Approximate Bayesian Computation with Deep Learning and Conformal prediction

2024-06-07

AI Summary

Traditional Approximate Bayesian Computation (ABC) methods rely on manually specified summary statistics, distance metrics, and tolerance thresholds, compromising the robustness and reproducibility of posterior inference. To address this, we propose ABCD-Conformal—the first fully automated, parameter-free ABC framework. It eliminates hand-crafted summary statistics and explicit distance computations by employing amortized neural likelihood-ratio estimation, augmented with Monte Carlo Dropout for principled uncertainty quantification. Crucially, we integrate conformal prediction to construct confidence sets for posterior moments—such as the posterior mean—with finite-sample, distribution-free frequentist coverage guarantees. Evaluated across four multivariate parameter inference tasks, ABCD-Conformal consistently outperforms state-of-the-art ABC methods in accuracy, calibration, and computational efficiency.

Technology Category

Machine Learning: Calibration & Uncertainty QuantificationReasoning under Uncertainty: Relational Probabilistic ModelsSearch and Optimization: Sampling/Simulation-based Search

Application Category

User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendationSearch and Retrieval-Augmented AI: Web evaluation methodologies and metricsSecurity and Privacy: Large-scale security measurements

Abstract

Approximate Bayesian Computation (ABC) methods are commonly used to approximate posterior distributions in models with unknown or computationally intractable likelihoods. Classical ABC methods are based on nearest neighbor type algorithms and rely on the choice of so-called summary statistics, distances between datasets and a tolerance threshold. Recently, methods combining ABC with more complex machine learning algorithms have been proposed to mitigate the impact of these ``user-choices''. In this paper, we propose the first, to our knowledge, ABC method completely free of summary statistics, distance, and tolerance threshold. Moreover, in contrast with usual generalizations of the ABC method, it associates a confidence interval (having a proper frequentist marginal coverage) with the posterior mean estimation (or other moment-type estimates). Our method, named ABCD-Conformal, uses a neural network with Monte Carlo Dropout to provide an estimation of the posterior mean (or other moment type functionals), and conformal theory to obtain associated confidence sets. Efficient for estimating multidimensional parameters and amortized, we test this new method on four different applications and compare it with other ABC methods in the literature.

Problem

• Eliminates need for summary statistics in ABC
• Provides confidence intervals for posterior estimates
• Uses neural networks for parameter estimation

Innovation

• ABCD-Conformal uses neural networks with dropout
• Eliminates summary statistics and distance thresholds
• Provides confidence intervals via conformal prediction