Support and Invertibility in Domain-Invariant Representations
This work addresses theoretical gaps in domain adaptation for machine learning practitioners, offering more robust bounds but is incremental in refining existing approaches.
The paper identifies flaws in theoretical justifications for domain-invariant representations in unsupervised domain adaptation, showing that non-invertible transformations and strict invariance can hinder consistent estimation. It proposes new generalization bounds that account for non-invertibility and support coverage, with experiments on benchmarks illustrating shortcomings of current methods.
Learning domain-invariant representations has become a popular approach to unsupervised domain adaptation and is often justified by invoking a particular suite of theoretical results. We argue that there are two significant flaws in such arguments. First, the results in question hold only for a fixed representation and do not account for information lost in non-invertible transformations. Second, domain invariance is often a far too strict requirement and does not always lead to consistent estimation, even under strong and favorable assumptions. In this work, we give generalization bounds for unsupervised domain adaptation that hold for any representation function by acknowledging the cost of non-invertibility. In addition, we show that penalizing distance between densities is often wasteful and propose a bound based on measuring the extent to which the support of the source domain covers the target domain. We perform experiments on well-known benchmarks that illustrate the short-comings of current standard practice.