An information-theoretic learning model based on importance sampling
This addresses distribution shift in machine learning, particularly for face verification, but appears incremental as it builds on existing importance sampling and minimax methods.
The paper tackles the problem of learning when training and test distributions differ by developing an information-theoretic model that minimizes worst-case loss under uncertainty, showing improved performance on face verification tasks with large distribution deviations.
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.