Bayesian Inference

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Bayesian inference combines prior beliefs with observed data to form a posterior distribution over unknown quantities, supporting predictions and decisions that account for uncertainty. Common approaches include Markov chain Monte Carlo, variational inference, Laplace approximations, and simulation-based inference; neural networks and normalizing flows increasingly help approximate or amortize these computations. Applications range from scientific inverse problems and time-series models to causal analysis, machine learning, and robotics. A central challenge is making inference scalable without losing posterior accuracy or calibrated uncertainty, especially when priors or likelihood models are misspecified.

Latest papers

318 papers48 papers in the last four weeks, up 109% on the four weeks before. 0.3% of all new papers.

Robust Sparse Bayesian Learning Based on Minimum Error Entropy for Noisy High-Dimensional Brain Activity Decoding
Aug 5, 2025Yuanhao Li, Badong Chen, Wenjun Bai +2Neural Decoding Bayesian Inference
Center for Advanced Intelligence Project, RIKEN, Tokyo 103-0027, Japan · Department of Computational Brain Imaging, ATR Neural Information Analysis Laboratories, Kyoto 619-0237, Japan · Institute of Artificial Intelligence and Robotics (IAIR), Xi’an Jiaotong University, Xi’an 710049, China +1
A Morse-Bott Framework for Blind Inverse Problems: Local Recovery Guarantees and the Failure of the MAP
Aug 4, 2025Minh-Hai Nguyen, Edouard Pauwels, Pierre WeissImage Deblurring Bayesian Inference
IRIT, Toulouse University, Toulouse, France · Toulouse School of Economics, Universit´e Toulouse Capitole et IUF, Toulouse, France
Formal Bayesian Transfer Learning via the Total Risk Prior
Jul 31, 2025Nathan Wycoff, Ali Arab, Lisa O. SinghBayesian Inference Transfer Learning
Department of Mathematics and Statistics, University of Massachusetts Amherst · Department of Computer Science, Georgetown University
LLMs are Bayesian, In Expectation, Not in Realization
Jul 15, 2025Leon Chlon, Fatima Sheaib, Zein Khamis +3Bayesian Inference In-Context Learning
Hassana Labs · Harvard University
The Bayesian Approach to Continual Learning: An Overview
Jul 11, 2025Tameem AdelTask-Incremental Learning Class-Incremental Learning
NPL, Maxwell Centre, University of Cambridge, JJ Thomson Avenue, Cambridge, CB3 OHE, United Kingdom.
Bayesian Invariance Modeling of Multi-Environment Data
Jun 27, 2025Luhuan Wu, Mingzhang Yin, Yixin Wang +2Bayesian Inference
Department of Applied Mathematics and Statistics, Johns Hopkins University. · Warrington College of Business, University of Florida. · Department of Statistics, University of Michigan. +2
Causal Posterior Estimation
May 27, 2025Simon Dirmeier, Antonietta MiraBayesian Inference Simulation-Based Inference
Swiss Data Science Center, ETH Zurich, Switzerland · Università della Svizzera italiana, Switzerland · Insubria University, Italy
Bayesian Deep Learning for Discrete Choice
May 23, 2025Daniel F. Villarraga, Ricardo A. DazianoBayesian Neural Networks Bayesian Inference
School of Civil and Environmental Engineering, Cornell University, 220 Hollister Hall, Ithaca, NY 14853, USA
Physics-Informed Sylvester Normalizing Flows for Bayesian Inference in Magnetic Resonance Spectroscopy
May 6, 2025Julian P. Merkofer, Dennis M. J. van de Sande, Alex A. Bhogal +1Normalizing Flows Bayesian Inference
Eindhoven University of Technology, Eindhoven, The Netherlands · University Medical Center Utrecht, Utrecht, The Netherlands
A Generalized Tangent Approximation based Variational Inference Framework for Strongly Super-Gaussian Likelihoods
Apr 7, 2025Somjit Roy, Pritam Dey, Debdeep Pati +1Bayesian Inference Variational Inference
Department of Statistics, Texas A&M University, College Station, TX 77843 · Department of Statistics, University of Wisconsin-Madison, Madison, WI 53706
The Fenchel-Young Generalization of Bayesian Principles
Feb 14, 2025Sophia Sklaviadis, Thomas Moellenhoff, Emtiyaz Khan +2Generalized Bayesian Inference Bayesian Inference
Instituto de Telecomunicacoes, and Instituto Superior Técnico, Lisbon, Portugal · RIKEN AIP
Variational Model Merging for Pareto Front Estimation in Multitask Finetuning
Dec 11, 2024Hugo Monzón Maldonado, Nico Daheim, Thomas Möllenhoff +2Bayesian Inference Multi-Task Learning
RIKEN Center for AI Project, Japan · Ubiquitous Knowledge Processing Lab (UKP Lab), Department of Computer Science, Technical University of Darmstadt and National Research Center for Applied Cybersecurity ATHENE, Germany · National Research Center for Applied Cybersecurity ATHENE, Germany
ReMAP: Lossless Residual Neural Lifting for Scalable MAP Inference in Arbitrary-Order Markov Random Fields
Nov 28, 2024Yaomin Wang, Chaolong Ying, Xiaodong Luo +1MAP Estimation Markov Random Fields
School of Data Science, The Chinese University of Hong Kong, Shenzhen · Shenzhen Research Institute of Big Data, China
Noise-Aware Differentially Private Variational Inference
Oct 25, 2024Talal Alrawajfeh, Joonas Jälkö, Antti HonkelaBayesian Inference Differential Privacy
University of Helsinki
Joint Bayesian Parameter and Model Order Estimation for Low-Rank Probability Mass Tensors
Oct 8, 2024Joseph K. Chege, Arie Yeredor, Martin HaardtBayesian Inference Tensor Decomposition
Communications Research Laboratory, Ilmenau University of Technology, Ilmenau, Germany · School of Electrical and Computer Engineering, Tel Aviv University, Tel Aviv, Israel
Hierarchical Bayesian Crowdsourcing with Item Difficulty
May 29, 2024Seong Woo Han, Ozan Adıgüzel, Bob CarpenterInter-Rater Reliability Latent Variable Models
University of Pennsylvania · Columbia University · Center for Computational Mathematics, Flatiron Institute
PhyloGFN: Phylogenetic inference with generative flow networks
Oct 12, 2023Mingyang Zhou, Zichao Yan, Elliot Layne +5Bayesian Inference Posterior Sampling
McGill University · McGill University, Mila · Universit´e de Montr´eal, Mila
A Bayesian Approach for the Network Reconstruction of Interdependent Critical Infrastructure Systems from Cascading Failures
Nov 28, 2022MirSaleh Bahavarnia, Hiba Baroud, Yu Wang +1Bayesian Inference
Department of Civil and Environmental Engineering, Vanderbilt University, Nashville, TN, USA. · School of Computer and Data Sciences at the University of Oregon, Eugene, OR, USA. · Department of Civil Engineering, University of Texas at Arlington, Arlington, TX, USA.

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Robust Sparse Bayesian Learning Based on Minimum Error Entropy for Noisy High-Dimensional Brain Activity Decoding

Yuanhao Li, Badong Chen, Wenjun Bai, Yasuharu Koike+1

Center for Advanced Intelligence Project, RIKEN, Tokyo 103-0027, Japan · Department of Computational Brain Imaging, ATR Neural Information Analysis Laboratories, Kyoto 619-0237, Japan · Institute of Artificial Intelligence and Robotics (IAIR), Xi’an Jiaotong University, Xi’an 710049, China+1

Neural Decoding Bayesian Inference

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Objective: Sparse Bayesian learning provides an effective framework to solve high-dimensional problems in brain signal decoding. However, conventional likelihoods regarding data distributions, such as Gaussian or Bernoulli, are potentially inadequate for handling the noisy recordings of brain activity. Hence, this work aims to formulate a robust sparse Bayesian learning framework to address noisy high-dimensional brain activity decoding. Methods: Motivated by the commendable robustness of the minimum error entropy learning criterion for addressing non-Gaussian signals, this study reformulated the sparse Bayesian learning framework under a generalized Bayesian paradigm, in which the model parameter is regulated with the minimum error entropy loss rather than a conventional likelihood function. Results: Our developed SBL-MEE algorithm was evaluated with two real-world brain decoding tasks of regression and classification scenarios, respectively. Experimental results demonstrated that our approach not only realizes superior brain decoding performance than existing methods, but also presents more physiologically interpretable decoder patterns. Conclusion: Although minimum error entropy is not constructed from an arbitrary probabilistic distribution, it is effective to establish noise-robust inference in sparse Bayesian learning method. Significance: This work provides a powerful tool to improve brain activity decoding capability, particularly regarding the noisy high-dimensional setting, thus promoting biomedical engineering applications such as brain-computer interface.