Stacking-Based Weighting for Large Language Bayes in M-Open Settings
Large Language Bayes (LLB) transforms a natural language problem description into a collection of candidate probabilistic programs and performs inference within each model, combining their predictions using Bayesian model averaging. While this provides a flexible framework for probabilistic inference without manual model specification, the resulting candidate model set is often misspecified in practice, and likelihood-based aggregation can concentrate on a single model, under-representing uncertainty across the sampled models. We propose a stacking-based aggregation method for LLB that selects model weights by optimizing predictive performance rather than marginal likelihood, while preserving the original language-model-driven model generation and within-model inference pipeline. Because leave-one-out predictive quantities are intractable in latent-variable models, we derive a variational lower bound that yields a tractable ELBO-based stacking objective. Across real-world probabilistic inference tasks, our method achieves comparable predictive performance to Bayesian model averaging while yielding more dispersed model weights, reducing concentration on a single candidate model under misspecification.