发表机构
Rochester Institute of Technology（罗切斯特理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出sHAIL-Causal，一种以不变性为门控的序贯阶梯程序，用于在Richness条件下发现真实因果预测器，解决了贪心搜索的失败并支持序贯环境下的有效置信保证。
AI 中文摘要
我们引入了sHAIL-Causal，即饱和分层原子增量学习（sHAIL）范式的因果特化：一种序贯阶梯程序，当饱和信号表明当前阶段的掌握已达到平台期时，它沿着嵌套假设类层级H_0 < H_1 <... < H_K逐级上升。一般sHAIL将饱和标准留作开放，而sHAIL-Causal则用拟合优度饱和与跨环境不变性的联合标准来实例化它，取代了结构风险最小化的复杂度控制。我们在理论上和通过模拟表明，仅基于复杂度的阶梯会被混杂预测器所诱惑，这些预测器降低了经验风险却不反映稳定的因果结构，而一个受不变性门控的阶梯在逐变量Richness条件下可证明地停在真实因果预测器集合上。我们表明，即使在Richness条件下，朴素贪心搜索也无法恢复因果集合，我们将这一失败归因于不变性统计量沿单变量路径的非单调性，并验证了一种结合有界穷举块种子与校准接受阈值的修复方案。然后我们将保证扩展到序贯到达的环境，产生一个在每次到达时都保持有效的置信保证，而一次性穷举搜索若不重复其完整组合搜索则无法提供此保证。最后，我们形式化了智慧教师的干预，该教师将饱和学习者从无聊的平台期提升。
英文摘要
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.
Comments17 pages, 2 figures, 2 tables. Introduces the general sHAIL learning framework and its causal specialization
