# Generalizing to unseen domains via distribution matching

## TL;DR

This paper introduces a domain generalization method based on distribution matching that minimizes discrepancies between training domains to improve performance on unseen domains, validated on benchmarks and real-world EEG data.

## Contribution

It provides a theoretical framework and an adversarial training approach for domain generalization, outperforming existing methods on benchmarks and real EEG data.

## Key findings

- Outperforms recent methods on standard benchmarks
- Effective in real-world EEG domain generalization
- Theoretical generalization bound derived

## Abstract

Supervised learning results typically rely on assumptions of i.i.d. data. Unfortunately, those assumptions are commonly violated in practice. In this work, we tackle such problem by focusing on domain generalization: a formalization where the data generating process at test time may yield samples from never-before-seen domains (distributions). Our work relies on the following lemma: by minimizing a notion of discrepancy between all pairs from a set of given domains, we also minimize the discrepancy between any pairs of mixtures of domains. Using this result, we derive a generalization bound for our setting. We then show that low risk over unseen domains can be achieved by representing the data in a space where (i) the training distributions are indistinguishable, and (ii) relevant information for the task at hand is preserved. Minimizing the terms in our bound yields an adversarial formulation which estimates and minimizes pairwise discrepancies. We validate our proposed strategy on standard domain generalization benchmarks, outperforming a number of recently introduced methods. Notably, we tackle a real-world application where the underlying data corresponds to multi-channel electroencephalography time series from different subjects, each considered as a distinct domain.