为决策树贝叶斯平均提供可信赖的采样复杂度与决策保障

Sample Complexity and Decision-Theoretic Guarantees for Bayesian Model Averaging over Decision Trees with Catalan-Exponential Priors

• 基于卡塔兰-指数先验构建完整贝叶斯决策树模型
• 首次给出非渐近条件下理性承诺阈值的闭式解
• 适用于需可靠决策保障的高风险场景

我们探讨：在何种条件下，对决策树进行贝叶斯模型平均（BMA）所得权重足以提供足够的认知信息，从而支持对平均分布的坚定利用？针对采用狄利克雷-多项式叶节点模型与卡塔兰-指数树大小先验（Schetinin&Jakaite, 2025）的贝叶斯决策树（BDTs），本文给出了闭式解，建立了完整的非渐近理性承诺阈值理论。

原文摘要 · Abstract (English)

We ask: when do Bayesian model averaging (BMA) weights over decision trees carry sufficient epistemic information to justify committed exploitation of the averaging distribution? We answer this question in closed form for Bayesian decision trees (BDTs) with Dirichlet-Multinomial leaf models and a Catalan-exponential tree-size prior (Schetinin&Jakaite, 2025), establishing a complete non-asymptotic theory of rational commitment thresholds.

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