# Learning relevant features for statistical inference

## TL;DR

This paper introduces a method to identify features most inferable from another data view using deep canonical correlation analysis, enabling joint distribution estimation and improved supervised learning.

## Contribution

The paper demonstrates that features with high correlation in DCCA are optimal for inference and introduces a non-parametric joint distribution representation for various inference tasks.

## Key findings

- Effective inference on occluded MNIST images.
- Representation captures multiple modes of data.
- Automatic regularization and faster convergence in supervised learning.

## Abstract

Given two views of data, we consider the problem of finding the features of one view which can be most faithfully inferred from the other. We find that these are also the most correlated variables in the sense of deep canonical correlation analysis (DCCA). Moreover, we show that these variables can be used to construct a non-parametric representation of the implied joint probability distribution, which can be thought of as a classical version of the Schmidt decomposition of quantum states. This representation can be used to compute the expectations of functions over one view of data conditioned on the other, such as Bayesian estimators and their standard deviations. We test the approach using inference on occluded MNIST images, and show that our representation contains multiple modes. Surprisingly, when applied to supervised learning (one dataset consists of labels), this approach automatically provides regularization and faster convergence compared to the cross-entropy objective. We also explore using this approach to discover salient independent variables of a single dataset.