Maximally Informative Hierarchical Representations of High-Dimensional Data

TL;DR

This paper introduces a principled, efficient method for constructing hierarchical data representations that maximize information retention, enabling unsupervised deep learning with linear complexity and practical applicability.

Contribution

It develops bounds on information content in hierarchical representations and proposes a simple, scalable optimization procedure for learning maximally informative deep representations.

Findings

Effective hierarchical representations capture most data information.

Linear computational complexity makes the method scalable.

Demonstrated success on synthetic and real-world datasets.

Abstract

We consider a set of probabilistic functions of some input variables as a representation of the inputs. We present bounds on how informative a representation is about input data. We extend these bounds to hierarchical representations so that we can quantify the contribution of each layer towards capturing the information in the original data. The special form of these bounds leads to a simple, bottom-up optimization procedure to construct hierarchical representations that are also maximally informative about the data. This optimization has linear computational complexity and constant sample complexity in the number of variables. These results establish a new approach to unsupervised learning of deep representations that is both principled and practical. We demonstrate the usefulness of the approach on both synthetic and real-world data.