Deep Variational Sufficient Dimensionality Reduction

TL;DR

This paper introduces DVSDR, a deep variational method for sufficient dimensionality reduction that preserves label information in a low-dimensional embedding, adaptable to semi-supervised learning and capable of data generation.

Contribution

The paper presents a novel deep variational approach for SDR using autoencoders, integrating graphical models and enabling semi-supervised learning.

Findings

DVSDR performs competitively on classification tasks.

It can generate novel data samples.

The method effectively preserves label information in reduced dimensions.

Abstract

We consider the problem of sufficient dimensionality reduction (SDR), where the high-dimensional observation is transformed to a low-dimensional sub-space in which the information of the observations regarding the label variable is preserved. We propose DVSDR, a deep variational approach for sufficient dimensionality reduction. The deep structure in our model has a bottleneck that represent the low-dimensional embedding of the data. We explain the SDR problem using graphical models and use the framework of variational autoencoders to maximize the lower bound of the log-likelihood of the joint distribution of the observation and label. We show that such a maximization problem can be interpreted as solving the SDR problem. DVSDR can be easily adopted to semi-supervised learning setting. In our experiment we show that DVSDR performs competitively on classification tasks while being able to generate novel data samples.