[Paper Review] Mapping conditional distributions for domain adaptation under generalized target shift

Matthieu Kirchmeyer, Alain Rakotomamonjy+2 more|arXiv (Cornell University)|Oct 26, 2021

Domain Adaptation and Few-Shot Learning36 references4 citations

TL;DR

This paper proposes OSTAR, a novel domain adaptation method under Generalized Target Shift (GeTarS) that uses optimal transport via a neural network to map source representations to target ones, preserving discriminative structure and enabling explicit control over target risk. It outperforms state-of-the-art methods by jointly learning a transport map, class proportions, and a classifier with strong theoretical guarantees under mild assumptions.

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.

Motivation & Objective

• Address the challenge of unsupervised domain adaptation under Generalized Target Shift (GeTarS), where both class priors and conditional distributions shift between source and target domains.
• Overcome limitations of existing domain-invariant representation learning methods, such as adversarial instability and loss of discriminative power.
• Preserve the structural integrity of the original problem by avoiding forced representation invariance.
• Provide strong theoretical guarantees for conditional distribution alignment, target proportion recovery, and explicit control of generalization risk.
• Develop a scalable, flexible, and stable method applicable to diverse domains, including non-vision tasks.

Proposed method

• Proposes OSTAR, a method that learns a neural optimal transport (OT) map between source and target conditional distributions to align representations without enforcing domain invariance.
• Uses a shared neural network-based OT map, implemented as a feedforward network with batch normalization and ReLU activations, to map source features to target features.
• Estimates target class proportions via a convex optimization problem using a confusion matrix estimator, enabling sample reweighting in the training objective.
• Jointly optimizes three components: the OT map, class proportion estimation, and a classifier trained on source labels with reweighted loss.
• Employs a Wasserstein-based generalization bound to explicitly control the target risk during optimization.
• Utilizes a two-stage training procedure: first minimizing a combined objective for OT and classification, then refining with a generalized objective for improved alignment.

Experimental results

Research questions

• RQ1 Can a neural optimal transport map effectively align source and target conditional distributions under GeTarS without enforcing domain-invariant representations?
• RQ2 Does OSTAR preserve the discriminative structure of target representations better than domain-invariant methods?
• RQ3 Can OSTAR recover target class proportions accurately and use them to improve generalization risk control?
• RQ4 How does OSTAR compare to state-of-the-art methods in terms of accuracy and robustness across diverse datasets with varying label shifts?
• RQ5 What theoretical guarantees does OSTAR provide under mild assumptions, particularly regarding uniqueness and distribution matching?

Key findings

• OSTAR achieves state-of-the-art performance on Digits, VisDA-12, Office-31, and Office-Home under GeTarS, outperforming methods like IW-WD, MARSc, and MARSg.
• On VisDA-12, OSTAR achieves a top-1 accuracy of 86.7%, surpassing the previous SOTA of 85.2%.
• On Office-31 with high label imbalance, OSTAR improves accuracy by 4.3 percentage points over the best baseline.
• The method recovers target class proportions with high accuracy, as confirmed by ablation studies showing improved performance when proportions are estimated correctly.
• Theoretical analysis confirms that OSTAR’s solution is unique, matches source and target conditionals at the optimum, and provides a Wasserstein-based bound on target risk.
• OSTAR converges faster than baseline methods, requiring only 50 epochs on Digits and 100 on larger datasets, with stable training due to the neural OT map’s inductive bias.