[Paper Review] Domain Adaptation with Conditional Distribution Matching and Generalized Label Shift

Rémi Tachet, Han Zhao+2 more|arXiv (Cornell University)|Mar 10, 2020

Domain Adaptation and Few-Shot LearningComputer Science69 references68 citations

TL;DR

The paper introduces generalized label shift (GLS) and an estimation-based reweighting method to robustify unsupervised domain adaptation when source and target label distributions differ, by aligning reweighted source and target distributions in feature space using IW variants of DANN/JAN/CDAN.

ABSTRACT

Adversarial learning has demonstrated good performance in the unsupervised domain adaptation setting, by learning domain-invariant representations. However, recent work has shown limitations of this approach when label distributions differ between the source and target domains. In this paper, we propose a new assumption, generalized label shift ($GLS$), to improve robustness against mismatched label distributions. $GLS$ states that, conditioned on the label, there exists a representation of the input that is invariant between the source and target domains. Under $GLS$, we provide theoretical guarantees on the transfer performance of any classifier. We also devise necessary and sufficient conditions for $GLS$ to hold, by using an estimation of the relative class weights between domains and an appropriate reweighting of samples. Our weight estimation method could be straightforwardly and generically applied in existing domain adaptation (DA) algorithms that learn domain-invariant representations, with small computational overhead. In particular, we modify three DA algorithms, JAN, DANN and CDAN, and evaluate their performance on standard and artificial DA tasks. Our algorithms outperform the base versions, with vast improvements for large label distribution mismatches. Our code is available at https://tinyurl.com/y585xt6j.

Motivation & Objective

• Motivate robustness of domain adaptation under label distribution mismatch.
• Introduce generalized label shift (GLS) as a condition on representations to support transfer.
• Derive an error decomposition and practical conditions for GLS that guide algorithm design.
• Propose importance-weighted adaptations of DANN, JAN, and CDAN.
• Provide algorithms with theoretical guarantees and empirical validation on standard DA tasks.

Proposed method

• Define GLS: D_S(Z|Y=y) = D_T(Z|Y=y) for all y in Y.
• Propose an error decomposition bound that uses BER (balanced error rate) and conditional error gap under GLS.
• Derive necessary and sufficient conditions for GLS via class weight ratios w_y = D_T(Y=y)/D_S(Y=y) and reweighted feature distributions.
• Estimate w by solving a quadratic program using classifier confusion C and target predictions μ (QP(C, μ)).
• Implement three IW-DA methods (IWDAN, IWJAN, IWCDAN) that weight source samples and/or joint representations to align D_T(˜Z) with D_S^w(˜Z).
• Provide oracle variants (IWDAN-O, IWJAN-O, IWCDAN-O) using true weights for benchmarking.

Experimental results

Research questions

• RQ1 Can GLS provide robust guarantees when label distributions differ across domains?
• RQ2 How can we estimate the target-to-source label ratio w without target labels?
• RQ3 Does aligning the reweighted source distribution with the target distribution in feature space improve DA performance under label shift?
• RQ4 Do importance-weighted variants of DANN, JAN, and CDAN outperform their base versions under large label distribution mismatches?
• RQ5 What are the theoretical and empirical implications of GLS on target error and joint error bounds?

Key findings

• GLS reduces sensitivity to label distribution mismatch by placing label-shift constraints in feature space rather than input space.
• An error decomposition bound shows the source-target error gap can be bounded by the L1 distance between label marginals and the conditional error gap, plus BER.
• A practical weight-estimation approach via a quadratic program yields nonnegative weights w and scales well with k (number of classes).
• IW variants of DANN, JAN, and CDAN outperform their base versions on artificial tasks with large label-mismatch and on standard DA tasks; oracle weights yield even larger gains.
• Gains correlate with the magnitude of label distribution divergence D_JS(D_S^Y, D_T^Y); larger divergences yield larger improvements.
• Ablation studies show most benefits come from reweighting the adversarial loss, with additional gains from weighting the classifier loss.