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

2025-10-17

AI Summary

In simulation-based inference (SBI), multi-observation fusion often degrades posterior sampling quality due to cumulative errors in individual score estimates, yet the underlying error propagation mechanism remains theoretically uncharacterized. Method: We derive the first mean-squared error (MSE) upper bound for composite score estimation in score-based diffusion models, integrating score matching, diffusion process modeling, and Gaussian approximation analysis within the GAUSS algorithmic framework. Contribution/Results: The analytically tractable bound quantifies the coupled dependence of inference accuracy on both per-observation score error magnitude and the number of observations. Rigorous validation under a Gaussian ground-truth model confirms the tightness of the bound. This work fills a fundamental theoretical gap in SBI—namely, the absence of error analysis for composite inference strategies—and provides a verifiable, theoretically grounded accuracy guarantee for large-scale observational fusion.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Probabilistic Inference
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

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.

Problem

• Analyzing error accumulation in compositional score-based SBI methods
• Establishing error bounds for multi-observation parameter inference
• Studying how observation quantity affects posterior estimation quality

Innovation

• Compositional score aggregation for multiple observations
• Error bound analysis for score-based diffusion methods
• Theoretical validation using Gaussian example with closed forms