Product Monte Carlo (PMC) is an algorithm that estimates expectations under a product of densities using only Monte Carlo samples from each individual density. By reformulating the intractable product expectation as a regression problem involving computable conditional expectations, PMC provides both point estimates and coherent Bayesian uncertainty quantification. The method achieves higher accuracy, better-calibrated uncertainty, and improved scalability compared to existing techniques, and it does not require density evaluations, enabling its use in simulation‑based inference such as protein image analysis.
arXiv:2610.19074v1 Announce Type: new Abstract: Reliable uncertainty quantification remains an important challenge in AI. Hierarchical Bayesian methods provide a principled framework for this by repr...
arXiv:2608.29349v1 Announce Type: new Abstract: Gaussian process (GP) regression with a single global GP (GP-glo) incurs cubic computational cost, limiting scalability to large datasets. Product-of-e...
The paper extends Neural Posterior Estimation (NPE) to handle simulators whose parameter spaces contain both discrete and continuous dimensions. It introduces an inference network that factorizes the joint posterior into discrete and continuous components, using an autoregressive classifier for the discrete part and a generative model for the continuous part, trained jointly with a single simulation-based objective. A diagnostic tool for assessing calibration of the mixed posterior is also proposed, and the method is shown to produce accurate, calibrated posteriors on toy and real scientific simulators.
arXiv:2607. 06252v1 Announce Type: cross Abstract: Many problems in science and engineering are difficult to model accurately, either due to unknown physical mechanisms, poorly quantified measurement uncertainty, or prohibitive computational costs of high-fidelity simulations.
arXiv:2504. 01894v2 Announce Type: replace Abstract: We present a bifidelity method for uncertainty quantification of parameter estimates in complex systems, leveraging generative models trained to sample the target conditional distribution.
arXiv:2601. 07944v2 Announce Type: replace-cross Abstract: Since the turn of the century, approximate Bayesian inference has steadily evolved as new computational techniques have been incorporated to handle increasingly complex, large-scale predictive problems.
arXiv:2606. 25188v1 Announce Type: new Abstract: Efficient uncertainty quantification (UQ) is essential for trustworthy large-scale learning.
arXiv:2606. 19643v1 Announce Type: cross Abstract: Motivated by the privacy, sensitivity and sharing limitations of health data, we present a comprehensive pipeline for inference of Bayesian mixture models within a federated learning setting, i.
The paper introduces a two-way guidance framework that jointly learns summary statistics and posterior distributions for Bayesian simulation-based inference. By imposing a structural restriction on the learned summary, the method ensures that the posterior remains sufficient, while the posterior objective simultaneously steers the summary toward sufficiency. The authors provide theoretical guarantees on posterior estimation error and the deviation of the learned summary from sufficiency, outlining conditions on simulation budgets needed to recover increasingly concentrated posteriors as observation size grows.
arXiv:2609.39525v1 Announce Type: new Abstract: Casting Bayesian inference as a neural network optimization problem targeting an amortized posterior is attractive, as it extends to otherwise intracta...
arXiv:2606. 27269v1 Announce Type: cross Abstract: Reliably quantifying predictive uncertainty is difficult for complex, high-dimensional, or misspecified models.
Conditional Mean Flows introduce a new approach for simulation-based inference that replaces the costly numerical integration of traditional flow matching with few-step sampling and tractable density evaluation. By identifying conditional flow maps through a mean flow objective and using independent masking, the method allows direct estimation of marginal likelihoods. Experiments demonstrate that single-step conditional mean flow density evaluation achieves error comparable to 200-step flow matching while accelerating downstream MCMC sampling by roughly 200‑fold.