arXiv：cs.LG· Ernest Fokou\'e·· 4 小时前AI 评分34
sHAIL-Causal：用于不变因果预测器发现的序列阶梯方法
sHAIL-Causal: A Sequential Staircase Procedure for Invariant Causal Predictor Discovery
AI 导读
研究者提出 sHAIL-Causal，将 sHAIL 框架特化为因果发现方法，用拟合优度饱和与跨环境不变性联合准则取代结构风险最小化的复杂度控制，理论上可停在真实因果预测器集合。该序列阶梯在逐步到达的环境中保持全程有效的置信保证。
正文
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.
| Comments: | 17 pages, 2 figures, 2 tables. Introduces the general sHAIL learning framework and its causal specialization |
| Subjects: | Machine Learning (stat.ML); Machine Learning (cs.LG) |
| MSC classes: | 62H22 (Causality), 62J05 (Linear regression), 62L10 (Sequential statistical analysis), 68T05 (Learning and adaptive systems) |
| Cite as: | arXiv:2610.07057 [stat.ML] |
| (or arXiv:2610.07057v1 [stat.ML] for this version) | |
| https://doi.org/10.48550/arXiv.2610.07057 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Ernest Fokoue [view email]
[v1]
Mon, 5 Oct 2026 04:36:23 UTC (36 KB)
来源：arXiv：cs.LG · arxiv.org