Domain Generalization by Functional Regression

TL;DR

This paper introduces a novel approach to domain generalization by framing it as a functional regression problem, enabling models to better adapt to unseen target distributions using a new linear operator learning algorithm.

Contribution

It proposes a new algorithm that learns a linear operator from input distributions to output conditionals, with a source-dependent RKHS construction and finite sample error bounds.

Findings

The algorithm effectively generalizes to new domains.

Finite sample error bounds are established for the method.

Numerical results demonstrate practical applicability.

Abstract

The problem of domain generalization is to learn, given data from different source distributions, a model that can be expected to generalize well on new target distributions which are only seen through unlabeled samples. In this paper, we study domain generalization as a problem of functional regression. Our concept leads to a new algorithm for learning a linear operator from marginal distributions of inputs to the corresponding conditional distributions of outputs given inputs. Our algorithm allows a source distribution-dependent construction of reproducing kernel Hilbert spaces for prediction, and, satisfies finite sample error bounds for the idealized risk. Numerical implementations and source code are available.