Bayesian Methods and Mixture Models

Latest papers

• Direct Message Approximation (DMA): A Consistency-Based Framework for Tractable Approximate Inference on Factor Graphs

  Ralf Herbrich, Rainer Schlosser, Jan Lemcke, Johann Ukrow, Anna Kazachkova, Nicolas Alder, Leonhard Hennicke, Theo Bardey, Nico Grimm, Luca Kleinschmidt, Philipp Kolbe, Cezary Kujath, Johanna Schlimme, Karl Matti Sch\"utz · 25 September 2026

  Approximate message passing on factor graphs underlies two dominant families of probabilistic inference algorithms: expectation propagation (EP) and variational message passing (VMP). Both methods approximate the marginal at each factor edge, forcing an iterative round-robin schedule, risking negati…

• Theoretical Study on the Evidential Learning-based Variational Autoencoder

  Ge Wang · 24 September 2026

  A normal--inverse-gamma (NIG) latent hierarchy has four parameters, but its induced latent law does not identify all four. For $\sigma^2\sim\mathrm{InvGamma}(\alpha,\beta)$, $\mu\mid\sigma^2\sim\mathcal{N}(\gamma,\sigma^2/\nu)$, and $z\mid\mu,\sigma^2\sim\mathcal{N}(\mu,\sigma^2)$, the marginal law …

• Aggregated Posterior Predictive Checks for Generative Modeling

  Shweta Dutta, Gemma E. Moran · 21 September 2026

  Latent variable generative models are commonly fit using simple priors over latent variables, but draws from these priors often fail to produce realistic data. This failure is due to a mismatch between the prior and the aggregated posterior, the distribution of latent variables induced by the fitted…

• Cross-Block Conditioning in Deep Boltzmann Machines for Statistical Data Fusion

  Junichiro Niimi · 15 September 2026

  Statistical data fusion combines two panels that share a block of covariates but observe disjoint outcome blocks, and in its traditional form no row observes both outcomes at once. That rules out the discriminative criterion one would rather train a Deep Boltzmann Machine with, since multi-predictio…

• Regularized Estimation and Feature Selection in Mixtures of Generalized Linear Experts

  Thin Nguyen-Van, Faicel Chamroukhi, Ha Hoang Van, Bao Tuyen Huynh · 10 September 2026

  Mixtures of experts (MoE) are conditional mixture models in which both the mixing proportions and the component densities depend on the predictors, and are widely used for regression, classification and model-based clustering of heterogeneous data. Fitting MoE by maximum likelihood becomes unstable,…

• Explainable Clustering of Mixture Models

  Maximilian Fleissner, Maedeh Zarvandi, Debarghya Ghoshdastidar · 7 September 2026

  The explainable clustering problem was first posed by Moshkovitz et al. (ICML 2020) and studies how well an axis-aligned decision tree with $K$ leaves can approximate a given clustering. The performance of the tree is measured via the \textit{price of explainability}, defined as the ratio between th…

• Doubly Stochastic Adaptive Neighbors Clustering via the Marcus Mapping

  Jinghui Yuan, Chusheng Zeng, Fangyuan Xie, Zhe Cao, Mulin Chen, Rong Wang, Feiping Nie, Yuan Yuan · 3 September 2026

  Clustering is a fundamental task in machine learning and data science, and similarity graph-based clustering is an important approach within this domain. Doubly stochastic symmetric similarity graphs provide numerous benefits for clustering problems and downstream tasks, yet learning such graphs rem…

• Semi-Supervised Classification with Informative Missing Labels in Weibull Mixture Models

  Jinran Wu, You-Gan Wang, Geoffrey J. McLachlan · 2 September 2026

  We consider semi-supervised classification from a partially classified sample arising from a two-component Weibull mixture. The feature is observed for all data, whereas some class labels are missing. The probability of a missing label is modelled as a function of classification uncertainty, giving …

• Poisson-Gamma Dynamical Systems with Time-varying Transition Dynamics

  Jiahao Wang, Yijun Wang, Nan Fang, Sikun Yang · 2 September 2026

  Bayesian methodologies for handling count-valued time series have gained prominence due to their ability to infer interpretable latent structures and to estimate uncertainties. Among these Bayesian models, Poisson-Gamma Dynamical Systems (PGDSs) are proven to be effective in capturing the evolving d…

• Diffusion models as plug-and-play priors

  Alexandros Graikos, Esmeralda S. Whitammer, Nebojsa Jojic, Dimitris Samaras · 31 August 2026

  We consider the problem of inferring high-dimensional data $\mathbf{x}$ in a model that consists of a prior $p(\mathbf{x})$ and an auxiliary differentiable constraint $c(\mathbf{x},\mathbf{y})$ on $x$ given some additional information $\mathbf{y}$. In this paper, the prior is an independently traine…

• Gauss--Hermite Quadrature for Gaussian-Mixture Entropy with an Action-Space Hermite Surrogate

  Jae Wan Shim · 26 August 2026

  Gaussian distributions are used to model uncertainty in signals and states, and Gaussian mixtures are often used when the underlying distribution is multimodal. Unlike a single Gaussian, a Gaussian mixture generally has no closed-form expression for differential entropy and therefore requires numeri…

• A Layered Simplex Architecture for Large Alphabets

  Meir Feder, Yaniv Fogel, Ruediger Urbanke · 21 August 2026

  Probability estimation over large alphabets under log loss is a well-studied problem, with celebrated methods such as the Good-Turing estimator. We introduce and study a new Bayesian estimator with four notable properties. First, its construction is exceptionally simple: multiply independent uniform…

• Does Mapping Non-Maximal Probabilities to GMM Components Matter for S-JEPA Encoder Representations?

  Wenxuan He, Yunpeng Li, Shan Liang · 20 August 2026

  S-JEPA uses soft Gaussian mixture model (GMM) posteriors instead of hard cluster labels to preserve uncertainty. It remains unclear whether the probability values alone are sufficient, or whether it also matters which GMM components receive the non-maximal probabilities. We test this with two matche…

• Beyond Independence: Learning Correlated Views for Variational Incomplete Multi-View Clustering

  Zheming Xu, Aiyue Tang, Shidi Chen, Xuechao Zou, Congyan Lang, Rogelio A. Mancisidor, Michael Kampffmeyer · 18 August 2026

  Incomplete multi-view clustering (IMVC) aims to uncover shared cluster structures from data with partially observed views. Although recent imputation-free methods based on variational inference demonstrate robustness to missing views, they commonly rely on a conditional independence assumption acros…

• Hierarchical Empirical-Bayes Naive Bayes: Minimax Smoothing and Calibration with AODE Extension

  Nguyen Thai Anh, Truong Viet Vu, Tran Thien Thanh, Vo Nguyen Quoc Bao, Ngo Hoang Tu · 12 August 2026

  The Naive Bayes (NB) classifier remains a standard choice for categorical data, yet its widely used smoothing rules, such as Laplace, Lidstone, Krichevsky-Trofimov, and the $m$-estimate, all prescribe a fixed smoothing strength that ignores feature cardinality, sample size, and class imbalance, indu…

• Scalable estimation of VARMA models

  Daniel Paulin, Victor Elvira · 7 August 2026

  Vector autoregressive moving-average (VARMA) models have long been considered impractical beyond moderate dimensions: the likelihood is non-convex, the parametrization is identified only up to equivalence, and every evaluation costs a pass over the entire series. Yet their moving-average term captur…

• Deep Generalised Mixed Models: a Novel Neural Network Structure for Analysing Hierarchical Data

  Nina van Gerwen, Dimitris Rizopoulos, Manon Hillegers, Loes Keijsers, Sten Willemsen · 7 August 2026

  The experience sampling method (ESM) is a longitudinal research design where participants report their thoughts, emotional states and behaviours multiple times a day. Our work is motivated by such data collected by the GrowIt! app, which was released to investigate daily emotions among adolescents d…

• Differentially Private Nonparametric Modal Learning with Applications to Regression and Clustering

  Arkajyoti Bhattacharjee, Arnab Auddy · 3 August 2026

  Density modes provide a localized and interpretable summary of multimodal distributions, but their estimation under rigorous differential privacy constraints remains largely unexplored. We study differentially private recovery of density modes for multivariate distributions under local smoothness, c…

• Rethinking Likelihood distributions: Student's t Likelihood Boosts Bayesian Neural Network Performance

  Pei-Hsuan Hsia, Lars H. Heyen, Arvid Weyrauch, Markus Goetz, Achim Streit, Sebastian Krumscheid, Charlotte Debus · 29 July 2026

  In Bayesian neural networks (BNNs), variational inference is a widely adopted framework for modeling uncertainty in a distributional way, with the evidence lower bound (ELBO) serving as the standard objective function. Several distributions contribute to the ELBO loss, such as the prior, approximate…

• DP-Splat: Bayesian Nonparametric Complexity Control for Gaussian Splatting

  Aqi Dong · 14 July 2026

  3D Gaussian Splatting represents scenes as finite mixtures of anisotropic Gaussians whose number of components $K$ is set by heuristic density control or user caps. Variational Bayes Gaussian Splatting (VBGS) recast splat fitting as conjugate variational inference, but $K$ remains fixed. We replace …

• Straight-Path Flow Matching for Incomplete Multi-View Clustering

  Yiteng Yuan, Junyan Wang, Zheyuan Liu, Hong Jia, Lei Fan, Zhulin Tao, Lianbo Guo · 8 July 2026

  Incomplete Multi-View Clustering addresses the problem of clustering multi-modal data when certain views are missing. Recent end-to-end generative approaches leverage diffusion models to recover missing views via stochastic noise-to-data trajectories. While expressive, such mechanisms are not explic…

• New methods to compute the generalized chi-square distribution

  Abhranil Das · 30 June 2026

  We present four new mathematical methods, two exact and two approximate, along with open-source software, to compute the cdf, pdf and inverse cdf of the generalized chi-square distribution. Some methods are geared for speed, while others are designed to be accurate far into the tails, using which we…

• Detection and Evaluation of Clusters within Sequential Data

  Alexander Van Werde, Albert Senen-Cerda, Gianluca Kosmella, Jaron Sanders · 23 June 2026

  Sequential data is ubiquitous -- it is routinely gathered to gain insights into complex processes such as behavioral, biological, or physical processes. Challengingly, such data not only has dependencies within the observed sequences, but the observations are also often high-dimensional, sparse, and…

• Variance-Tilted Diffusion Models for Diverse Sampling

  Iskander Azangulov, Leo Zhang, Kianoosh Ashouritaklimi · 23 June 2026

  Diffusion models are typically sampled independently, even when the downstream objective is to obtain a diverse set of candidates. We introduce a variance-weighted batch distribution that favours collections of samples with large empirical spread after a prescribed linear feature map. The target is …

• Bayesian Model Averaging under Predictor Redundancy via Density-Ratio Posterior Compression

  Hanqing Li, Xuewen Lu, Yuting Chen · 23 June 2026

  Bayesian model averaging in support-indexed regression induces a posterior distribution over active predictor supports. Under predictor redundancy, posterior mass can spread across many nearly interchangeable supports, making exact-support summaries unstable or hard to interpret even when prediction…