The paper introduces Dirichlet Process Mixtures (DPMs) as a new non‑parametric conditional probability distribution (CPD) model for Semiparametric Bayesian Networks (SPBNs). By replacing kernel density estimators with DPMs, the authors achieve a more compact representation that reduces inference costs and improves density estimation accuracy. Experiments on synthetic and real‑world data show that DPM‑based SPBNs outperform existing SPBNs and other continuous‑variable Bayesian network models in both density estimation and structure learning tasks.
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.
arXiv:2509.13267v3 Announce Type: replace-cross Abstract: A discrete Bayesian network is a directed acyclic graph (DAG) consisting of categorical variables. Two popular approaches for DBN modeling in...
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.
The paper introduces Semi-Linear Gaussian Bayesian Networks (SLGBN), a new class of continuous Bayesian networks that combine linear Gaussian models with nonlinear conditional mean functions estimated via penalized B-splines within generalized additive models. SLGBN preserves Gaussian conditional distributions while allowing nonlinear relationships, and the authors provide parameter estimation procedures and a greedy hill‑climbing algorithm for structure learning. Experiments comparing SLGBN to semiparametric and linear Gaussian models show that SLGBN achieves better goodness‑of‑fit and structure recovery, especially when using the EBIC* score, while maintaining computational efficiency.
arXiv:2607. 24583v1 Announce Type: new Abstract: Large scale Bayesian nonparametrics (BNP) learner such as Stochastic Variational Inference (SVI) can handle datasets with large class number and large training size at fractional cost.
The paper introduces additive tree models for estimating the density ratio between two distributions, using a novel balancing loss that enables training with supervised learning algorithms such as forward‑stagewise optimization and gradient boosting. The loss also functions as a pseudo‑likelihood, allowing generalized Bayesian inference via backfitting samplers for Bayesian additive regression trees, which provides uncertainty quantification. Experiments show that the boosting algorithms achieve high accuracy with low computational cost, and the Bayesian approach offers competitive accuracy while delivering uncertainty estimates, demonstrated on microbiome compositional data.
BayesNDE is a neural density estimator that uses Bayesian generative modeling to estimate densities without relying on invertible networks or Jacobian-determinant calculations. It constructs an adaptive proposal for each observation by inferring a sample-specific latent posterior, and then applies bridge sampling to combine proposal samples with separate posterior samples for density estimation. Experiments on synthetic datasets show improved density estimation and structure recovery, while real-world applications demonstrate better anomaly detection.
arXiv:2510. 12744v2 Announce Type: replace-cross Abstract: We develop a unified statistical framework for softmax-gated Gaussian mixture of experts (SGMoE) that addresses three long-standing obstacles in parameter estimation and model selection: (i) non-identifiability of gating parameters up to common translations, (ii) intrinsic gate-expert interactions that induce coupled differential relations in the likelihood, and (iii) the tight numerator-denominator coupling in the softmax-induced conditional density.
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...
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:2608. 19067v1 Announce Type: cross Abstract: The empirical success of diffusion models in generative modelling has motivated theoretical work, including quantitative error bounds and qualitative analyses that characterise the different phases of denoising.
The paper addresses the challenge of estimating joint probability distributions in high-dimensional settings by factorizing them autoregressively and using nonparametric conditional estimators. It establishes theoretical convergence bounds that link the difficulty of joint estimation to the hardest factor in the factorization, especially when conditional estimators adapt to sparsity in an undirected dependence graph. Empirical results show that an autoregressive estimator built with parallel gradient boosting achieves competitive performance on simulated and real datasets, even without optimizing factorization order.