Consistency in Models for Distributed Learning under Communication Constraints

Motivated by sensor networks and other distributed settings, several models for distributed learning are presented. The models differ from classical works in statistical pattern recognition by allocating observations of an independent and identically distributed (i.i.d.) sampling process amongst members of a network of simple learning agents. The agents are limited in their ability to communicate to a central fusion center and thus, the amount of information available for use in classification or regression is constrained. For several basic communication models in both the binary classification and regression frameworks, we question the existence of agent decision rules and fusion rules that result in a universally consistent ensemble. The answers to this question present new issues to consider with regard to universal consistency. Insofar as these models present a useful picture of distributed scenarios, this paper addresses the issue of whether or not the guarantees provided by Stone's Theorem in centralized environments hold in distributed settings.Comment: To appear in the IEEE Transactions on Information Theor

Distributed Learning in Wireless Sensor Networks

The problem of distributed or decentralized detection and estimation in applications such as wireless sensor networks has often been considered in the framework of parametric models, in which strong assumptions are made about a statistical description of nature. In certain applications, such assumptions are warranted and systems designed from these models show promise. However, in other scenarios, prior knowledge is at best vague and translating such knowledge into a statistical model is undesirable. Applications such as these pave the way for a nonparametric study of distributed detection and estimation. In this paper, we review recent work of the authors in which some elementary models for distributed learning are considered. These models are in the spirit of classical work in nonparametric statistics and are applicable to wireless sensor networks.Comment: Published in the Proceedings of the 42nd Annual Allerton Conference on Communication, Control and Computing, University of Illinois, 200

Distributed Machine Learning via Sufficient Factor Broadcasting

Matrix-parametrized models, including multiclass logistic regression and sparse coding, are used in machine learning (ML) applications ranging from computer vision to computational biology. When these models are applied to large-scale ML problems starting at millions of samples and tens of thousands of classes, their parameter matrix can grow at an unexpected rate, resulting in high parameter synchronization costs that greatly slow down distributed learning. To address this issue, we propose a Sufficient Factor Broadcasting (SFB) computation model for efficient distributed learning of a large family of matrix-parameterized models, which share the following property: the parameter update computed on each data sample is a rank-1 matrix, i.e., the outer product of two "sufficient factors" (SFs). By broadcasting the SFs among worker machines and reconstructing the update matrices locally at each worker, SFB improves communication efficiency --- communication costs are linear in the parameter matrix's dimensions, rather than quadratic --- without affecting computational correctness. We present a theoretical convergence analysis of SFB, and empirically corroborate its efficiency on four different matrix-parametrized ML models

Distributed Regression in Sensor Networks: Training Distributively with Alternating Projections

Wireless sensor networks (WSNs) have attracted considerable attention in recent years and motivate a host of new challenges for distributed signal processing. The problem of distributed or decentralized estimation has often been considered in the context of parametric models. However, the success of parametric methods is limited by the appropriateness of the strong statistical assumptions made by the models. In this paper, a more flexible nonparametric model for distributed regression is considered that is applicable in a variety of WSN applications including field estimation. Here, starting with the standard regularized kernel least-squares estimator, a message-passing algorithm for distributed estimation in WSNs is derived. The algorithm can be viewed as an instantiation of the successive orthogonal projection (SOP) algorithm. Various practical aspects of the algorithm are discussed and several numerical simulations validate the potential of the approach.Comment: To appear in the Proceedings of the SPIE Conference on Advanced Signal Processing Algorithms, Architectures and Implementations XV, San Diego, CA, July 31 - August 4, 200

Distributed Kernel Regression: An Algorithm for Training Collaboratively

This paper addresses the problem of distributed learning under communication constraints, motivated by distributed signal processing in wireless sensor networks and data mining with distributed databases. After formalizing a general model for distributed learning, an algorithm for collaboratively training regularized kernel least-squares regression estimators is derived. Noting that the algorithm can be viewed as an application of successive orthogonal projection algorithms, its convergence properties are investigated and the statistical behavior of the estimator is discussed in a simplified theoretical setting.Comment: To be presented at the 2006 IEEE Information Theory Workshop, Punta del Este, Uruguay, March 13-17, 200

Pervasive Parallel And Distributed Computing In A Liberal Arts College Curriculum

We present a model for incorporating parallel and distributed computing (PDC) throughout an undergraduate CS curriculum. Our curriculum is designed to introduce students early to parallel and distributed computing topics and to expose students to these topics repeatedly in the context of a wide variety of CS courses. The key to our approach is the development of a required intermediate-level course that serves as a introduction to computer systems and parallel computing. It serves as a requirement for every CS major and minor and is a prerequisite to upper-level courses that expand on parallel and distributed computing topics in different contexts. With the addition of this new course, we are able to easily make room in upper-level courses to add and expand parallel and distributed computing topics. The goal of our curricular design is to ensure that every graduating CS major has exposure to parallel and distributed computing, with both a breadth and depth of coverage. Our curriculum is particularly designed for the constraints of a small liberal arts college, however, much of its ideas and its design are applicable to any undergraduate CS curriculum