# Domain Generalization by Functional Regression

arXiv: https://arxiv.org/abs/2302.04724 · HTML: https://mlsanity.com/paper/2302.04724/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 26 references that are in the map.
- First posted on arXiv 9 Feb 2023.

## Builds on (most cited first, 6 of 6)

- [Domain Generalization via Invariant Feature Representation](https://mlsanity.com/paper/1301.2115/) (2013)
- [Domain Generalization by Marginal Transfer Learning](https://mlsanity.com/paper/1711.07910/) (2017)
- [Learning Theory for Distribution Regression](https://mlsanity.com/paper/1411.2066/) (2014)
- [Learning linear operators: Infinite-dimensional regression as a well-behaved non-compact inverse problem](https://mlsanity.com/paper/2211.08875/) (2022)
- [Minimax Optimal Kernel Operator Learning via Multilevel Training](https://mlsanity.com/paper/2209.14430/) (2022)
- [Variance-Aware Estimation of Kernel Mean Embedding](https://mlsanity.com/paper/2210.06672/) (2022)

## Built on by (most cited first, 3 of 3)

- [Multiparameter regularization and aggregation in the context of polynomial functional regression](https://mlsanity.com/paper/2405.04147/) (2024)
- [Stabilizing Test-Time Adaptation of High-Dimensional Simulation Surrogates via D-Optimal Statistics](https://mlsanity.com/paper/2602.15820/) (2026)
- [Generalization Analysis of Transformers in Distribution Regression](https://mlsanity.com/paper/2606.29256/) (2026)

## Abstract (arXiv)

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.