The Information Sieve

TL;DR

The paper proposes a hierarchical information decomposition framework for unsupervised learning, extracting latent factors that explain data dependence and noise, with applications in ICA, compression, and data imputation.

Contribution

It introduces a novel hierarchical information sieve framework for unsupervised learning, providing a practical implementation for discrete variables and broad applications.

Findings

Effective in independent component analysis

Improves data compression methods

Accurately predicts missing data

Abstract

We introduce a new framework for unsupervised learning of representations based on a novel hierarchical decomposition of information. Intuitively, data is passed through a series of progressively fine-grained sieves. Each layer of the sieve recovers a single latent factor that is maximally informative about multivariate dependence in the data. The data is transformed after each pass so that the remaining unexplained information trickles down to the next layer. Ultimately, we are left with a set of latent factors explaining all the dependence in the original data and remainder information consisting of independent noise. We present a practical implementation of this framework for discrete variables and apply it to a variety of fundamental tasks in unsupervised learning including independent component analysis, lossy and lossless compression, and predicting missing values in data.