Approximate Message Passing

Also known as AMP

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Latest papers

10 papers1 paper in the last four weeks, with none the four weeks before. 0.0% of all new papers.

Direct Message Approximation (DMA): A Consistency-Based Framework for Tractable Approximate Inference on Factor Graphs
Sep 24, 2026Ralf Herbrich, Rainer Schlosser, Jan Lemcke +11Efficient Inference Uncertainty Quantification
Hasso Plattner Institute University of Potsdam Potsdam, Germany
DAIF: A Data-Driven Intermediate Fusion Framework for Multimodal Supervised Learning via Approximate Message Passing
Aug 3, 2026Sagnik Nandy, Samriddha Lahiry, Pragya Sur +1Latent Variable Models Approximate Message Passing
Ohio State University · National University of Singapore · Harvard University
Replica Symmetry Breaking and Algorithmic Thresholds in Empirical Risk Minimization under Multi-Index Model
Jun 26, 2026Andrea Montanari, Kangjie ZhouApproximate Message Passing Statistical Learning Theory
Department of Mathematics and Department of Statistics, Stanford University · Department of Statistics, Columbia University
Easy, robust approximate message passing for planted spike models
May 30, 2026Misha Ivkov, Tselil SchrammRandom Matrix Theory Principal Component Analysis
*Stanford University. · †Stanford University.
Stabilizing Private LASSO under Heterogeneous Covariates via Anisotropic Objective Perturbation
May 2, 2026Haruka Tanzawa, Ayaka SakataDifferential Privacy Linear Regression
Department of Information Science · RIKEN center for AIP
Decoupled Descent: Exact Test Error Tracking Via Approximate Message Passing
Apr 30, 2026Max LovigNeural Network Generalization Gradient Descent
Statistics and Data Science, Yale University
Universality of first-order methods on random and deterministic matrices
Apr 13, 2026Nicola Gorini, Chris Jones, Dmitriy Kunisky +1Approximate Message Passing Random Matrix Theory
Bocconi University. · UC Davis. · Johns Hopkins University. +1
Privacy-Accuracy Trade-offs in High-Dimensional LASSO under Perturbation Mechanisms
Mar 27, 2026Ayaka Sakata, Haruka TanzawaApproximate Message Passing Privacy-Preserving ML
Department of Information Science, Ochanomizu University · RIKEN center for AIP
Rigorous Asymptotics for First-Order Algorithms Through the Dynamical Cavity Method
Mar 15, 2026Yatin Dandi, David Gamarnik, Francisco Pernice +1Approximate Message Passing Mean-Field Theory
Statistical Physics of Computation Laboratory, École polytechnique fédérale de Lausanne (EPFL) CH-1015 Lausanne. · Sloan School of Management, Operations Research Center and Institute of Data, Systems and Society (IDSS), MIT. · CSAIL and LIDS, MIT.
On Universality of Non-Separable Approximate Message Passing Algorithms
Jun 28, 2025Max Lovig, Tianhao Wang, Zhou FanMean-Field Theory Approximate Message Passing
Department of Statistics and Data Science, Yale University · Halicioglu Data Science Institute, University of California, San Diego

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

Ralf Herbrich, Rainer Schlosser, Jan Lemcke, Johann Ukrow+10

Hasso Plattner Institute University of Potsdam Potsdam, Germany

Efficient Inference Uncertainty Quantification Bayesian Inference Approximate Message Passing

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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 negative-precision messages, and, for VMP, collapsing to point estimates at Dirac-delta factors. We introduce Direct Message Approximation (DMA), which approximates factor-to-variable messages directly rather than the marginal. For normalisable factors, we define a consistency condition (requiring exactness when all other incoming messages are Dirac deltas) to guide message construction. We prove a master theorem (proper messages, any graph) bounding marginal KL from message KL, with three structural corollaries: Dirac-input consistency, no EP-style inner-loop iteration, and no negative-precision messages. Further, we prove a complementary

O(1/r^2)

guarantee for the inherently improper backward message of the product factor, whose closed-form treatment has resisted prior work. As a concrete instantiation, we derive explicit DMA messages for the product and leaky-ReLU factors and assemble a Bayesian neural network (BNN) inference algorithm with one forward/backward sweep per training example and no gradient learning-rate hyperparameter, validating that the structural guarantees translate to predictive uncertainty that widens in data-sparse regions, including under model mismatch.