arXiv subjects

Stephen Wright

Publications and source records attributed to Stephen Wright.

26 records · Page 2Linked to original sources

arXiv2018

ATOMO: Communication-efficient Learning via Atomic Sparsification

Distributed model training suffers from communication overheads due to frequent gradient updates transmitted between compute nodes. To mitigate these overheads, several studies propose the use of sparsified stochastic gradients. We argue that these are facets of a general sparsification method that can operate on any possible atomic decomposition. Notable examples include element-wise, singular value, and Fourier decompositions. We present ATOMO, a general framework for atomic sparsification of stochastic gradients. Given a gradient, an atomic decomposition, and a sparsity budget, ATOMO gives a random unbiased sparsification of the atoms minimizing variance. We show that recent methods such as QSGD and TernGrad are special cases of ATOMO and that sparsifiying the singular value decomposition of neural networks gradients, rather than their coordinates, can lead to significantly faster distributed training.

stat.ML↗

arXiv2018

Dissipativity Theory for Accelerating Stochastic Variance Reduction: A Unified Analysis of SVRG and Katyusha Using Semidefinite Programs

Techniques for reducing the variance of gradient estimates used in stochastic programming algorithms for convex finite-sum problems have received a great deal of attention in recent years. By leveraging dissipativity theory from control, we provide a new perspective on two important variance-reduction algorithms: SVRG and its direct accelerated variant Katyusha. Our perspective provides a physically intuitive understanding of the behavior of SVRG-like methods via a principle of energy conservation. The tools discussed here allow us to automate the convergence analysis of SVRG-like methods by capturing their essential properties in small semidefinite programs amenable to standard analysis and computational techniques. Our approach recovers existing convergence results for SVRG and Katyusha and generalizes the theory to alternative parameter choices. We also discuss how our approach complements the linear coupling technique. Our combination of perspectives leads to a better understanding of accelerated variance-reduced stochastic methods for finite-sum problems.

math.OC↗

arXiv2017

Online Learning for Changing Environments using Coin Betting

A key challenge in online learning is that classical algorithms can be slow to adapt to changing environments. Recent studies have proposed "meta" algorithms that convert any online learning algorithm to one that is adaptive to changing environments, where the adaptivity is analyzed in a quantity called the strongly-adaptive regret. This paper describes a new meta algorithm that has a strongly-adaptive regret bound that is a factor of $\sqrt{\log(T)}$ better than other algorithms with the same time complexity, where $T$ is the time horizon. We also extend our algorithm to achieve a first-order (i.e., dependent on the observed losses) strongly-adaptive regret bound for the first time, to our knowledge. At its heart is a new parameter-free algorithm for the learning with expert advice (LEA) problem in which experts sometimes do not output advice for consecutive time steps (i.e., \emph{sleeping} experts). This algorithm is derived by a reduction from optimal algorithms for the so-called coin betting problem. Empirical results show that our algorithm outperforms state-of-the-art methods in both learning with expert advice and metric learning scenarios.

stat.ML↗

arXiv2017

Improved Strongly Adaptive Online Learning using Coin Betting

This paper describes a new parameter-free online learning algorithm for changing environments. In comparing against algorithms with the same time complexity as ours, we obtain a strongly adaptive regret bound that is a factor of at least $\sqrt{\log(T)}$ better, where $T$ is the time horizon. Empirical results show that our algorithm outperforms state-of-the-art methods in learning with expert advice and metric learning scenarios.

stat.ML↗

arXiv2015

Forward - Backward Greedy Algorithms for Atomic Norm Regularization

In many signal processing applications, the aim is to reconstruct a signal that has a simple representation with respect to a certain basis or frame. Fundamental elements of the basis known as "atoms" allow us to define "atomic norms" that can be used to formulate convex regularizations for the reconstruction problem. Efficient algorithms are available to solve these formulations in certain special cases, but an approach that works well for general atomic norms, both in terms of speed and reconstruction accuracy, remains to be found. This paper describes an optimization algorithm called CoGEnT that produces solutions with succinct atomic representations for reconstruction problems, generally formulated with atomic-norm constraints. CoGEnT combines a greedy selection scheme based on the conditional gradient approach with a backward (or "truncation") step that exploits the quadratic nature of the objective to reduce the basis size. We establish convergence properties and validate the algorithm via extensive numerical experiments on a suite of signal processing applications. Our algorithm and analysis also allow for inexact forward steps and for occasional enhancements of the current representation to be performed. CoGEnT can outperform the basic conditional gradient method, and indeed many methods that are tailored to specific applications, when the enhancement and truncation steps are defined appropriately. We also introduce several novel applications that are enabled by the atomic-norm framework, including tensor completion, moment problems in signal processing, and graph deconvolution.

cs.DS↗

arXiv2013

Genomic identification of founding haplotypes reveals the history of the selfing species Capsella rubella

The shift from outcrossing to self-fertilization is among the most common transitions in plants. Until recently, however, a genome-wide view of this transition has been obscured by a dearth of appropriate data and the lack of appropriate population genomic methods to interpret such data. Here, we present novel analyses detailing the origin of the selfing species, Capsella rubella, which recently split from its outcrossing sister, Capsella grandiflora. Due to the recency of the split, most variation within C. rubella is found within C. grandiflora. We can therefore identify genomic regions where two C. rubella individuals have inherited the same or different segments of ancestral diversity (i.e. founding haplotypes) present in C. rubella's founder(s). Based on this analysis, we show that C. rubella was founded by multiple individuals drawn from a diverse ancestral population closely related to extant C. grandiflora, that drift and selection have rapidly homogenized most of this ancestral variation since C. rubella's founding, and that little novel variation has accumulated within this time. Despite the extensive loss of ancestral variation, the approximately 25% of the genome for which two C. rubella individuals have inherited different founding haplotypes makes up roughly 90% of the genetic variation between them. To extend these findings, we develop a coalescent model that utilizes the inferred frequency of founding haplotypes and variation within founding haplotypes to estimate that C. rubella was founded by a potentially large number of individuals 50-100 kya, and has subsequently experienced a 20X reduction in its effective population size. As population genomic data from an increasing number of outcrossing/selfing pairs are generated, analyses like this here will facilitate a fine-scaled view of the evolutionary and demographic impact of the transition to self-fertilization.

q-bio.PE↗

arXiv2008

LASSO-Patternsearch algorithm with application to ophthalmology and genomic data

The LASSO-Patternsearch algorithm is proposed to efficiently identify patterns of multiple dichotomous risk factors for outcomes of interest in demographic and genomic studies. The patterns considered are those that arise naturally from the log linear expansion of the multivariate Bernoulli density. The method is designed for the case where there is a possibly very large number of candidate patterns but it is believed that only a relatively small number are important. A LASSO is used to greatly reduce the number of candidate patterns, using a novel computational algorithm that can handle an extremely large number of unknowns simultaneously. The patterns surviving the LASSO are further pruned in the framework of (parametric) generalized linear models. A novel tuning procedure based on the GACV for Bernoulli outcomes, modified to act as a model selector, is used at both steps. We applied the method to myopia data from the population-based Beaver Dam Eye Study, exposing physiologically interesting interacting risk factors. We then applied the method to data from a generative model of Rheumatoid Arthritis based on Problem 3 from the Genetic Analysis Workshop 15, successfully demonstrating its potential to efficiently recover higher order patterns from attribute vectors of length typical of genomic studies.

math.ST↗

arXiv2001

Decomposition Algorithms for Stochastic Programming on a Computational Grid

We describe algorithms for two-stage stochastic linear programming with recourse and their implementation on a grid computing platform. In particular, we examine serial and asynchronous versions of the L-shaped method and a trust-region method. The parallel platform of choice is the dynamic, heterogeneous, opportunistic platform provided by the Condor system. The algorithms are of master-worker type (with the workers being used to solve second-stage problems, and the MW runtime support library (which supports master-worker computations) is key to the implementation. Computational results are presented on large sample average approximations of problems from the literature.

math.OC↗