as well as improved discriminative prediction on
Martian spectroscopic and handwritten digit domains.
| Ian Gemp, Ishan Durugkar, Mario Parente, M. Darby Dyar, Sridhar
Mahadevan | null | 1608.05983 | null | null |
A Non-convex One-Pass Framework for Generalized Factorization Machine
and Rank-One Matrix Sensing | stat.ML cs.LG | We develop an efficient alternating framework for learning a generalized
version of Factorization Machine (gFM) on steaming data with provable
guarantees. When the instances are sampled from $d$ dimensional random Gaussian
vectors and the target second order coefficient matrix in gFM is of rank $k$,
our algorithm converges linearly, achieves $O(\epsilon)$ recovery error after
retrieving $O(k^{3}d\log(1/\epsilon))$ training instances, consumes $O(kd)$
memory in one-pass of dataset and only requires matrix-vector product
operations in each iteration. The key ingredient of our framework is a
construction of an estimation sequence endowed with a so-called Conditionally
Independent RIP condition (CI-RIP). As special cases of gFM, our framework can
be applied to symmetric or asymmetric rank-one matrix sensing problems, such as
inductive matrix completion and phase retrieval.
| Ming Lin and Jieping Ye | null | 1608.05995 | null | null |
Distributed Probabilistic Bisection Search using Social Learning | cs.SI cs.LG cs.MA | We present a novel distributed probabilistic bisection algorithm using social
learning with application to target localization. Each agent in the network
first constructs a query about the target based on its local information and
obtains a noisy response. Agents then perform a Bayesian update of their
beliefs followed by an averaging of the log beliefs over local neighborhoods.
This two stage algorithm consisting of repeated querying and averaging runs
until convergence. We derive bounds on the rate of convergence of the beliefs
at the correct target location. Numerical simulations show that our method
outperforms current state of the art methods.
| Athanasios Tsiligkaridis and Theodoros Tsiligkaridis | null | 1608.06007 | null | null |
Feedback-Controlled Sequential Lasso Screening | cs.LG cs.AI cs.CV stat.ML | One way to solve lasso problems when the dictionary does not fit into
available memory is to first screen the dictionary to remove unneeded features.
Prior research has shown that sequential screening methods offer the greatest
promise in this endeavor. Most existing work on sequential screening targets
the context of tuning parameter selection, where one screens and solves a
sequence of $N$ lasso problems with a fixed grid of geometrically spaced
regularization parameters. In contrast, we focus on the scenario where a target
regularization parameter has already been chosen via cross-validated model
selection, and we then need to solve many lasso instances using this fixed
value. In this context, we propose and explore a feedback controlled sequential
screening scheme. Feedback is used at each iteration to select the next problem
to be solved. This allows the sequence of problems to be adapted to the
instance presented and the number of intermediate problems to be automatically
selected. We demonstrate our feedback scheme using several datasets including a
dictionary of approximate size 100,000 by 300,000.
| Yun Wang, Xu Chen and Peter J. Ramadge | null | 1608.0601 | null | null |
The Symmetry of a Simple Optimization Problem in Lasso Screening | cs.LG cs.AI cs.CV stat.ML | Recently dictionary screening has been proposed as an effective way to
improve the computational efficiency of solving the lasso problem, which is one
of the most commonly used method for learning sparse representations. To
address today's ever increasing large dataset, effective screening relies on a
tight region bound on the solution to the dual lasso. Typical region bounds are
in the form of an intersection of a sphere and multiple half spaces. One way to
tighten the region bound is using more half spaces, which however, adds to the
overhead of solving the high dimensional optimization problem in lasso
screening. This paper reveals the interesting property that the optimization
problem only depends on the projection of features onto the subspace spanned by
the normals of the half spaces. This property converts an optimization problem
in high dimension to much lower dimension, and thus sheds light on reducing the
computation overhead of lasso screening based on tighter region bounds.
| Yun Wang and Peter J. Ramadge | null | 1608.06014 | null | null |
Surprisal-Driven Feedback in Recurrent Networks | cs.LG cs.NE | Recurrent neural nets are widely used for predicting temporal data. Their
inherent deep feedforward structure allows learning complex sequential
patterns. It is believed that top-down feedback might be an important missing
ingredient which in theory could help disambiguate similar patterns depending
on broader context. In this paper we introduce surprisal-driven recurrent
networks, which take into account past error information when making new
predictions. This is achieved by continuously monitoring the discrepancy
between most recent predictions and the actual observations. Furthermore, we
show that it outperforms other stochastic and fully deterministic approaches on
enwik8 character level prediction task achieving 1.37 BPC on the test portion
of the text.
| Kamil M Rocki | null | 1608.06027 | null | null |
Towards Instance Optimal Bounds for Best Arm Identification | cs.LG cs.DS stat.ML | In the classical best arm identification (Best-$1$-Arm) problem, we are given
$n$ stochastic bandit arms, each associated with a reward distribution with an
unknown mean. We would like to identify the arm with the largest mean with
probability at least $1-\delta$, using as few samples as possible.
Understanding the sample complexity of Best-$1$-Arm has attracted significant
attention since the last decade. However, the exact sample complexity of the
problem is still unknown.
Recently, Chen and Li made the gap-entropy conjecture concerning the instance
sample complexity of Best-$1$-Arm. Given an instance $I$, let $\mu_{[i]}$ be
the $i$th largest mean and $\Delta_{[i]}=\mu_{[1]}-\mu_{[i]}$ be the
corresponding gap. $H(I)=\sum_{i=2}^n\Delta_{[i]}^{-2}$ is the complexity of
the instance. The gap-entropy conjecture states that
$\Omega\left(H(I)\cdot\left(\ln\delta^{-1}+\mathsf{Ent}(I)\right)\right)$ is an
instance lower bound, where $\mathsf{Ent}(I)$ is an entropy-like term
determined by the gaps, and there is a $\delta$-correct algorithm for
Best-$1$-Arm with sample complexity
$O\left(H(I)\cdot\left(\ln\delta^{-1}+\mathsf{Ent}(I)\right)+\Delta_{[2]}^{-2}\ln\ln\Delta_{[2]}^{-1}\right)$.
If the conjecture is true, we would have a complete understanding of the
instance-wise sample complexity of Best-$1$-Arm.
We make significant progress towards the resolution of the gap-entropy
conjecture. For the upper bound, we provide a highly nontrivial algorithm which
requires \[O\left(H(I)\cdot\left(\ln\delta^{-1}
+\mathsf{Ent}(I)\right)+\Delta_{[2]}^{-2}\ln\ln\Delta_{[2]}^{-1}\mathrm{polylog}(n,\delta^{-1})\right)\]
samples in expectation. For the lower bound, we show that for any Gaussian
Best-$1$-Arm instance with gaps of the form $2^{-k}$, any $\delta$-correct
monotone algorithm requires $\Omega\left(H(I)\cdot\left(\ln\delta^{-1} +
\mathsf{Ent}(I)\right)\right)$ samples in expectation.
| Lijie Chen, Jian Li, Mingda Qiao | null | 1608.06031 | null | null |
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