Joint Distribution Optimal Transportation for Domain Adaptation

TL;DR

This paper introduces a novel optimal transport-based method for unsupervised domain adaptation that estimates a target prediction function without labeled target data by aligning joint distributions.

Contribution

It proposes a joint distribution optimal transport approach that simultaneously optimizes the coupling and the prediction function, with proven convergence and applicability to classification and regression.

Findings

Achieves or surpasses state-of-the-art results on real-world tasks

Provides an efficient algorithm with convergence guarantees

Demonstrates versatility across different hypothesis classes and loss functions

Abstract

This paper deals with the unsupervised domain adaptation problem, where one wants to estimate a prediction function $f$ in a given target domain without any labeled sample by exploiting the knowledge available from a source domain where labels are known. Our work makes the following assumption: there exists a non-linear transformation between the joint feature/label space distributions of the two domain $\mathcal{P}_s$ and $\mathcal{P}_t$. We propose a solution of this problem with optimal transport, that allows to recover an estimated target $\mathcal{P}^f_t=(X,f(X))$ by optimizing simultaneously the optimal coupling and $f$. We show that our method corresponds to the minimization of a bound on the target error, and provide an efficient algorithmic solution, for which convergence is proved. The versatility of our approach, both in terms of class of hypothesis or loss functions is demonstrated with real world classification and regression problems, for which we reach or surpass state-of-the-art results.