On Learning Invariant Representation for Domain Adaptation

TL;DR

This paper challenges the assumption that learning domain-invariant features guarantees successful adaptation, introduces a new theoretical bound considering class-conditional shifts, and empirically validates these insights.

Contribution

It provides a counterexample to common beliefs, proposes a new generalization bound accounting for conditional shift, and establishes a fundamental tradeoff via an information-theoretic lower bound.

Findings

Counterexample shows invariance alone is insufficient for adaptation.

A new bound explicitly considers class-conditional distribution shifts.

Experimental results support the theoretical tradeoff and insights.

Abstract

Due to the ability of deep neural nets to learn rich representations, recent advances in unsupervised domain adaptation have focused on learning domain-invariant features that achieve a small error on the source domain. The hope is that the learnt representation, together with the hypothesis learnt from the source domain, can generalize to the target domain. In this paper, we first construct a simple counterexample showing that, contrary to common belief, the above conditions are not sufficient to guarantee successful domain adaptation. In particular, the counterexample exhibits \emph{conditional shift}: the class-conditional distributions of input features change between source and target domains. To give a sufficient condition for domain adaptation, we propose a natural and interpretable generalization upper bound that explicitly takes into account the aforementioned shift. Moreover, we shed new light on the problem by proving an information-theoretic lower bound on the joint error of \emph{any} domain adaptation method that attempts to learn invariant representations. Our result characterizes a fundamental tradeoff between learning invariant representations and achieving small joint error on both domains when the marginal label distributions differ from source to target. Finally, we conduct experiments on real-world datasets that corroborate our theoretical findings. We believe these insights are helpful in guiding the future design of domain adaptation and representation learning algorithms.