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.

Information Lattice Learning as Probabilistic Graphical Model Structure Learning
Jun 11, 2026Haizi Yu, Lav R. VarshneyGraph Structure Learning Interpretable ML
Kocree, Inc. · AI Innovation Institute, Stony Brook University
Equivariant Neural Belief Propagation
Jun 4, 2026Zehua Cheng, Wei Dai, Jiahao SunEquivariant Representation Learning Factor Graph Optimization
Department of Computer Science, University of Oxford, Oxford, United Kingdom · FLock.io, London, United Kingdom
In-Context Graphical Inference
Jun 3, 2026Zehua Cheng, Wei Dai, Jiahao SunAmortized Inference Probabilistic Graphical Models
Department of Computer Science, University of Oxford, Oxford, United Kingdom · FLock.io, London, United Kingdom
Mitigating False Credit Propagation: Probabilistic Graphical Reward Aggregation for Rubric-Based Reinforcement Learning
Jun 2, 2026Can Lv, Mingju Chen, Heng Chang +1Reward Modeling RL for Language Models
Beijing Advanced Innovation Center for Future Blockchain and Privacy Computing, School of Artificial Intelligence, Beihang University · Tsinghua University
Composing Non-Conjugate Factor Graphs with Closed-Form Variational Inference
May 28, 2026Mykola Lukashchuk, Kyrylo Yemets, Wouter M. Kouw +4Factor Graph Optimization Mixture-of-Experts Inference
Eindhoven University of Technology, the Netherlands · Lviv Polytechnic National University, Lviv, Ukraine · Lazy Dynamics, Utrecht, the Netherlands +1
Testing properties of trees in graphical models with covariance queries
May 15, 2026Sofiya Burova, Francisco Calvillo, Gábor Lugosi +1Probabilistic Graphical Models
IMTECH and Departament de Matem`atiques, Universitat Polit`nica de Catalunya, Barcelona, Spain and Department of Economics and Business, Pompeu Fabra University, Barcelona, Spain. · LPSM, Sorbonne Universit´e, 4 Place Jussieu, 75005 Paris, France · ICREA, Pg. Llu´ıs Companys 23, 08010 Barcelona, Spain; Department of Economics and Business, Pompeu Fabra University, Barcelona, Spain; Barcelona School of Economics. +1
ANCHOR: Abductive Network Construction with Hierarchical Orchestration for Reliable Probability Inference in Large Language Models
May 11, 2026Wentao Qiu, Guanran Luo, Zhongquan Jian +3Abductive Reasoning Bayesian Networks
School of Informatics, Xiamen University, Xiamen, China · School of Computer and Data Science, Minjiang University, Fuzhou, China · School of Film, Xiamen University, Xiamen, China +2
Exact and Approximate Algorithms for Polytree Learning
May 5, 2026Juha Harviainen, Frank Sommer, Manuel SorgeGraph Structure Learning Bayesian Networks
Department of Computer Science, University of Helsinki, Helsinki, Finland · Institute of Computer Science, Friedrich-Schiller Universität Jena, Jena, Germany · Institute of Logic and Computation, TU Wien, Vienna, Austria
Probabilistic Graphical Model using Graph Neural Networks for Bayesian Inversion of Discrete Structural Component States
Apr 26, 2026Teng Li, Stephen Wu, Yong Huang +2Graph Neural Networks Bayesian Inverse Problems
Key Lab of Smart Prevention and Mitigation of Civil Engineering Disasters of the Ministry of Industry and Information Technology, Harbin Institute of Technology, Harbin 150090, China · Key Lab of Structures Dynamic Behavior and Control of the Ministry of Education, School of Civil Engineering, Harbin, Institute of Technology, Harbin 150090, China · The Institute of Statistical Mathematics, Research Organization of Information and Systems, 10-3 Midori-cho, Tachikawa, Tokyo 190-8562, Japan +2
Local Inconsistency Resolution: The Interplay between Attention and Control in Probabilistic Models
Apr 18, 2026Oliver E. Richardson, Mandana Samiei, Mehran Shakerinava +4Bayesian Inference Probabilistic Graphical Models
Université de Montréal · School of Computer Science, McGill University · Institut Polytechnique de Paris +1
On the Relationship between Bayesian Networks and Probabilistic Structural Causal Models
Mar 28, 2026Peter J. F. Lucas, Eleonora Zullo, Fabio StellaStructural Causal Models Bayesian Networks
ICIS, Radboud University, Nijmegen, the Netherlands · Dipartimento di Informatica, Sistemistica e comunicazion University of Milano-Bicocca, Milan, Italy
Amalgam: Hybrid LLM-PGM Synthesis Algorithm for Accuracy and Realism
Mar 28, 2026Antheas Kapenekakis, Bent Thomsen, Katja Hose +1Synthetic Tabular Data Generation Generative Modeling
Aalborg University, Aalborg, Denmark · TU Wien, Vienna, Austria
Binary Expansion Group Intersection Network
Mar 25, 2026Sicheng Zhou, Kai ZhangProbabilistic Graphical Models Markov Random Fields
Department of Electrical Engineering and Computer Science. Massachusetts Institute of Technology, Cambridge, MA 02139. · Department of Statistics and Operations Research, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599.
Learning Dynamic Belief Graphs for Theory-of-mind Reasoning
Mar 20, 2026Ruxiao Chen, Xilei Zhao, Thomas J. Cova +2Computational Cognitive Modeling LLM Reasoning with Graphs
Department of Civil and Systems Engineering, Johns Hopkins University, Baltimore, MD, USA · Civil and Coastal Engineering, University of Florida, Gainesville, FL, USA · School of the Environment, Society & Sustainability, University of Utah, Salt Lake City, UT, USA +1
Learning Bayesian and Markov Networks with an Unreliable Oracle
Mar 10, 2026Juha Harviainen, Pekka Parviainen, Vidya Sagar SharmaGraph Structure Learning Bayesian Network Structure Learning
University of Helsinki, Finland · University of Bergen, Norway · Indian Institute of Technology Madras, India
FastBUS: A Fast Bayesian Framework for Unified Weakly-Supervised Learning
Feb 28, 2026Ziquan Wang, Haobo Wang, Ke Chen +2Gaussian Belief Propagation Weakly Supervised Learning
the School of Software Technology, Zhejiang University, Hangzhou 310027, China · the State Key Laboratory of Blockchain and Data Security, Zhejiang University, Zhejiang 310027, China, and also with the Hangzhou High-Tech Zone (Binjiang) Institute of Blockchain and Data Security, Binjiang 310000, China · the School of Computer Science and Engineering, Southeast University, Nanjing 210096, China +1
Including Node Textual Metadata in Laplacian-constrained Gaussian Graphical Models
Feb 17, 2026Jianhua Wang, Killian Cressant, Pedro Braconnot Velloso +1Graph Structure Learning Probabilistic Graphical Models
Université Paris-Nanterre, LEME, IUT Ville d’Avray, Ville d’Avray, France · Conservatoire National des Arts et Métiers, CNAM, Paris, France
Gaussian Belief Propagation Network for Depth Completion
Jan 29, 2026Jie Tang, Pingping Xie, Jian Li +1Markov Random Fields Depth Estimation
National University of Defense Technology, Changsha, China · Hong Kong University of Science and Technology, Hong Kong, China
Learning Task Mixtures from Task Affinities: A Probabilistic Graphical Model for Supervised Fine-Tuning
Jul 16, 2025Prateek Chanda, Saral Sureka, Parth Pratim Chatterjee +3Supervised Fine-Tuning Multi-Task Learning
IIT Bombay · IBM Research · Red Hat AI Innovation +1
Extracting Probabilistic Knowledge from Large Language Models for Bayesian Network Parameterization
May 21, 2025Aliakbar Nafar, Kristen Brent Venable, Zijun Cui +1Bayesian Networks Probabilistic Graphical Models
Michigan State University · Florida Institute for Human and Machine Cognition (IHMC) University of West Florida
Delta-AI: Local objectives for amortized inference in sparse graphical models
Oct 3, 2023Jean-Pierre Falet, Hae Beom Lee, Esmeralda S. Whitammer +6Amortized Inference Probabilistic Graphical Models
Mila – Qu´ebec AI Institute, Universit´e de Montr´eal · Mila – Québec AI Institute, Université de Montréal
A polynomial time algebraic solution to exact marginal inference in Markov Random Field models
Sep 25, 2017Ikhlef BecharEfficient Inference Markov Random Fields
Aix Marseille Univ, Universit´e de Toulon, CNRS, ENSAM, LSIS La Garde 83957, France

Jun 11, 2026J/K move · Enter open · S save

Information Lattice Learning as Probabilistic Graphical Model Structure Learning

Haizi Yu, Lav R. Varshney

Kocree, Inc. · AI Innovation Institute, Stony Brook University

Graph Structure Learning Interpretable ML Probabilistic Graphical Models

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Information lattice learning (ILL) learns interpretable rules of a signal by alternately projecting the signal onto a partition lattice that encodes a hierarchy of abstractions and lifting selected rules back to the signal domain. When the signal is a probability mass function, we show the probabilistic rules learned by ILL admit a natural probabilistic graphical model (PGM) interpretation and develop this interpretation in detail. A partition in ILL induces a deterministic quotient variable, and a rule is the marginal law of that quotient variable. A rule set is therefore a collection of marginal constraints over interpretable abstractions. General lifting is the feasible family of all joint distributions satisfying those constraints, while special lifting chooses a maximum-ignorance reconstruction, implemented in ILL by an L2 uniformity principle closely related to maximum entropy. Under a Shannon-entropy lifting, the same constraints yield a log-linear factor graph whose factors are indexed by learned abstractions. The information lattice itself, however, is not a Bayesian network: its edges encode refinement and coarsening of abstractions, not conditional dependence. Thus ILL is best viewed as structure learning for interpretable constraint-based factor graphs over quotient variables. This view clarifies how ILL relates to graphical models and maximum entropy models, while suggesting new directions for inference, identifiability, and hybrid symbolic-probabilistic learning.