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13,002 | $QD$-Learning: A Collaborative Distributed Strategy for Multi-Agent
Reinforcement Learning Through Consensus + Innovations | stat.ML | The paper considers a class of multi-agent Markov decision processes (MDPs),
in which the network agents respond differently (as manifested by the
instantaneous one-stage random costs) to a global controlled state and the
control actions of a remote controller. The paper investigates a distributed
reinforcement learnin... | computer science |
13,003 | New inference strategies for solving Markov Decision Processes using
reversible jump MCMC | cs.LG | In this paper we build on previous work which uses inferences techniques, in
particular Markov Chain Monte Carlo (MCMC) methods, to solve parameterized
control problems. We propose a number of modifications in order to make this
approach more practical in general, higher-dimensional spaces. We first
introduce a new tar... | computer science |
13,004 | Sparse Signal Recovery in the Presence of Intra-Vector and Inter-Vector
Correlation | cs.IT | This work discusses the problem of sparse signal recovery when there is
correlation among the values of non-zero entries. We examine intra-vector
correlation in the context of the block sparse model and inter-vector
correlation in the context of the multiple measurement vector model, as well as
their combination. Algor... | computer science |
13,005 | Equivalence of distance-based and RKHS-based statistics in hypothesis
testing | stat.ME | We provide a unifying framework linking two classes of statistics used in
two-sample and independence testing: on the one hand, the energy distances and
distance covariances from the statistics literature; on the other, maximum mean
discrepancies (MMD), that is, distances between embeddings of distributions to
reproduc... | computer science |
13,006 | Scalable Text and Link Analysis with Mixed-Topic Link Models | cs.LG | Many data sets contain rich information about objects, as well as pairwise
relations between them. For instance, in networks of websites, scientific
papers, and other documents, each node has content consisting of a collection
of words, as well as hyperlinks or citations to other nodes. In order to
perform inference on... | computer science |
13,007 | Optimal Low-Rank Tensor Recovery from Separable Measurements: Four
Contractions Suffice | stat.ML | Tensors play a central role in many modern machine learning and signal
processing applications. In such applications, the target tensor is usually of
low rank, i.e., can be expressed as a sum of a small number of rank one
tensors. This motivates us to consider the problem of low rank tensor recovery
from a class of lin... | computer science |
13,008 | A New Perspective on Boosting in Linear Regression via Subgradient
Optimization and Relatives | math.ST | In this paper we analyze boosting algorithms in linear regression from a new
perspective: that of modern first-order methods in convex optimization. We show
that classic boosting algorithms in linear regression, namely the incremental
forward stagewise algorithm (FS$_\varepsilon$) and least squares boosting
(LS-Boost($... | computer science |
13,009 | Large-scale Machine Learning for Metagenomics Sequence Classification | cs.CE | Metagenomics characterizes the taxonomic diversity of microbial communities
by sequencing DNA directly from an environmental sample. One of the main
challenges in metagenomics data analysis is the binning step, where each
sequenced read is assigned to a taxonomic clade. Due to the large volume of
metagenomics datasets,... | computer science |
13,010 | Proximal Newton-type methods for minimizing composite functions | stat.ML | We generalize Newton-type methods for minimizing smooth functions to handle a
sum of two convex functions: a smooth function and a nonsmooth function with a
simple proximal mapping. We show that the resulting proximal Newton-type
methods inherit the desirable convergence behavior of Newton-type methods for
minimizing s... | computer science |
13,011 | Multiclass Diffuse Interface Models for Semi-Supervised Learning on
Graphs | stat.ML | We present a graph-based variational algorithm for multiclass classification
of high-dimensional data, motivated by total variation techniques. The energy
functional is based on a diffuse interface model with a periodic potential. We
augment the model by introducing an alternative measure of smoothness that
preserves s... | computer science |
13,012 | Coherence and sufficient sampling densities for reconstruction in
compressed sensing | cs.LG | We give a new, very general, formulation of the compressed sensing problem in
terms of coordinate projections of an analytic variety, and derive sufficient
sampling rates for signal reconstruction. Our bounds are linear in the
coherence of the signal space, a geometric parameter independent of the
specific signal and m... | computer science |
13,013 | On the Complexity Analysis of Randomized Block-Coordinate Descent
Methods | math.OC | In this paper we analyze the randomized block-coordinate descent (RBCD)
methods proposed in [8,11] for minimizing the sum of a smooth convex function
and a block-separable convex function. In particular, we extend Nesterov's
technique developed in [8] for analyzing the RBCD method for minimizing a
smooth convex functio... | computer science |
13,014 | Schatten-$p$ Quasi-Norm Regularized Matrix Optimization via Iterative
Reweighted Singular Value Minimization | math.OC | In this paper we study general Schatten-$p$ quasi-norm (SPQN) regularized
matrix minimization problems. In particular, we first introduce a class of
first-order stationary points for them, and show that the first-order
stationary points introduced in [11] for an SPQN regularized $vector$
minimization problem are equiva... | computer science |
13,015 | Robust Large Scale Non-negative Matrix Factorization using Proximal
Point Algorithm | stat.ML | A robust algorithm for non-negative matrix factorization (NMF) is presented
in this paper with the purpose of dealing with large-scale data, where the
separability assumption is satisfied. In particular, we modify the Linear
Programming (LP) algorithm of [9] by introducing a reduced set of constraints
for exact NMF. In... | computer science |
13,016 | Two-stage Sampled Learning Theory on Distributions | math.ST | We focus on the distribution regression problem: regressing to a real-valued
response from a probability distribution. Although there exist a large number
of similarity measures between distributions, very little is known about their
generalization performance in specific learning tasks. Learning problems
formulated on... | computer science |
13,017 | Near-optimal-sample estimators for spherical Gaussian mixtures | cs.LG | Statistical and machine-learning algorithms are frequently applied to
high-dimensional data. In many of these applications data is scarce, and often
much more costly than computation time. We provide the first sample-efficient
polynomial-time estimator for high-dimensional spherical Gaussian mixtures.
For mixtures of... | computer science |
13,018 | Exact Post Model Selection Inference for Marginal Screening | stat.ME | We develop a framework for post model selection inference, via marginal
screening, in linear regression. At the core of this framework is a result that
characterizes the exact distribution of linear functions of the response $y$,
conditional on the model being selected (``condition on selection" framework).
This allows... | computer science |
13,019 | Estimating complex causal effects from incomplete observational data | stat.ME | Despite the major advances taken in causal modeling, causality is still an
unfamiliar topic for many statisticians. In this paper, it is demonstrated from
the beginning to the end how causal effects can be estimated from observational
data assuming that the causal structure is known. To make the problem more
challengin... | computer science |
13,020 | Non-uniform Feature Sampling for Decision Tree Ensembles | stat.ML | We study the effectiveness of non-uniform randomized feature selection in
decision tree classification. We experimentally evaluate two feature selection
methodologies, based on information extracted from the provided dataset: $(i)$
\emph{leverage scores-based} and $(ii)$ \emph{norm-based} feature selection.
Experimenta... | computer science |
13,021 | Topic words analysis based on LDA model | cs.SI | Social network analysis (SNA), which is a research field describing and
modeling the social connection of a certain group of people, is popular among
network services. Our topic words analysis project is a SNA method to visualize
the topic words among emails from Obama.com to accounts registered in Columbus,
Ohio. Base... | computer science |
13,022 | Convex Optimization: Algorithms and Complexity | math.OC | This monograph presents the main complexity theorems in convex optimization
and their corresponding algorithms. Starting from the fundamental theory of
black-box optimization, the material progresses towards recent advances in
structural optimization and stochastic optimization. Our presentation of
black-box optimizati... | computer science |
13,023 | Cumulative Restricted Boltzmann Machines for Ordinal Matrix Data
Analysis | stat.ML | Ordinal data is omnipresent in almost all multiuser-generated feedback -
questionnaires, preferences etc. This paper investigates modelling of ordinal
data with Gaussian restricted Boltzmann machines (RBMs). In particular, we
present the model architecture, learning and inference procedures for both
vector-variate and ... | computer science |
13,024 | Block stochastic gradient iteration for convex and nonconvex
optimization | math.OC | The stochastic gradient (SG) method can minimize an objective function
composed of a large number of differentiable functions, or solve a stochastic
optimization problem, to a moderate accuracy. The block coordinate
descent/update (BCD) method, on the other hand, handles problems with multiple
blocks of variables by up... | computer science |
13,025 | Relax, no need to round: integrality of clustering formulations | stat.ML | We study exact recovery conditions for convex relaxations of point cloud
clustering problems, focusing on two of the most common optimization problems
for unsupervised clustering: $k$-means and $k$-median clustering. Motivations
for focusing on convex relaxations are: (a) they come with a certificate of
optimality, and... | computer science |
13,026 | High Dimensional Low Rank plus Sparse Matrix Decomposition | cs.NA | This paper is concerned with the problem of low rank plus sparse matrix
decomposition for big data. Conventional algorithms for matrix decomposition
use the entire data to extract the low-rank and sparse components, and are
based on optimization problems with complexity that scales with the dimension
of the data, which... | computer science |
13,027 | Spectral Sparsification of Random-Walk Matrix Polynomials | cs.DS | We consider a fundamental algorithmic question in spectral graph theory:
Compute a spectral sparsifier of random-walk matrix-polynomial
$$L_\alpha(G)=D-\sum_{r=1}^d\alpha_rD(D^{-1}A)^r$$ where $A$ is the adjacency
matrix of a weighted, undirected graph, $D$ is the diagonal matrix of weighted
degrees, and $\alpha=(\alph... | computer science |
13,028 | Supersparse Linear Integer Models for Optimized Medical Scoring Systems | stat.ML | Scoring systems are linear classification models that only require users to
add, subtract and multiply a few small numbers in order to make a prediction.
These models are in widespread use by the medical community, but are difficult
to learn from data because they need to be accurate and sparse, have coprime
integer co... | computer science |
13,029 | A New Sampling Technique for Tensors | stat.ML | In this paper we propose new techniques to sample arbitrary third-order
tensors, with an objective of speeding up tensor algorithms that have recently
gained popularity in machine learning. Our main contribution is a new way to
select, in a biased random way, only $O(n^{1.5}/\epsilon^2)$ of the possible
$n^3$ elements ... | computer science |
13,030 | NP-Hardness and Inapproximability of Sparse PCA | cs.LG | We give a reduction from {\sc clique} to establish that sparse PCA is
NP-hard. The reduction has a gap which we use to exclude an FPTAS for sparse
PCA (unless P=NP). Under weaker complexity assumptions, we also exclude
polynomial constant-factor approximation algorithms. | computer science |
13,031 | Approximating Sparse PCA from Incomplete Data | cs.LG | We study how well one can recover sparse principal components of a data
matrix using a sketch formed from a few of its elements. We show that for a
wide class of optimization problems, if the sketch is close (in the spectral
norm) to the original data matrix, then one can recover a near optimal solution
to the optimiza... | computer science |
13,032 | Interpretable Aircraft Engine Diagnostic via Expert Indicator
Aggregation | stat.ML | Detecting early signs of failures (anomalies) in complex systems is one of
the main goal of preventive maintenance. It allows in particular to avoid
actual failures by (re)scheduling maintenance operations in a way that
optimizes maintenance costs. Aircraft engine health monitoring is one
representative example of a fi... | computer science |
13,033 | Distributed Gaussian Learning over Time-varying Directed Graphs | math.OC | We present a distributed (non-Bayesian) learning algorithm for the problem of
parameter estimation with Gaussian noise. The algorithm is expressed as
explicit updates on the parameters of the Gaussian beliefs (i.e. means and
precision). We show a convergence rate of $O(1/k)$ with the constant term
depending on the numb... | computer science |
13,034 | An equation-of-state-meter of QCD transition from deep learning | cs.LG | Supervised learning with a deep convolutional neural network is used to
identify the QCD equation of state (EoS) employed in relativistic hydrodynamic
simulations of heavy-ion collisions from the simulated final-state particle
spectra $\rho(p_T,\Phi)$. High-level correlations of $\rho(p_T,\Phi)$ learned
by the neural n... | computer science |
13,035 | Correlated signal inference by free energy exploration | stat.ML | The inference of correlated signal fields with unknown correlation structures
is of high scientific and technological relevance, but poses significant
conceptual and numerical challenges. To address these, we develop the
correlated signal inference (CSI) algorithm within information field theory
(IFT) and discuss its n... | computer science |
13,036 | Iterative Hard Thresholding Methods for $l_0$ Regularized Convex Cone
Programming | math.OC | In this paper we consider $l_0$ regularized convex cone programming problems.
In particular, we first propose an iterative hard thresholding (IHT) method and
its variant for solving $l_0$ regularized box constrained convex programming.
We show that the sequence generated by these methods converges to a local
minimizer.... | computer science |
13,037 | Network Sampling: From Static to Streaming Graphs | cs.SI | Network sampling is integral to the analysis of social, information, and
biological networks. Since many real-world networks are massive in size,
continuously evolving, and/or distributed in nature, the network structure is
often sampled in order to facilitate study. For these reasons, a more thorough
and complete unde... | computer science |
13,038 | The Algebraic Combinatorial Approach for Low-Rank Matrix Completion | cs.LG | We present a novel algebraic combinatorial view on low-rank matrix completion
based on studying relations between a few entries with tools from algebraic
geometry and matroid theory. The intrinsic locality of the approach allows for
the treatment of single entries in a closed theoretical and practical
framework. More s... | computer science |
13,039 | Demystifying Information-Theoretic Clustering | cs.LG | We propose a novel method for clustering data which is grounded in
information-theoretic principles and requires no parametric assumptions.
Previous attempts to use information theory to define clusters in an
assumption-free way are based on maximizing mutual information between data and
cluster labels. We demonstrate ... | computer science |
13,040 | Stochastic blockmodel approximation of a graphon: Theory and consistent
estimation | stat.ME | Non-parametric approaches for analyzing network data based on exchangeable
graph models (ExGM) have recently gained interest. The key object that defines
an ExGM is often referred to as a graphon. This non-parametric perspective on
network modeling poses challenging questions on how to make inference on the
graphon und... | computer science |
13,041 | Learning Mixtures of Discrete Product Distributions using Spectral
Decompositions | stat.ML | We study the problem of learning a distribution from samples, when the
underlying distribution is a mixture of product distributions over discrete
domains. This problem is motivated by several practical applications such as
crowd-sourcing, recommendation systems, and learning Boolean functions. The
existing solutions e... | computer science |
13,042 | Near-Optimal Entrywise Sampling for Data Matrices | cs.LG | We consider the problem of selecting non-zero entries of a matrix $A$ in
order to produce a sparse sketch of it, $B$, that minimizes $\|A-B\|_2$. For
large $m \times n$ matrices, such that $n \gg m$ (for example, representing $n$
observations over $m$ attributes) we give sampling distributions that exhibit
four importa... | computer science |
13,043 | Finding sparse solutions of systems of polynomial equations via
group-sparsity optimization | cs.IT | The paper deals with the problem of finding sparse solutions to systems of
polynomial equations possibly perturbed by noise. In particular, we show how
these solutions can be recovered from group-sparse solutions of a derived
system of linear equations. Then, two approaches are considered to find these
group-sparse sol... | computer science |
13,044 | Semi-Stochastic Gradient Descent Methods | stat.ML | In this paper we study the problem of minimizing the average of a large
number ($n$) of smooth convex loss functions. We propose a new method, S2GD
(Semi-Stochastic Gradient Descent), which runs for one or several epochs in
each of which a single full gradient and a random number of stochastic
gradients is computed, fo... | computer science |
13,045 | Protein Contact Prediction by Integrating Joint Evolutionary Coupling
Analysis and Supervised Learning | cs.LG | Protein contacts contain important information for protein structure and
functional study, but contact prediction from sequence remains very
challenging. Both evolutionary coupling (EC) analysis and supervised machine
learning methods are developed to predict contacts, making use of different
types of information, resp... | computer science |
13,046 | Model-based functional mixture discriminant analysis with hidden process
regression for curve classification | stat.ME | In this paper, we study the modeling and the classification of functional
data presenting regime changes over time. We propose a new model-based
functional mixture discriminant analysis approach based on a specific hidden
process regression model that governs the regime changes over time. Our
approach is particularly a... | computer science |
13,047 | Model-based clustering and segmentation of time series with changes in
regime | stat.ME | Mixture model-based clustering, usually applied to multidimensional data, has
become a popular approach in many data analysis problems, both for its good
statistical properties and for the simplicity of implementation of the
Expectation-Maximization (EM) algorithm. Within the context of a railway
application, this pape... | computer science |
13,048 | Time series modeling by a regression approach based on a latent process | stat.ME | Time series are used in many domains including finance, engineering,
economics and bioinformatics generally to represent the change of a measurement
over time. Modeling techniques may then be used to give a synthetic
representation of such data. A new approach for time series modeling is
proposed in this paper. It cons... | computer science |
13,049 | Piecewise regression mixture for simultaneous functional data clustering
and optimal segmentation | stat.ME | This paper introduces a novel mixture model-based approach for simultaneous
clustering and optimal segmentation of functional data which are curves
presenting regime changes. The proposed model consists in a finite mixture of
piecewise polynomial regression models. Each piecewise polynomial regression
model is associat... | computer science |
13,050 | Modèle à processus latent et algorithme EM pour la régression non
linéaire | math.ST | A non linear regression approach which consists of a specific regression
model incorporating a latent process, allowing various polynomial regression
models to be activated preferentially and smoothly, is introduced in this
paper. The model parameters are estimated by maximum likelihood performed via a
dedicated expeca... | computer science |
13,051 | A regression model with a hidden logistic process for feature extraction
from time series | stat.ME | A new approach for feature extraction from time series is proposed in this
paper. This approach consists of a specific regression model incorporating a
discrete hidden logistic process. The model parameters are estimated by the
maximum likelihood method performed by a dedicated Expectation Maximization
(EM) algorithm. ... | computer science |
13,052 | Linear Coupling: An Ultimate Unification of Gradient and Mirror Descent | cs.DS | First-order methods play a central role in large-scale machine learning. Even
though many variations exist, each suited to a particular problem, almost all
such methods fundamentally rely on two types of algorithmic steps: gradient
descent, which yields primal progress, and mirror descent, which yields dual
progress.
... | computer science |
13,053 | In Defense of MinHash Over SimHash | stat.CO | MinHash and SimHash are the two widely adopted Locality Sensitive Hashing
(LSH) algorithms for large-scale data processing applications. Deciding which
LSH to use for a particular problem at hand is an important question, which has
no clear answer in the existing literature. In this study, we provide a
theoretical answ... | computer science |
13,054 | Sequential Changepoint Approach for Online Community Detection | stat.ML | We present new algorithms for detecting the emergence of a community in large
networks from sequential observations. The networks are modeled using
Erdos-Renyi random graphs with edges forming between nodes in the community
with higher probability. Based on statistical changepoint detection
methodology, we develop thre... | computer science |
13,055 | Neural Hypernetwork Approach for Pulmonary Embolism diagnosis | cs.LG | This work introduces an integrative approach based on Q-analysis with machine
learning. The new approach, called Neural Hypernetwork, has been applied to a
case study of pulmonary embolism diagnosis. The objective of the application of
neural hyper-network to pulmonary embolism (PE) is to improve diagnose for
reducing ... | computer science |
13,056 | Distributed Clustering and Learning Over Networks | math.OC | Distributed processing over networks relies on in-network processing and
cooperation among neighboring agents. Cooperation is beneficial when agents
share a common objective. However, in many applications agents may belong to
different clusters that pursue different objectives. Then, indiscriminate
cooperation will lea... | computer science |
13,057 | Daily Stress Recognition from Mobile Phone Data, Weather Conditions and
Individual Traits | cs.CY | Research has proven that stress reduces quality of life and causes many
diseases. For this reason, several researchers devised stress detection systems
based on physiological parameters. However, these systems require that
obtrusive sensors are continuously carried by the user. In our paper, we
propose an alternative a... | computer science |
13,058 | Exact and Heuristic Algorithms for Semi-Nonnegative Matrix Factorization | math.NA | Given a matrix $M$ (not necessarily nonnegative) and a factorization rank
$r$, semi-nonnegative matrix factorization (semi-NMF) looks for a matrix $U$
with $r$ columns and a nonnegative matrix $V$ with $r$ rows such that $UV$ is
the best possible approximation of $M$ according to some metric. In this paper,
we study th... | computer science |
13,059 | Learning graphical models from the Glauber dynamics | cs.LG | In this paper we consider the problem of learning undirected graphical models
from data generated according to the Glauber dynamics. The Glauber dynamics is
a Markov chain that sequentially updates individual nodes (variables) in a
graphical model and it is frequently used to sample from the stationary
distribution (to... | computer science |
13,060 | Iterative Hessian sketch: Fast and accurate solution approximation for
constrained least-squares | math.OC | We study randomized sketching methods for approximately solving least-squares
problem with a general convex constraint. The quality of a least-squares
approximation can be assessed in different ways: either in terms of the value
of the quadratic objective function (cost approximation), or in terms of some
distance meas... | computer science |
13,061 | Active Inference for Binary Symmetric Hidden Markov Models | stat.ML | We consider active maximum a posteriori (MAP) inference problem for Hidden
Markov Models (HMM), where, given an initial MAP estimate of the hidden
sequence, we select to label certain states in the sequence to improve the
estimation accuracy of the remaining states. We develop an analytical approach
to this problem for... | computer science |
13,062 | Learning Theory for Distribution Regression | math.ST | We focus on the distribution regression problem: regressing to vector-valued
outputs from probability measures. Many important machine learning and
statistical tasks fit into this framework, including multi-instance learning
and point estimation problems without analytical solution (such as
hyperparameter or entropy es... | computer science |
13,063 | Covariate-assisted spectral clustering | stat.ML | Biological and social systems consist of myriad interacting units. The
interactions can be represented in the form of a graph or network. Measurements
of these graphs can reveal the underlying structure of these interactions,
which provides insight into the systems that generated the graphs. Moreover, in
applications s... | computer science |
13,064 | Asymmetric Minwise Hashing | stat.ML | Minwise hashing (Minhash) is a widely popular indexing scheme in practice.
Minhash is designed for estimating set resemblance and is known to be
suboptimal in many applications where the desired measure is set overlap (i.e.,
inner product between binary vectors) or set containment. Minhash has inherent
bias towards sma... | computer science |
13,065 | Characterization of the equivalence of robustification and
regularization in linear and matrix regression | math.ST | The notion of developing statistical methods in machine learning which are
robust to adversarial perturbations in the underlying data has been the subject
of increasing interest in recent years. A common feature of this work is that
the adversarial robustification often corresponds exactly to regularization
methods whi... | computer science |
13,066 | Big Learning with Bayesian Methods | cs.LG | Explosive growth in data and availability of cheap computing resources have
sparked increasing interest in Big learning, an emerging subfield that studies
scalable machine learning algorithms, systems, and applications with Big Data.
Bayesian methods represent one important class of statistic methods for machine
learni... | computer science |
13,067 | Circumventing the Curse of Dimensionality in Prediction: Causal
Rate-Distortion for Infinite-Order Markov Processes | cs.LG | Predictive rate-distortion analysis suffers from the curse of dimensionality:
clustering arbitrarily long pasts to retain information about arbitrarily long
futures requires resources that typically grow exponentially with length. The
challenge is compounded for infinite-order Markov processes, since conditioning
on fi... | computer science |
13,068 | A deep-structured fully-connected random field model for structured
inference | stat.ML | There has been significant interest in the use of fully-connected graphical
models and deep-structured graphical models for the purpose of structured
inference. However, fully-connected and deep-structured graphical models have
been largely explored independently, leaving the unification of these two
concepts ripe for ... | computer science |
13,069 | Improved Error Bounds Based on Worst Likely Assignments | stat.ML | Error bounds based on worst likely assignments use permutation tests to
validate classifiers. Worst likely assignments can produce effective bounds
even for data sets with 100 or fewer training examples. This paper introduces a
statistic for use in the permutation tests of worst likely assignments that
improves error b... | computer science |
13,070 | Signatures of Infinity: Nonergodicity and Resource Scaling in
Prediction, Complexity, and Learning | cs.IT | We introduce a simple analysis of the structural complexity of
infinite-memory processes built from random samples of stationary, ergodic
finite-memory component processes. Such processes are familiar from the well
known multi-arm Bandit problem. We contrast our analysis with
computation-theoretic and statistical infer... | computer science |
13,071 | A Probabilistic $\ell_1$ Method for Clustering High Dimensional Data | math.ST | In general, the clustering problem is NP-hard, and global optimality cannot
be established for non-trivial instances. For high-dimensional data,
distance-based methods for clustering or classification face an additional
difficulty, the unreliability of distances in very high-dimensional spaces. We
propose a distance-ba... | computer science |
13,072 | Deep Convolutional Neural Networks Based on Semi-Discrete Frames | cs.LG | Deep convolutional neural networks have led to breakthrough results in
practical feature extraction applications. The mathematical analysis of these
networks was pioneered by Mallat, 2012. Specifically, Mallat considered
so-called scattering networks based on identical semi-discrete wavelet frames
in each network layer... | computer science |
13,073 | Spectral Learning of Large Structured HMMs for Comparative Epigenomics | stat.ML | We develop a latent variable model and an efficient spectral algorithm
motivated by the recent emergence of very large data sets of chromatin marks
from multiple human cell types. A natural model for chromatin data in one cell
type is a Hidden Markov Model (HMM); we model the relationship between multiple
cell types by... | computer science |
13,074 | Optimal Rates for Random Fourier Features | math.ST | Kernel methods represent one of the most powerful tools in machine learning
to tackle problems expressed in terms of function values and derivatives due to
their capability to represent and model complex relations. While these methods
show good versatility, they are computationally intensive and have poor
scalability t... | computer science |
13,075 | No penalty no tears: Least squares in high-dimensional linear models | stat.ME | Ordinary least squares (OLS) is the default method for fitting linear models,
but is not applicable for problems with dimensionality larger than the sample
size. For these problems, we advocate the use of a generalized version of OLS
motivated by ridge regression, and propose two novel three-step algorithms
involving l... | computer science |
13,076 | Stay on path: PCA along graph paths | stat.ML | We introduce a variant of (sparse) PCA in which the set of feasible support
sets is determined by a graph. In particular, we consider the following
setting: given a directed acyclic graph $G$ on $p$ vertices corresponding to
variables, the non-zero entries of the extracted principal component must
coincide with vertice... | computer science |
13,077 | Sequential Nonparametric Testing with the Law of the Iterated Logarithm | stat.ML | We propose a new algorithmic framework for sequential hypothesis testing with
i.i.d. data, which includes A/B testing, nonparametric two-sample testing, and
independence testing as special cases. It is novel in several ways: (a) it
takes linear time and constant space to compute on the fly, (b) it has the same
power gu... | computer science |
13,078 | Detectability thresholds and optimal algorithms for community structure
in dynamic networks | stat.ML | We study the fundamental limits on learning latent community structure in
dynamic networks. Specifically, we study dynamic stochastic block models where
nodes change their community membership over time, but where edges are
generated independently at each time step. In this setting (which is a special
case of several e... | computer science |
13,079 | Communication Lower Bounds for Statistical Estimation Problems via a
Distributed Data Processing Inequality | cs.LG | We study the tradeoff between the statistical error and communication cost of
distributed statistical estimation problems in high dimensions. In the
distributed sparse Gaussian mean estimation problem, each of the $m$ machines
receives $n$ data points from a $d$-dimensional Gaussian distribution with
unknown mean $\the... | computer science |
13,080 | An Empirical Study of Stochastic Variational Algorithms for the Beta
Bernoulli Process | stat.ML | Stochastic variational inference (SVI) is emerging as the most promising
candidate for scaling inference in Bayesian probabilistic models to large
datasets. However, the performance of these methods has been assessed primarily
in the context of Bayesian topic models, particularly latent Dirichlet
allocation (LDA). Deri... | computer science |
13,081 | Categorical Matrix Completion | cs.NA | We consider the problem of completing a matrix with categorical-valued
entries from partial observations. This is achieved by extending the
formulation and theory of one-bit matrix completion. We recover a low-rank
matrix $X$ by maximizing the likelihood ratio with a constraint on the nuclear
norm of $X$, and the obser... | computer science |
13,082 | Regret Guarantees for Item-Item Collaborative Filtering | cs.LG | There is much empirical evidence that item-item collaborative filtering works
well in practice. Motivated to understand this, we provide a framework to
design and analyze various recommendation algorithms. The setup amounts to
online binary matrix completion, where at each time a random user requests a
recommendation a... | computer science |
13,083 | Multi-scale exploration of convex functions and bandit convex
optimization | math.MG | We construct a new map from a convex function to a distribution on its
domain, with the property that this distribution is a multi-scale exploration
of the function. We use this map to solve a decade-old open problem in
adversarial bandit convex optimization by showing that the minimax regret for
this problem is $\tild... | computer science |
13,084 | Perturbed Iterate Analysis for Asynchronous Stochastic Optimization | stat.ML | We introduce and analyze stochastic optimization methods where the input to
each gradient update is perturbed by bounded noise. We show that this framework
forms the basis of a unified approach to analyze asynchronous implementations
of stochastic optimization algorithms.In this framework, asynchronous
stochastic optim... | computer science |
13,085 | Fast Stochastic Algorithms for SVD and PCA: Convergence Properties and
Convexity | cs.LG | We study the convergence properties of the VR-PCA algorithm introduced by
\cite{shamir2015stochastic} for fast computation of leading singular vectors.
We prove several new results, including a formal analysis of a block version of
the algorithm, and convergence from random initialization. We also make a few
observatio... | computer science |
13,086 | A Linearly-Convergent Stochastic L-BFGS Algorithm | math.OC | We propose a new stochastic L-BFGS algorithm and prove a linear convergence
rate for strongly convex and smooth functions. Our algorithm draws heavily from
a recent stochastic variant of L-BFGS proposed in Byrd et al. (2014) as well as
a recent approach to variance reduction for stochastic gradient descent from
Johnson... | computer science |
13,087 | No Regret Bound for Extreme Bandits | stat.ML | Algorithms for hyperparameter optimization abound, all of which work well
under different and often unverifiable assumptions. Motivated by the general
challenge of sequentially choosing which algorithm to use, we study the more
specific task of choosing among distributions to use for random hyperparameter
optimization.... | computer science |
13,088 | Dimensionality Reduction of Collective Motion by Principal Manifolds | math.NA | While the existence of low-dimensional embedding manifolds has been shown in
patterns of collective motion, the current battery of nonlinear dimensionality
reduction methods are not amenable to the analysis of such manifolds. This is
mainly due to the necessary spectral decomposition step, which limits control
over the... | computer science |
13,089 | Towards an Axiomatic Approach to Hierarchical Clustering of Measures | stat.ML | We propose some axioms for hierarchical clustering of probability measures
and investigate their ramifications. The basic idea is to let the user
stipulate the clusters for some elementary measures. This is done without the
need of any notion of metric, similarity or dissimilarity. Our main results
then show that for e... | computer science |
13,090 | Heavy-tailed Independent Component Analysis | cs.LG | Independent component analysis (ICA) is the problem of efficiently recovering
a matrix $A \in \mathbb{R}^{n\times n}$ from i.i.d. observations of $X=AS$
where $S \in \mathbb{R}^n$ is a random vector with mutually independent
coordinates. This problem has been intensively studied, but all existing
efficient algorithms w... | computer science |
13,091 | Precise Phase Transition of Total Variation Minimization | cs.IT | Characterizing the phase transitions of convex optimizations in recovering
structured signals or data is of central importance in compressed sensing,
machine learning and statistics. The phase transitions of many convex
optimization signal recovery methods such as $\ell_1$ minimization and nuclear
norm minimization are... | computer science |
13,092 | Efficient reconstruction of transmission probabilities in a spreading
process from partial observations | cs.LG | An important problem of reconstruction of diffusion network and transmission
probabilities from the data has attracted a considerable attention in the past
several years. A number of recent papers introduced efficient algorithms for
the estimation of spreading parameters, based on the maximization of the
likelihood of ... | computer science |
13,093 | Detecting phase transitions in collective behavior using manifold's
curvature | math.DS | If a given behavior of a multi-agent system restricts the phase variable to a
invariant manifold, then we define a phase transition as change of physical
characteristics such as speed, coordination, and structure. We define such a
phase transition as splitting an underlying manifold into two sub-manifolds
with distinct... | computer science |
13,094 | Optimization over Sparse Symmetric Sets via a Nonmonotone Projected
Gradient Method | math.OC | We consider the problem of minimizing a Lipschitz differentiable function
over a class of sparse symmetric sets that has wide applications in engineering
and science. For this problem, it is known that any accumulation point of the
classical projected gradient (PG) method with a constant stepsize $1/L$
satisfies the $L... | computer science |
13,095 | Learning without Recall: A Case for Log-Linear Learning | cs.SI | We analyze a model of learning and belief formation in networks in which
agents follow Bayes rule yet they do not recall their history of past
observations and cannot reason about how other agents' beliefs are formed. They
do so by making rational inferences about their observations which include a
sequence of independ... | computer science |
13,096 | Sparse Nonlinear Regression: Parameter Estimation and Asymptotic
Inference | stat.ML | We study parameter estimation and asymptotic inference for sparse nonlinear
regression. More specifically, we assume the data are given by $y = f( x^\top
\beta^* ) + \epsilon$, where $f$ is nonlinear. To recover $\beta^*$, we propose
an $\ell_1$-regularized least-squares estimator. Unlike classical linear
regression, t... | computer science |
13,097 | Generalized Conjugate Gradient Methods for $\ell_1$ Regularized Convex
Quadratic Programming with Finite Convergence | math.OC | The conjugate gradient (CG) method is an efficient iterative method for
solving large-scale strongly convex quadratic programming (QP). In this paper
we propose some generalized CG (GCG) methods for solving the
$\ell_1$-regularized (possibly not strongly) convex QP that terminate at an
optimal solution in a finite numb... | computer science |
13,098 | Where You Are Is Who You Are: User Identification by Matching Statistics | cs.LG | Most users of online services have unique behavioral or usage patterns. These
behavioral patterns can be exploited to identify and track users by using only
the observed patterns in the behavior. We study the task of identifying users
from statistics of their behavioral patterns. Specifically, we focus on the
setting i... | computer science |
13,099 | Convexified Modularity Maximization for Degree-corrected Stochastic
Block Models | math.ST | The stochastic block model (SBM) is a popular framework for studying
community detection in networks. This model is limited by the assumption that
all nodes in the same community are statistically equivalent and have equal
expected degrees. The degree-corrected stochastic block model (DCSBM) is a
natural extension of S... | computer science |
13,100 | Minimum Regret Search for Single- and Multi-Task Optimization | stat.ML | We propose minimum regret search (MRS), a novel acquisition function for
Bayesian optimization. MRS bears similarities with information-theoretic
approaches such as entropy search (ES). However, while ES aims in each query at
maximizing the information gain with respect to the global maximum, MRS aims at
minimizing the... | computer science |
13,101 | DOLPHIn - Dictionary Learning for Phase Retrieval | math.OC | We propose a new algorithm to learn a dictionary for reconstructing and
sparsely encoding signals from measurements without phase. Specifically, we
consider the task of estimating a two-dimensional image from squared-magnitude
measurements of a complex-valued linear transformation of the original image.
Several recent ... | computer science |
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