Unnamed: 0
int64
0
41k
title
stringlengths
4
274
category
stringlengths
5
18
summary
stringlengths
22
3.66k
theme
stringclasses
8 values
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