98,072 research outputs found
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 Constrained Recursive Nonlinear Least-Squares Estimation: Algorithms and Asymptotics
This paper focuses on the problem of recursive nonlinear least squares
parameter estimation in multi-agent networks, in which the individual agents
observe sequentially over time an independent and identically distributed
(i.i.d.) time-series consisting of a nonlinear function of the true but unknown
parameter corrupted by noise. A distributed recursive estimator of the
\emph{consensus} + \emph{innovations} type, namely , is
proposed, in which the agents update their parameter estimates at each
observation sampling epoch in a collaborative way by simultaneously processing
the latest locally sensed information~(\emph{innovations}) and the parameter
estimates from other agents~(\emph{consensus}) in the local neighborhood
conforming to a pre-specified inter-agent communication topology. Under rather
weak conditions on the connectivity of the inter-agent communication and a
\emph{global observability} criterion, it is shown that at every network agent,
the proposed algorithm leads to consistent parameter estimates. Furthermore,
under standard smoothness assumptions on the local observation functions, the
distributed estimator is shown to yield order-optimal convergence rates, i.e.,
as far as the order of pathwise convergence is concerned, the local parameter
estimates at each agent are as good as the optimal centralized nonlinear least
squares estimator which would require access to all the observations across all
the agents at all times. In order to benchmark the performance of the proposed
distributed estimator with that of the centralized nonlinear
least squares estimator, the asymptotic normality of the estimate sequence is
established and the asymptotic covariance of the distributed estimator is
evaluated. Finally, simulation results are presented which illustrate and
verify the analytical findings.Comment: 28 pages. Initial Submission: Feb. 2016, Revised: July 2016,
Accepted: September 2016, To appear in IEEE Transactions on Signal and
Information Processing over Networks: Special Issue on Inference and Learning
over Network
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 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
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