Mapping conditional distributions for domain adaptation under generalized target shift

TL;DR

This paper introduces a novel optimal transport-based method for unsupervised domain adaptation under generalized target shift, effectively aligning source and target distributions without relying on restrictive invariance assumptions.

Contribution

It proposes a flexible, scalable approach using neural networks to learn an optimal transport map that aligns conditional distributions across domains, with strong theoretical guarantees.

Findings

Outperforms state-of-the-art methods on multiple datasets

Recovers target class proportions accurately

Provides theoretical guarantees on alignment and generalization

Abstract

We consider the problem of unsupervised domain adaptation (UDA) between a source and a target domain under conditional and label shift a.k.a Generalized Target Shift (GeTarS). Unlike simpler UDA settings, few works have addressed this challenging problem. Recent approaches learn domain-invariant representations, yet they have practical limitations and rely on strong assumptions that may not hold in practice. In this paper, we explore a novel and general approach to align pretrained representations, which circumvents existing drawbacks. Instead of constraining representation invariance, it learns an optimal transport map, implemented as a NN, which maps source representations onto target ones. Our approach is flexible and scalable, it preserves the problem's structure and it has strong theoretical guarantees under mild assumptions. In particular, our solution is unique, matches conditional distributions across domains, recovers target proportions and explicitly controls the target generalization risk. Through an exhaustive comparison on several datasets, we challenge the state-of-the-art in GeTarS.