arXiv subjects

Pietro Carlotti

Publications and source records attributed to Pietro Carlotti.

3 recordsLinked to original sources

arXiv2026

Product Monte Carlo: Expectation Under a Product of Densities

Aggregating independently computed sub-sample inferences is a well-known challenge in large-scale Bayesian computation, federated learning, and opinion pooling. The core problem is to approximate a distribution whose density is proportional to a product of individual densities. We propose Product Monte Carlo (PMC), an algorithm for computing arbitrary expectations under a product of densities using only Monte Carlo draws from individual densities. We turn the intractable product expectation into a regression problem by expressing it through a family of computable conditional expectations. Besides the point estimate, our fully Bayesian regression formulation provides coherent uncertainty quantification and principled diagnostics. We establish theoretical guarantees on consistency and characterize convergence rates for the PMC estimator. Across simulated and real-data experiments varying the number, dimensionality, and heterogeneity of the component distributions, PMC achieves higher estimation accuracy, better-calibrated uncertainty coverage, and improved scalability at a lower computational cost than existing methods. In addition, PMC requires no density evaluation, making it applicable to simulation-based inference, as we demonstrate in an application with protein images.

stat.ME↗

arXiv2026

Density-Informed Pseudo-Counts for Calibrated Evidential Deep Learning

Evidential Deep Learning (EDL) is a popular framework for uncertainty-aware classification that models predictive uncertainty via Dirichlet distributions parameterized by neural networks. Despite its popularity, its theoretical foundations and behavior under distributional shift remain poorly understood. In this work, we provide a principled statistical interpretation by proving that EDL training corresponds to amortized variational inference in a hierarchical Bayesian model with a tempered pseudo-likelihood. This perspective reveals a major drawback: standard EDL conflates epistemic and aleatoric uncertainty, leading to systematic overconfidence on out-of-distribution (OOD) inputs. To address this, we introduce Density-Informed Pseudo-count EDL (DIP-EDL), a new parametrization that decouples class prediction from the magnitude of uncertainty by separately estimating the conditional label distribution and the marginal covariate density. This separation preserves evidence in high-density regions while shrinking predictions toward a uniform prior for OOD data. Theoretically, we prove that DIP-EDL achieves asymptotic concentration. Empirically, we show that our method enhances interpretability and improves robustness and uncertainty calibration under distributional shift.

stat.ML↗

arXiv2026

A Bayesian Critique of Rank-Based Methods for Surrogate Marker Evaluation

Surrogate markers are often employed in clinical trials to replace primary outcomes that may be difficult, expensive, or time-consuming to measure directly. These markers can accelerate the evaluation of new treatments, provided they reliably capture the causal relationship between treatment and true clinical benefit. Parast et al. (2024) recently proposed a rank-based approach for evaluating surrogate markers, characterized by its nonparametric nature and minimal assumptions. While this method is useful in small-sample model-agnostic settings, it has several limitations, including a lack of clear causal interpretation, low statistical power, and insufficient robustness to different data-generating mechanisms. In this paper, we propose a Bayesian approach that addresses these shortcomings by focusing on causal treatment effect estimands and, in doing so, improves power through covariate adjustment. We demonstrate the advantages of our proposed method through a simulation study designed to highlight gains in both accuracy and power.

stat.ME↗