Geometric Domain Adaptation via Optimal Transport for Linear Regression in R^2
Optimal Transport has become recently a powerful method for domain adaptation by aligning source and target distributions. We study a supervised domain adaptation problem where source and target domains are related by a rotation or a translation or a homothety in $\mathbb{R}^2$. We prove that the optimal transport map recovers the underlying map when using a $p-$norm cost with $p \geq 2$. Based on this insight, we develop a method combining $K-$means and optimal transport to estimate the underlying map, enabling adaptation of linear regression models when target data is scarce. Simulations demonstrate improved performance over baseline methods. Rather than relying on highly expressive dee...
| Authors | Brian Britos, Mathias Bourel |
|---|---|
| Primary category | stat.ML |
| Published | 12 June 2026 |
| Last updated at source | 12 June 2026 |
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