25,764 research outputs found
Generalized Information Bottleneck for Gaussian Variables
The information bottleneck (IB) method offers an attractive framework for
understanding representation learning, however its applications are often
limited by its computational intractability. Analytical characterization of the
IB method is not only of practical interest, but it can also lead to new
insights into learning phenomena. Here we consider a generalized IB problem, in
which the mutual information in the original IB method is replaced by
correlation measures based on Renyi and Jeffreys divergences. We derive an
exact analytical IB solution for the case of Gaussian correlated variables. Our
analysis reveals a series of structural transitions, similar to those
previously observed in the original IB case. We find further that although
solving the original, Renyi and Jeffreys IB problems yields different
representations in general, the structural transitions occur at the same
critical tradeoff parameters, and the Renyi and Jeffreys IB solutions perform
well under the original IB objective. Our results suggest that formulating the
IB method with alternative correlation measures could offer a strategy for
obtaining an approximate solution to the original IB problem.Comment: 7 pages, 3 figure
Nonlinear Information Bottleneck
Information bottleneck (IB) is a technique for extracting information in one
random variable that is relevant for predicting another random variable
. IB works by encoding in a compressed "bottleneck" random variable
from which can be accurately decoded. However, finding the optimal
bottleneck variable involves a difficult optimization problem, which until
recently has been considered for only two limited cases: discrete and
with small state spaces, and continuous and with a Gaussian joint
distribution (in which case optimal encoding and decoding maps are linear). We
propose a method for performing IB on arbitrarily-distributed discrete and/or
continuous and , while allowing for nonlinear encoding and decoding
maps. Our approach relies on a novel non-parametric upper bound for mutual
information. We describe how to implement our method using neural networks. We
then show that it achieves better performance than the recently-proposed
"variational IB" method on several real-world datasets
Asymptotic Sum-Capacity of Random Gaussian Interference Networks Using Interference Alignment
We consider a dense n-user Gaussian interference network formed by paired
transmitters and receivers placed independently at random in Euclidean space.
Under natural conditions on the node position distributions and signal
attenuation, we prove convergence in probability of the average per-user
capacity C_Sigma/n to 1/2 E log(1 + 2SNR).
The achievability result follows directly from results based on an
interference alignment scheme presented in recent work of Nazer et al. Our main
contribution comes through the converse result, motivated by ideas of
`bottleneck links' developed in recent work of Jafar. An information theoretic
argument gives a capacity bound on such bottleneck links, and probabilistic
counting arguments show there are sufficiently many such links to tightly bound
the sum-capacity of the whole network.Comment: 5 pages; to appear at ISIT 201
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