Probabilistic Graphical Models

Also known as PGM

Probabilistic graphical models use Bayesian networks, Markov random fields, and factor graphs to represent variables, dependencies, and conditional independence, making complex uncertainty easier to analyze. Work develops exact methods such as variable elimination, alongside approximate belief propagation, variational inference, sampling, and amortized neural inference; structure-learning methods seek graphs and parameters from data or expert knowledge. These models support applications including causal discovery, robotics and planning, vision, scientific modeling, and calibrated prediction, with evaluations ranging from synthetic networks to benchmarks such as NYUv2 and KITTI. A central challenge is making inference and learning scalable while retaining accuracy, reliable uncertainty estimates, and guarantees when graphs are large, loopy, or only partially observed.

Latest papers

52 papers9 papers in the last four weeks, up 29% on the four weeks before. 0.1% of all new papers.

Robust Latent Variable Graphical Models: Exact Recovery and Fundamental Limits
Oct 19, 2026Chuansen Peng, Xiaojing ShenRobust Estimation Graph Structure Learning
School of Mathematics, Sichuan University, Chengdu 610064, China
DD-GBP: Anytime Multi-Arm Planning and Continuous Execution via Distributed Dynamic Gaussian Belief Propagation
Oct 14, 2026Zhao Jin, Fengyi Dai, Yuetong Yin +3Motion Planning Multi-Robot Motion Planning
State Key Laboratory of Tribology in Advanced Equipment, Department of Mechanical Engineering, Tsinghua University, Beijing, 100084, China · Beijing Key Laboratory of Transformative High-end Manufacturing Equipment and Technology, Department of Mechanical Engineering, Tsinghua University, Beijing 100084, China · State Key Laboratory of High-end Heavy-load Robots, Midea Group, Foshan 528300, China
Student Copula Markov Networks
Oct 13, 2026Salha Mamane, Cheikh Tidiane SeckProbabilistic Graphical Models Graph Structure Learning
School of Statistics and Actuarial Science, University of the Witwatersrand · Department of Mathematics, Alioune Diop University of Bambey
DeepFlow: Two Convergent Differentiable Approaches for Pairwise Conditional Random Fields
Oct 12, 2026John S. H. BaxterConditional Random Fields Probabilistic Graphical Models
Laboratoire Traitement du Signal et de l’Image (INSERM UMR 1099), Université de Rennes, Rennes, France
When Edge Independence Fails: Joint Graph Diffusion with Latent Sociability Priors
Oct 9, 2026Adarsh Jamadandi, Nicolas Keriven, Aline RoumyGraph Generation Graph Diffusion
CNRS, IRISA, Rennes, France1 · INRIA, Rennes, France2
Neural expectation-maximization and meta-models
Oct 8, 2026Zhuolin FuTransformer Transformer Attention
Hierarchy-GBP: Accelerating Factor Graph Inference via Abstraction and Recovery
Oct 4, 2026Yuzhou Cheng, Tom Yates, Ignacio Alzugaray +3Gaussian Belief Propagation Belief Propagation
Imperial College London, London, United Kingdom.
Amortized Bayesian Inference on Multilevel Models of Arbitrary Structure
Sep 30, 2026Daniel Habermann, Andreas Bulling, Stefan T. Radev +1Amortized Inference Hierarchical Bayesian Modeling
Department of Statistics TU Dortmund University, Germany · Institute for Visualisation and Interactive Systems University of Stuttgart, Germany · Department of Cognitive Science Rensselaer Polytechnic Institute, USA
Counterfactual Probing for Parallel Unmasking with Hidden Forest Structure
Sep 29, 2026Ryotaro Kawata, Satoshi Hayakawa, Taiji SuzukiSample Complexity Probabilistic Graphical Models
The University of Tokyo · RIKEN AIP
Probabilistic Modelling of Operational Design Domains, A New Approach for Testing AI Systems
Sep 21, 2026Hans-Werner WiesbrockProbabilistic Graphical Models Knowledge Representation
ITPower Solutions GmbH Kolonnenstrasse 26 10829 Berlin, Germany
On Generalized Naive Bayes with Continuous Features
Sep 20, 2026Ábrahám Papp, Botond Szilágyi, Edith Alice KovácsCopula Models Probabilistic Graphical Models
Department of Analysis and Operations Research, Institute of Mathematics, Budapest University of Technology and Economics · Department of Chemical and Environmental Process Engineering, Faculty of Chemical Technology and Biotechnology, Budapest University of Technology and Economics
On Probabilistic Inference Through Parametric Tensor Decomposition in Base Tensor Networks
Sep 20, 2026Sagad Hamid, Tanya BraunEfficient Inference Probabilistic Graphical Models
Computer Science Department, University of Münster, Münster, Germany
Fast Graph Laplacian Estimation using Effective Resistance
Sep 20, 2026Christoffer Kjellson, Claudio Altafini, Emma TeglingGraph Structure Learning Probabilistic Graphical Models
Department of Automatic Control, Lund University · ELLIIT Strategic Research Area · Division of Automatic Control, Department of Electrical Engineering, Linköping University
ABSOL: Aggregated Bayesian Subsampling Orchestrated with LLMs
Sep 14, 2026Jackson Hassell, Chen Shen, Estevam HruschkaGraph Structure Learning Bayesian Network Structure Learning
Megagon Labs
Local Robustness Quantification for Naive Bayes Classifiers and Generative Forests: a General Approach
Sep 10, 2026Adrián Detavernier, Jasper De BockDistribution Shift Robustness Adversarial Robustness
Foundations Lab for imprecise probabilities Ghent University Ghent, Belgium
A computational approach to maximum likelihood thresholds for colored Gaussian graphical models
Sep 2, 2026Roser Homs, Olga Kuznetsova, Bernadette J. StolzProbabilistic Graphical Models
Universitat Polit`ecnica de Catalunya - BarcelonaTech (UPC) · Aalto University · Department of Machine Learning and Systems Biology, Max Planck Institute of Biochemistry; Munich Center for Machine Learning; Laboratory for Topology and Neuroscience, School of Life Sciences, ´Ecole Polytechnique F´ed´erale de Lausanne, 1015 Lausanne, Switzerland
Text-Guided Visual Dependency Graph Learning with Cross-Modal Attention Priors
Aug 19, 2026Fei Wang, Yutong Zhang, Yang Ye +3Multimodal Graph Learning Probabilistic Graphical Models
Stony Brook University, USA · Sichuan University, China · Universiti Sains Malaysia, Malaysia +1
LLM-Augmented Causal Discovery: Probabilistic Fusion of Edge Existence and Orientation
Aug 19, 2026Neville K. Kitson, Anthony ConstantinouBayesian Network Structure Learning Causal Discovery
Machine Intelligence and Decision Systems (MInDS) Group, School of Electronic Engineering and Computer Science, Queen Mary University of London, London, United Kingdom, E1 4NS.
Probabilistic Circuits as Reasoning Machines in Artificial Intelligence (Part I)
Aug 17, 2026Robert PeharzProbabilistic Circuits Probabilistic Graphical Models
Institute of Machine Learning and Neural Computation Graz University of Technology
Information Geometry of Message Passing
Aug 16, 2026Mykola Lukashchuk, Kyrylo Yemets, Alex Ledbetter +1Belief Propagation Probabilistic Graphical Models
Eindhoven University of Technology · Lviv Polytechnic National University · Lazy Dynamics, Utrecht, the Netherlands
Hallucinations and Constraints : Regulating surgical workflow recognition beyond accuracy
Aug 10, 2026John S. H. Baxter, Pierre JanninHallucination Detection Probabilistic Graphical Models
Université de Rennes, Inserm, Laboratoire Traitement du Signal et de l’Image (LTSI - UMR 1099), F-35000 Rennes, France
Accelerated Random-Sweep Gibbs Sampling for Gaussian Graphical Models via Dual Normal Factor Graphs
Jul 30, 2026Borna Khodabandeh, Mehdi MolkaraieFactor Graph Optimization Markov Chain Monte Carlo
Department of Statistics, University of Oxford, Oxford OX1 3LB, UK · Department of Signal Theory and Communications, UPC, 08034 Barcelona, Spain · Department of Statistical Sciences, University of Toronto, ON M5G 1X6, Canada
Amortized Bayesian Causal Discovery of Extended Factor Graphs
Jul 24, 2026Yichen Gu, Yuxuan Song, Weizhou Qian +2Causal Discovery Probabilistic Graphical Models
Department of Electrical and Computer Engineering University of Michigan Ann Arbor, MI 48109, USA · Department of Computational Medicine and Bioinformatics University of Michigan, Ann Arbor Ann Arbor, MI 48109, USA · Department of Statistics University of Michigan, Ann Arbor Ann Arbor, MI 48109, USA +1
Mixing-Free and Signal-Optimal Learning of Gaussian Graphical Models from Glauber Dynamics
Jul 20, 2026Vignesh Tirukkonda, Gautam DasarathyGraph Structure Learning Probabilistic Graphical Models
Arizona State University
Decomposition for Bayesian Networks: Local and Parallel Inference
Jul 6, 2026Pei Heng, Xinyi Hu, Yi SunParameter Estimation Bayesian Networks
Institute of Statistics and Data Science, Xinjiang University of Finance and Economics, Urumqi, China
Characterizing and Identifying Separable Graphical Models
Jul 1, 2026Christopher Meek, Kayvan SadeghiCausal Structure Learning Probabilistic Graphical Models
Department of Statistics, University of Washington · Department of Statistical Science, University College London
Learning Gaussian Graphical Models from a Glauber Trajectory Without Mixing
Jun 30, 2026Eric Shen, Tony Wu, Mahbod Majid +1Graph Structure Learning Probabilistic Graphical Models
MIT
Lifted Causal Inference
Jun 26, 2026Malte Luttermann, Tanya Braun, Ralf Möller +1Causal Effect Estimation Efficient Inference
Institute for Humanities-Centered Artificial Intelligence, University of Hamburg, Hamburg, Germany. · German Research Center for Artificial Intelligence (DFKI), Lübeck, Germany. · Data Science Group, University of Münster, Münster, Germany.
Reduction of Probabilistic Chemical Reaction Networks
Jun 26, 2026Mauricio Montes, Gregoire Sergeant-PerthuisBelief Propagation Probabilistic Graphical Models
COSAM, Auburn University, Auburn, AL, USA · CQSB, Sorbonne Universite, Paris, France
Graphical-Probabilistic Modeling of Generative Flows in LLM-Native Software Systems
Jun 14, 2026Víctor A. Braberman, Flavia Bonomo-BrabermanSoftware Engineering Probabilistic Graphical Models
Departamento de Computación, FCEN, Universidad de Buenos Aires / ICC, UBA-CONICET Buenos Aires, Argentina

Oct 19, 2026J/K move · Enter open · S save

Robust Latent Variable Graphical Models: Exact Recovery and Fundamental Limits

Chuansen Peng, Xiaojing Shen

School of Mathematics, Sichuan University, Chengdu 610064, China

Robust Estimation Graph Structure Learning Probabilistic Graphical Models Minimax Estimation Low-Rank Matrix Decomposition

Open paper AskPDF arXiv

We study robust estimation of a Gaussian precision matrix that decomposes as a sparse matrix minus a symmetric, possibly indefinite, low-rank matrix, a structure that arises when latent-variable marginalization is combined with conditioning on linear measurements. The proposed convex estimator replaces the sample covariance by the centered Gaussian measure-transformed (MT) covariance, which preserves the signed graph of the sparse component under the nominal model, and penalizes the low-rank component by the nuclear norm of a congruence transform, an atomic norm that encodes structural side information. Our main result is a primal--dual witness theorem: under restricted invertibility and irrepresentability conditions on the Fisher information, the raw convex optimizer is unique, has no false edges, recovers the signs of all sufficiently strong edges, and has exactly the true rank and inertia. These conditions reduce to the graphical-lasso conditions when the low-rank part is absent, and we verify them from primitive incoherence and near-isotropy assumptions. Over a class on which they hold uniformly, we prove information-theoretic limits for Frobenius estimation, signed graph recovery, and inertia recovery. In particular, inertia recovery requires

N\gtrsim p/ν_{\min}^2

samples, where

ν_{\min}

is the smallest nonzero eigenvalue modulus of the low-rank part; the spectral beta-min condition of the witness theorem is necessary up to a

\sqrt{\log p}

factor; and the Frobenius risk attains the minimax rate up to a factor

\sqrt{μ(1+\min\{d,r\})\log p}

, where

μ

is the incoherence parameter,

d

the maximal degree, and

r

the rank. We further quantify robustness under Huber contamination, with a bias bound that is sharp for the MT functional and vanishes for remote outliers, and give a globally convergent linearized ADMM with closed-form updates.