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Measure-Theoretic Anti-Causal Representation Learning
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Proposes ACIA, a measure-theoretic two-level (low-level causal dynamics, high-level causal abstraction) representation learning framework for anti-causal settings that handles perfect and imperfect interventions without explicit SCMs, evaluated on CMNIST, RMNIST, Ball Agent, and Camelyon17.
Problem
Anti-causal representation learning (labels cause features, with environment-induced spurious correlations) requires robust OOD generalization without explicit structural causal model knowledge and under both perfect and imperfect interventions.
Approach
A two-level representation built from product causal spaces and interventional kernels: low-level representations capture label-to-observation generation, and high-level representations are kernel-integrated abstractions trained with environment-independence (R1) and intervention-consistency (R2) regularizers in a min-max objective.
Key results
- ACIA reports 99.20% accuracy on CMNIST and 99.10% on RMNIST, versus 95.50% and 93.50% for the best baselines (VREx).
- On Camelyon17 ACIA reports 84.40% accuracy, versus 65.5% for LECI, the best baseline in the table.
- Under imperfect interventions ACIA reports similar results across the four datasets (e.g., 84.4% on Camelyon17).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use ACIA instead of VREx | CMNIST · CMNIST | accuracy: 95.50 -> 99.20 | Helped |
| Use ACIA instead of LECI | CMNIST · CMNIST | environment independence: 0.83 -> 0.00 | No clear effect |
| Use ACIA instead of VREx | RMNIST · RMNIST | accuracy: 93.50 -> 99.10 | Helped |
| Use ACIA instead of LECI | RMNIST · RMNIST | intervention robustness: 0.04 -> 0.01 | Helped |
| Use ACIA instead of VREx | Ball Agent · Ball Agent | accuracy: 74.00 -> 99.98 | Helped |
| Use ACIA instead of LECI | Ball Agent · Ball Agent | environment independence: 0.46 -> 0.52 | Hurt |
| Use ACIA instead of LECI | Camelyon17 · Camelyon17 | accuracy: 65.50 -> 84.40 | Helped |
| Use ACIA instead of LECI | Camelyon17 · Camelyon17 | environment independence: 0.23 -> 0.28 | Hurt |
| Apply imperfect rather than perfect interventions with ACIA | ACIA · CMNIST | accuracy: 99.20 -> 99.4 | No clear effect |
Surprising findings
- Several baselines (e.g., Rex, DANN on Camelyon17) score near chance or far below ERM-like methods, and LECI wins on EI and some invariance metrics on Ball Agent and Camelyon17 despite lower accuracy.
Limitations
- Theoretical results rely on assumptions (complete separable product causal space, empirical measure convergence) and proofs contain informal steps.
- Proposed future work targets confounded-descendant and mixed causal-anticausal settings, which are not handled.
- Some reported numbers are inconsistent across text and tables (e.g., ACIA Camelyon17 accuracy 87.00% in text vs 84.40% in table; Ball Agent 99.72% vs 99.98%).
Experimental setup
Datasets: CMNIST RMNIST Ball Agent Camelyon17
Benchmarks: CMNIST RMNIST Ball Agent Camelyon17
Metrics: test accuracy environment independence (EI) low-level invariance (LLI) intervention robustness (IR)
Baselines: GDRO MMD CORAL DANN IRM Rex VREx ACTIR CausalDA LECI
Builds on: IRM Rex causal dynamics measure-theoretic causality (causal spaces) LECI
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