Partial Identifiability for Domain Adaptation

TL;DR

This paper introduces a theoretical framework for partial identifiability in unsupervised domain adaptation, leveraging causal mechanisms and latent variable models to improve the understanding and performance of adaptation methods.

Contribution

It proposes a novel latent variable model with invariant and changing components, establishing conditions for partial identifiability of data and label distributions across domains.

Findings

iMSDA outperforms existing algorithms on benchmarks

Latent variables are shown to be partially identifiable under mild conditions

The framework enhances understanding of distribution shifts in domain adaptation

Abstract

Unsupervised domain adaptation is critical to many real-world applications where label information is unavailable in the target domain. In general, without further assumptions, the joint distribution of the features and the label is not identifiable in the target domain. To address this issue, we rely on the property of minimal changes of causal mechanisms across domains to minimize unnecessary influences of distribution shifts. To encode this property, we first formulate the data-generating process using a latent variable model with two partitioned latent subspaces: invariant components whose distributions stay the same across domains and sparse changing components that vary across domains. We further constrain the domain shift to have a restrictive influence on the changing components. Under mild conditions, we show that the latent variables are partially identifiable, from which it follows that the joint distribution of data and labels in the target domain is also identifiable. Given the theoretical insights, we propose a practical domain adaptation framework called iMSDA. Extensive experimental results reveal that iMSDA outperforms state-of-the-art domain adaptation algorithms on benchmark datasets, demonstrating the effectiveness of our framework.