Optimal Transport-Based Domain Adaptation for Rotated Linear Regression
This work addresses domain adaptation challenges in applications like sensor calibration or image orientation, but it is incremental, building on existing OT-based methods for specific geometric transformations.
The paper tackles the problem of domain adaptation for linear regression under rotational shifts, showing that optimal transport can recover the underlying rotation in 2D with p-norm costs, and proposes an algorithm combining K-means, OT, and SVD to estimate rotation angles and adapt models, particularly benefiting sparse target data.
Optimal Transport (OT) has proven effective for domain adaptation (DA) by aligning distributions across domains with differing statistical properties. Building on the approach of Courty et al. (2016), who mapped source data to the target domain for improved model transfer, we focus on a supervised DA problem involving linear regression models under rotational shifts. This ongoing work considers cases where source and target domains are related by a rotation-common in applications like sensor calibration or image orientation. We show that in $\mathbb{R}^2$ , when using a p-norm cost with $p $\ge$ 2$, the optimal transport map recovers the underlying rotation. Based on this, we propose an algorithm that combines K-means clustering, OT, and singular value decomposition (SVD) to estimate the rotation angle and adapt the regression model. This method is particularly effective when the target domain is sparsely sampled, leveraging abundant source data for improved generalization. Our contributions offer both theoretical and practical insights into OT-based model adaptation under geometric transformations.