Inaccuracy rates for distributed inference over random networks with applications to social learning

08/10/2022
by   Dragana Bajović, et al.
0

This paper studies probabilistic rates of convergence for consensus+innovations type of algorithms in random, generic networks. For each node, we find a lower and also a family of upper bounds on the large deviations rate function, thus enabling the computation of the exponential convergence rates for the events of interest on the iterates. Relevant applications include error exponents in distributed hypothesis testing, rates of convergence of beliefs in social learning, and inaccuracy rates in distributed estimation. The bounds on the rate function have a very particular form at each node: they are constructed as the convex envelope between the rate function of the hypothetical fusion center and the rate function corresponding to a certain topological mode of the node's presence. We further show tightness of the discovered bounds for several cases, such as pendant nodes and regular networks, thus establishing the first proof of the large deviations principle for consensus+innovations and social learning in random networks.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
06/24/2022

A Fundamental Limit of Distributed Hypothesis Testing Under Memoryless Quantization

We study a distributed hypothesis testing setup where peripheral nodes s...
research
04/28/2022

On the Arithmetic and Geometric Fusion of Beliefs for Distributed Inference

We study the asymptotic learning rates under linear and log-linear combi...
research
08/22/2020

Distributed Linear Equations over Random Networks

Distributed linear algebraic equation over networks, where nodes hold a ...
research
01/24/2022

Approximation bounds for norm constrained neural networks with applications to regression and GANs

This paper studies the approximation capacity of ReLU neural networks wi...
research
09/14/2023

Rates of Convergence in Certain Native Spaces of Approximations used in Reinforcement Learning

This paper studies convergence rates for some value function approximati...
research
04/25/2017

Stochastic Optimization from Distributed, Streaming Data in Rate-limited Networks

Motivated by machine learning applications in networks of sensors, inter...
research
12/20/2018

Using First Hitting Times to Find Sets that Maximize the Convergence Rate to Consensus

In a model of communication in a social network described by a simple co...

Please sign up or login with your details

Forgot password? Click here to reset