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

2026-05-31

AI Summary

This study investigates under what conditions Bayesian Model Averaging (BMA) in Bayesian decision trees yields sufficient epistemic confidence to justify deterministic decisions. Focusing on Bayesian decision trees equipped with Dirichlet–Multinomial leaf models and a Catalan-exponential prior over tree size, the work establishes—for the first time—theoretical non-asymptotic rational commitment thresholds in closed form. These thresholds precisely characterize the quantitative relationship between sample complexity and decision reliability in finite-sample settings. The analysis provides the first non-asymptotic decision-theoretic guarantee for the safe and effective use of BMA in making high-stakes decisions under limited data, thereby bridging a critical gap between Bayesian model averaging theory and practical decision-making requirements.

Abstract

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.

Problem

• Bayesian model averaging
• decision trees
• Catalan-exponential priors
• rational commitment
• sample complexity

Innovation

• Bayesian model averaging
• decision trees
• Catalan-exponential prior
• non-asymptotic guarantees
• rational commitment