Domain Adaptation under Continuous Spurious Shift

TMLR Paper8591 Authors

Abstract: Recent advances in domain adaptation have shown promise in transferring knowledge across domains characterized by a continuous value or vector, such as varying patient ages, where ``age'' serves as a continuous index. However, these approaches often fail when spurious features shift continuously along with the domain index. This paper introduces a new method designed to withstand the continuous shifting of spurious features during domain adaptation. Our method enhances domain adaptation performance by aligning representations across continuously indexed domains, inspired by principles of causal transportability. Theoretical analysis provides insight into how our approach encourages transportable representations across different domains under certain assumptions. Empirical results, from both semi-synthetic and real-world medical datasets, indicate that our method outperforms state-of-the-art domain adaptation methods.

Submission Type: Long submission (more than 12 pages of main content)

Previous TMLR Submission Url: https://openreview.net/forum?id=uYatRBQeVZ

Changes Since Last Submission:

- **Causal Framing (AE Suggestion 1).** Clarified and moderated the **causal framing**, avoiding overstatement and positioning CADA as a **causality-inspired method** for continuous-domain adaptation rather than a fully causal identification procedure.

- **Causal Assumption (AE Suggestion 2).** Made the **causal assumptions explicit**, including front-door conditions, positivity/support overlap, and which mechanisms are invariant vs. domain-specific; added discussion of their limitations, justification, and when they may fail; the assumptions also become more reasonable given that we now position our method as a **causality-inspired method** rather than a typical **causal method** in this resubmission.

- Strengthened the connection between the **SCM, identification arguments, and the training objective**, clarifying how the learned components relate to the interventional formulation while acknowledging remaining gaps.

- Clarified the roles of key variables (**$R$, $V$, $K$**) and the purpose of enforcing **$K \perp V$** as a practical alignment objective rather than a purely causal requirement.

- Expanded **reproducibility and robustness details**, including adding multi-seed experimental results (mean ± std), hyperparameter search ranges, training procedures, and construction of continuous spurious shift.

- Added new experimental results for **ablations and sensitivity analyses**, including $x'$-sampling strategies and bin-size sensitivity for discretized baselines, showing the method’s robustness.

- Strengthened **baseline comparisons**, clarifying differences between DG vs. DA settings, continuous vs. discrete baselines, and the effect of discretization/merging.

- Extended **empirical evaluation**, including additional metrics (macro-F1, per-class F1) and experiments (e.g., age-as-input), further supporting the empirical findings.

Assigned Action Editor: ~Krikamol_Muandet1

Submission Number: 8591