31,451 research outputs found
Extending Gossip Algorithms to Distributed Estimation of U-Statistics
Efficient and robust algorithms for decentralized estimation in networks are
essential to many distributed systems. Whereas distributed estimation of sample
mean statistics has been the subject of a good deal of attention, computation
of -statistics, relying on more expensive averaging over pairs of
observations, is a less investigated area. Yet, such data functionals are
essential to describe global properties of a statistical population, with
important examples including Area Under the Curve, empirical variance, Gini
mean difference and within-cluster point scatter. This paper proposes new
synchronous and asynchronous randomized gossip algorithms which simultaneously
propagate data across the network and maintain local estimates of the
-statistic of interest. We establish convergence rate bounds of and
for the synchronous and asynchronous cases respectively, where
is the number of iterations, with explicit data and network dependent
terms. Beyond favorable comparisons in terms of rate analysis, numerical
experiments provide empirical evidence the proposed algorithms surpasses the
previously introduced approach.Comment: to be presented at NIPS 201
Distributed Partitioned Big-Data Optimization via Asynchronous Dual Decomposition
In this paper we consider a novel partitioned framework for distributed
optimization in peer-to-peer networks. In several important applications the
agents of a network have to solve an optimization problem with two key
features: (i) the dimension of the decision variable depends on the network
size, and (ii) cost function and constraints have a sparsity structure related
to the communication graph. For this class of problems a straightforward
application of existing consensus methods would show two inefficiencies: poor
scalability and redundancy of shared information. We propose an asynchronous
distributed algorithm, based on dual decomposition and coordinate methods, to
solve partitioned optimization problems. We show that, by exploiting the
problem structure, the solution can be partitioned among the nodes, so that
each node just stores a local copy of a portion of the decision variable
(rather than a copy of the entire decision vector) and solves a small-scale
local problem
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