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sHAIL-Causal proposes a novel sequential learning framework that uses cross-environment invariance to distinguish true causal predictors from confounded correlations, addressing a critical limitation of standard complexity-based model selection. Theoretically and via simulation, the method guarantees convergence to the correct causal set under specific richness conditions while offering superior confidence bounds for sequentially arriving environments compared to exhaustive search. This work advances the theoretical foundations of causal discovery by integrating invariance principles directly into the incremental learning process.
sHAIL-Causal: A Sequential Staircase Procedure for Invariant Causal Predictor Discovery
arXiv:2610.07057v1 Announce Type: cross Abstract: We introduce sHAIL-Causal, the causal specialization of the Saturated Hierarchical Atomic Incremental Learning (sHAIL) paradigm: a sequential staircase procedure that ascends a nested hierarchy of hypothesis classes H_0 < H_1 < ... < H_K once a saturation signal indicates that mastery of the current stage has plateaued. Where general sHAIL leaves the saturation criterion open, sHAIL-Causal instantiates it with a joint criterion of goodness-of-fit saturation and cross-environment invariance, replacing the complexity control of Structural Risk Minimization. We show, theoretically and by simulation, that complexity-only staircases are seduced by confounded predictors that lower empirical risk without reflecting stable causal structure, whereas an invariance-gated staircase provably halts at the true causal predictor set under a per-variable Richness condition. We show that naive greedy search fails to recover the causal set even under Richness, trace the failure to non-monotonicity of the invariance statistic along single-variable paths, and validate a fix combining bounded-exhaustive block-seeding with a calibrated acceptance threshold. We then extend the guarantee to environments arriving sequentially, yielding a confidence guarantee that stays valid at every arrival, which one-shot exhaustive search cannot offer without repeating its full combinatorial search. We close by formalizing the intervention of a wise teacher who lifts a saturated learner off a plateau of boredom.
Abstract:We introduce sHAIL-Causal, the causal specialization of the Saturated Hierarchical Atomic Incremental Learning (sHAIL) paradigm: a sequential staircase procedure that ascends a nested hierarchy of hypothesis classes H_0 < H_1 < ... < H_K once a saturation signal indicates that mastery of the current stage has plateaued. Where general sHAIL leaves the saturation criterion open, sHAIL-Causal instantiates it with a joint criterion of goodness-of-fit saturation and cross-environment invariance, replacing the complexity control of Structural Risk Minimization. We show, theoretically and by simulation, that complexity-only staircases are seduced by confounded predictors that lower empirical risk without reflecting stable causal structure, whereas an invariance-gated staircase provably halts at the true causal predictor set under a per-variable Richness condition. We show that naive greedy search fails to recover the causal set even under Richness, trace the failure to non-monotonicity of the invariance statistic along single-variable paths, and validate a fix combining bounded-exhaustive block-seeding with a calibrated acceptance threshold. We then extend the guarantee to environments arriving sequentially, yielding a confidence guarantee that stays valid at every arrival, which one-shot exhaustive search cannot offer without repeating its full combinatorial search. We close by formalizing the intervention of a wise teacher who lifts a saturated learner off a plateau of boredom.
17 pages, 2 figures, 2 tables. Introduces the general sHAIL learning framework and its causal specialization
Machine Learning (stat.ML); Machine Learning (cs.LG)
arXiv:2610.07057 [stat.ML]
(or arXiv:2610.07057v1 [stat.ML] for this version)
https://doi.org/10.48550/arXiv.2610.07057 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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