Domain Generalization by Functional Regression
This work addresses domain generalization for machine learning models, presenting a novel theoretical approach that is incremental in applying functional regression to this specific problem.
The paper tackles domain generalization by framing it as a functional regression problem, resulting in a new algorithm that learns a linear operator from input marginal distributions to output conditional distributions, with finite sample error bounds provided for the idealized risk.
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.