Scalable Vector Gaussian Information Bottleneck

TL;DR

This paper introduces a scalable vector Gaussian information bottleneck model that produces multiple layered representations, optimizing relevance and complexity tradeoffs, with a neural network-based algorithm and experimental validation on MNIST.

Contribution

It develops an analytic characterization for vector Gaussian sources and proposes a neural network-based variational inference algorithm for general sources.

Findings

Optimal relevance-complexity region characterized for vector Gaussian sources.

Proposed method generalizes better to unseen data on MNIST.

Algorithm effectively parametrized with neural networks.

Abstract

In the context of statistical learning, the Information Bottleneck method seeks a right balance between accuracy and generalization capability through a suitable tradeoff between compression complexity, measured by minimum description length, and distortion evaluated under logarithmic loss measure. In this paper, we study a variation of the problem, called scalable information bottleneck, in which the encoder outputs multiple descriptions of the observation with increasingly richer features. The model, which is of successive-refinement type with degraded side information streams at the decoders, is motivated by some application scenarios that require varying levels of accuracy depending on the allowed (or targeted) level of complexity. We establish an analytic characterization of the optimal relevance-complexity region for vector Gaussian sources. Then, we derive a variational inference type algorithm for general sources with unknown distribution; and show means of parametrizing it using neural networks. Finally, we provide experimental results on the MNIST dataset which illustrate that the proposed method generalizes better to unseen data during the training phase.