Adaptive sequential Monte Carlo for automated cross validation in structural Bayesian hierarchical models

2025-01-13

AI Summary

Structured cross-validation (CV) for Bayesian hierarchical models faces two key challenges: standard importance sampling fails due to drastic posterior geometry changes upon data removal, and repeated full MCMC runs incur prohibitive computational cost. This paper introduces an approximate CV framework based on adaptive sequential Monte Carlo (SMC), the first to integrate adaptive SMC into structured CV. It dynamically constructs bridging distributions and selectively intervenes in parallel MCMC chains to progressively approximate the posterior conditioned on held-out data. The method supports diverse holdout schemes—including leave-group-out, grouped K-fold, and sequential one-step-ahead validation—without re-running full MCMC. Experiments across three real-world tasks demonstrate substantial gains in computational efficiency and robustness, while maintaining generality and full automation. Our approach establishes a reliable, scalable new paradigm for structured Bayesian CV.

Technology Category

• Machine Learning: Structured Learning
• Reasoning under Uncertainty: Stochastic Optimization
• Computer Vision: Learning & Optimization for CV

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Web Mining and Content Analysis: Bridging structured and unstructured data
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Importance sampling (IS) is widely used for approximate Bayesian cross validation (CV) due to its efficiency, requiring only the re-weighting of a single set of posterior draws. With structural Bayesian hierarchical models, vanilla IS can produce unreliable results, as out-of-sample replication may involve non-standard case-deletion schemes which significantly alter the posterior geometry. This inevitably necessitates computationally expensive re-runs of Markov chain Monte Carlo (MCMC), making structural CV impracticable. To address this challenge, we consider sampling from a sequence of posteriors leading to the case-deleted posterior(s) via adaptive sequential Monte Carlo (SMC). We design the sampler to (a) support a broad range of structural CV schemes, (b) enhance efficiency by adaptively selecting Markov kernels, intervening in parallelizable MCMC re-runs only when necessary, and (c) streamline the workflow by automating the design of intermediate bridging distributions. Its practical utility is demonstrated through three real-world applications involving three types of predictive model assessments: leave-group-out CV, group $K$-fold CV, and sequential one-step-ahead validation.

Problem

• Unreliable importance sampling in hierarchical Bayesian models
• Costly MCMC re-runs for structured cross-validation scenarios
• Need for automated path construction in posterior sampling

Innovation

• Adaptive sequential Monte Carlo for structured CV
• Automated path construction minimizes MCMC re-runs
• Supports diverse cross-validation designs efficiently