An information-theoretic learning model based on importance sampling

TL;DR

This paper introduces an information-theoretic learning model that uses importance sampling to handle distribution deviations, aiming to improve robustness in real-world applications where training and test distributions differ.

Contribution

It develops a minimax learning framework based on importance sampling and reformulates risk estimation as a minimization problem with a novel connection to p-norm loss.

Findings

Outperforms existing models under large distribution deviations

Reformulates risk minimization as a p-norm loss minimization

Demonstrates effectiveness on face verification datasets

Abstract

A crucial assumption underlying the most current theory of machine learning is that the training distribution is identical to the test distribution. However, this assumption may not hold in some real-world applications. In this paper, we develop a learning model based on principles of information theory by minimizing the worst-case loss at prescribed levels of uncertainty. We reformulate the empirical estimation of the risk functional and the distribution deviation constraint based on the importance sampling method. The objective of the proposed approach is to minimize the loss under maximum degradation and hence the resulting problem is a minimax problem which can be converted to an unconstrained minimum problem using the Lagrange method with the Lagrange multiplier $T$. We reveal that the minimization of the objective function under logarithmic transformation is equivalent to the minimization of the p-norm loss with $p=\frac{1}{T}$. We applied the proposed model to the face verification task on Racial Faces in the Wild datasets and showed that the proposed model performs better under large distribution deviations.