Perturb and Correct: Post-Hoc Ensembles using Affine Redundancy

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.

Out-of-Distribution (OOD) data poses a significant threat to machine learning models, often leading to model failure during deployment. All existing OOD detection methods are post-hoc, relying on evaluation metrics such as accuracy and AUC-ROC during inference to indirectly assess the model's response to OOD data by measuring deviations. In contrast to existing approaches, the proposed work shifts the paradigm from OOD detection to OOD prediction by proposing a pre-hoc anticipatory framework called PLSP for OOD prediction. We make several key contributions: (a) a dataset-independent metric called the CREDibility Score (CREDS) is proposed for OOD prediction; (b) credibility curves are introduced to study the maximum credibility a model can attain; and (c) credibility heat maps (and volume under surface) are introduced to characterize pre-hoc model behavior across different datasets. This work provides a novel perspective on signal processing under distributional shifts. Experiments across multiple datasets demonstrate that the proposed metric serves as a valuable measure for improving the robustness of machine learning models toward OOD prediction.

State-of-the-art post-hoc out-of-distribution detection methods rely on intermediate layer activation editing. However, they exhibit inconsistent performance across datasets and models. We show that this instability is driven by differences in the activation distributions, and identify a failure mode of scaling-based methods that arises when penultimate layer activations are not rectified. Motivated by this analysis, we propose RAS, a hyperparameter-free post-hoc method that replaces sorted activation magnitudes with a fixed in-distribution reference profile. Our simple plug-and-play method shows strong and consistent performance across datasets and architectures without assumptions on the penultimate layer activation function, and without requiring any hyperparameter tuning, while empirically preserving in-distribution classification accuracy. We further analyze what drives the improvement, showing that both inhibiting and exciting activation shifts independently contribute to better out-of-distribution discrimination.