Optimal transport method adapts linear regression to rotated data
Researchers prove optimal transport can recover rotations in 2D for scarce target data
A new paper from Brian Britos and Mathias Bourel tackles supervised domain adaptation for linear regression in 2D, where source and target domains differ by a geometric transformation (rotation, translation, or homothety). The authors prove that optimal transport (OT), specifically using p-norm costs with p≥2, can exactly recover the underlying transformation map. This theoretical insight is leveraged into a practical method that first clusters source data with K-means, then applies OT to align clusters, enabling model adaptation even with very limited target data.
The approach emphasizes interpretability over black-box deep learning, making it suitable for fields like geospatial analysis, medical imaging, or robotics where transformations are common. Simulations show significant performance gains over naive baselines. While restricted to R², the work provides both a clear theoretical foundation and a deployable algorithm for regression under geometric shifts, offering a principled way to transfer models across rotated or scaled environments.
- Proven that optimal transport with p-norm cost (p≥2) recovers rotations, translations, and homotheties in R²
- Method combines K-means clustering with optimal transport for adaptation with scarce target data
- Outperforms baseline methods while maintaining interpretability — no deep learning required
Why It Matters
Enables robust model transfer under geometric shifts with limited data, improving regression in fields like robotics and geospatial analysis.