Error analysis of a compositional score-based algorithm for simulation-based inference

2025/10/17 by Camille Touron, Touron, Camille, Gabriel Victorino Cardoso +5
Computer Science · Mathematics · #Bayesian Modeling and Causal Inference #FOS: Computer and information sciences #Gaussian Processes and Bayesian Inference #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Markov Chains and Monte Carlo Methods

paper · pdf · doi:10.48550/arxiv.2510.15817

openalex publication_date 2025/10/17 · openalex created_date 2025/10/21 · openalex updated_date 2026/07/28

Abstract

Simulation-based inference (SBI) has become a widely used framework in applied sciences for estimating the parameters of stochastic models that best explain experimental observations. A central question in this setting is how to effectively combine multiple observations in order to improve parameter inference and obtain sharper posterior distributions. Recent advances in score-based diffusion methods address this problem by constructing a compositional score, obtained by aggregating individual posterior scores within the diffusion process. While it is natural to suspect that the accumulation of individual errors may significantly degrade sampling quality as the number of observations grows, this important theoretical issue has so far remained unexplored. In this paper, we study the compositional score produced by the GAUSS algorithm of Linhart et al. (2024) and establish an upper bound on its mean squared error in terms of both the individual score errors and the number of observations. We illustrate our theoretical findings on a Gaussian example, where all analytical expressions can be derived in a closed form.

Citations

• Compositional amortized inference for large-scale hierarchical Bayesian models
• Compositional simulation-based inference for time series
• Diffusion posterior sampling for simulation-based inference in tall data settings
• Wasserstein Convergence Guarantees for a General Class of Score-Based Generative Models
• Sequential Neural Score Estimation: Likelihood-Free Inference with Conditional Score Based Diffusion Models
• Compositional Score Modeling for Simulation-based Inference
• Analysis of Neural Fragility: Bounding the Norm of a Rank-One Perturbation Matrix
• Practical bounds on the error of Bayesian posterior approximations: A nonasymptotic approach

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• Improved Sample Complexity For Diffusion Model Training Without Empirical Risk Minimizer Access
• Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions