Joint-product representation learning for domain generalization in classification and regression

In this work, we study the problem of generalizing a prediction (classification or regression) model trained on a set of source domains to an unseen target domain, where the source and target domains are different but related, i.e, the domain generalization problem. The challenge in this problem lies in the domain difference, which could degrade the generalization ability of the prediction model. To tackle this challenge, we propose to learn a neural network representation function to align a joint distribution and a product distribution in the representation space, and show that such joint-product distribution alignment conveniently leads to the alignment of multiple domains. In particular, we align the joint distribution and the product distribution under the L2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^{2}$$\end{document}-distance, and show that this distance can be analytically estimated by exploiting its variational characterization and a linear variational function. This allows us to comfortably align the two distributions by minimizing the estimated distance with respect to the network representation function. Our experiments on synthetic and real-world datasets for classification and regression demonstrate the effectiveness of the proposed solution. For example, it achieves the best average classification accuracy of 82.26% on the text dataset Amazon Reviews, and the best average regression error of 0.114 on the WiFi dataset UJIIndoorLoc.