PeTeR: Post-Training Robustification of Probabilistic Circuits

2026-07-08

AI Summary

This work addresses the vulnerability of probabilistic circuits to overfitting and poor generalization under data noise, limited samples, or distribution shifts. To mitigate this, the authors propose PeTeR, the first data-free post-training framework that enhances the robustness of pretrained probabilistic circuits to distributional shifts without requiring retraining. PeTeR leverages distributionally robust optimization by modeling worst-case distributions within a Wasserstein ball and introduces a data-agnostic parameter adjustment mechanism grounded in this principle. Empirical evaluations across multiple density estimation benchmarks demonstrate that PeTeR significantly improves model robustness against both random and adversarial perturbations, matching or outperforming existing data-dependent robust learning baselines.

Abstract

Probabilistic circuits (PCs) can model complex joint distributions while supporting exact and efficient computation of many inference queries. However, standard likelihood-based PC learning is vulnerable to overfitting and fragile generalization when confronted with data noise, small sample sizes, or distribution shifts. This can be mitigated using distributionally-robust optimization which consider worst-case distributions within a Wasserstein ball of the empirical distribution, but current methods are limited to training a model from scratch in this framework. Instead, we propose PeTeR: a novel, data-free post-training framework designed to robustify pre-trained PCs against distribution shifts without retraining from scratch. Empirical evaluations across multiple density estimation benchmarks demonstrate that PeTeR effectively robustifies baseline models against both random and adversarial perturbations, achieving competitive or superior performance to data-dependent robust learning baselines.

Problem

• probabilistic circuits
• distribution shift
• robustness
• overfitting
• generalization

Innovation

• post-training robustification
• probabilistic circuits
• distributional robustness
• Wasserstein ball
• data-free adaptation