We analyze oversquashing in topological message-passing using relational structures.
problem Oversquashing in topological message-passing remains understudied.
method A unifying axiomatic framework that bridges graph and topological message-passing.
result Potential to advance topological deep learning.
New algorithms accelerate MAP inference in Markov fields with faster convergence.
problem Finding the most likely configuration in discrete-valued Markov random fields.
method Entropy-regularized linear programming with accelerated gradient methods.
result Accelerated algorithms find optimal solutions faster, especially when the LP is tight.
Develops a Gaussian-based message-passing algorithm for noisy matrix completion.
problem Noisy matrix completion problems.
method Gaussian parameterized belief propagation algorithm.
result Advantages over traditional methods in non-Gaussian noise scenarios.
Factor graphs have recently gained increasing attention as a unified framework for representing and constructing algorithms for signal processing, estimation, and control. One capability that does not seem to be well explored within the factor graph tool kit is the ability to handle deterministic nonlinear transformati…
Analyze message passing algorithms using free probability theory.
problem Dynamics of message passing algorithms for probabilistic models.
method Use freeness assumptions of random matrix theory.
result Recover and analyze properties of message passing algorithms.
Convex message passing algorithms converge to a fixed point.
problem Understanding convergence properties of convex message passing methods.
method Proving convergence of coordinate descent applied to piecewise-affine convex objectives, and showing this applies to various message passing methods.
result The iterates converge to a fixed point of the method, and the algorithm terminates in a known number of iterations.
New algorithm improves graph inference tasks.
problem Complex graph reasoning and prediction tasks.
method Policy Message Passing algorithm reformulates graph inference as stochastic sequential processes.
result Consistently outperforms state-of-the-art models.
Novel neural network solves PDEs with multi-scale resolution.
problem Solving time-dependent PDEs with varying spatial and temporal scales.
method Multi-scale message passing neural network with temporal and spatial gating modules.
result Outperforms baselines on PDEs with diverse scales.
New distribution simplifies covariance matrix inference.
problem Efficient inference for covariance matrices in large models.
method Incorporates Inverse G-Wishart distribution for variational message passing.
result Elegant and succinct expression of variational message passing fragments.
We address the problem of computing approximate marginals in Gaussian probabilistic models by using mean field and fractional Bethe approximations. We define the Gaussian fractional Bethe free energy in terms of the moment parameters of the approximate marginals, derive a lower and an upper bound on the fractional Beth…
Topo-MLP learns network representations without message passing.
problem Lack of efficient higher-order network modeling methods.
method Proposes Topo-MLP, a simplicial neural network algorithm using MLP and HONC loss.
result Demonstrates improved robustness and efficiency in representation learning.
ALBU improves LDA performance on small datasets.
problem Limited data impairs variational Bayes in LDA.
method Approximate Loopy Belief message passing algorithm.
result ALBU learns latent distributions more accurately than VB, especially for smaller data sets.
Message passing is the key to graph neural networks, but new terms are needed to avoid confusion.
problem Current methods of graph neural networks cannot solve all problems over given input graphs.
method Demonstrates that any function of interest can be expressed using pairwise message passing over a modified graph.
result Message passing is the fundamental approach for graph neural networks, and new terms are needed to avoid confusion.
A new algorithm improves topic model accuracy in small data sets.
problem Limited data leads to inaccurate topic model identification.
method Developed a novel variational message passing algorithm (ALBU) for LDA.
result ALBU learns latent distributions more accurately than Variational Bayes (VB) in small data sets.
Tree-AMP simplifies inference in complex tree-structured models.
problem Inference in high-dimensional tree-structured models.
method Approximate Message Passing algorithms for various machine learning tasks.
result Theoretical performance predictions and automated entropy estimation.
Rich and complex time-series data, such as those generated from engineering systems, financial markets, videos or neural recordings, are now a common feature of modern data analysis. Explaining the phenomena underlying these diverse data sets requires flexible and accurate models. In this paper, we promote Gaussian pro…
New algorithm minimizes FE objectives for synthetic AIF agents.
problem Minimizing Free Energy for synthetic active inference agents.
method Variational message passing on Constrained FFGs.
result Message passing algorithms induce epistemic behavior in AIF agents.
Paper proposes efficient methods for forecasting with large datasets.
problem Forecasting with large, high-dimensional economic data sets.
method Bayesian hierarchical priors, factor graphs, message passing algorithms, Generalized Approximate Message Passing (GAMP).
result The proposed methods outperform traditional approaches in forecasting U.S. price inflation.
Efficiently estimates rotations with corrupted data.
problem Rotation synchronization under high corruption and noise.
method Message passing algorithm with reweighted least squares.
result Superior performance over state-of-the-art methods.
ADMP-GNN dynamically adjusts message-passing layers for better graph learning performance.
problem Fixed message-passing steps in GNNs do not account for nodes' varying computational needs.
method Proposes ADMP-GNN, which dynamically adjusts the number of message-passing layers for each node.
result Improves performance on node classification tasks compared to baseline GNN models.
A message passing algorithm is derived for recovering communities within a graph generated by a variation of the Barabási-Albert preferential attachment model. The estimator is assumed to know the arrival times, or order of attachment, of the vertices. The derivation of the algorithm is based on belief propagation unde…
Adapts BP-based algorithms for deep learning, improving performance and accuracy.
problem Training deep neural networks with discrete weights and activations.
method Message-passing algorithms based on Belief Propagation, with reinforcement field.
result Comparable performance to SGD-inspired heuristics (BinaryNet) and higher accuracy in predictions.
New algorithm improves signal reconstruction from noisy measurements with side information.
problem Reconstructing unknown signals from noisy linear measurements with side information.
method Integrates side information into approximate message passing (AMP) and tracks performance using state evolution.
result AMP-SI performance is accurately predicted by state evolution.
New algorithm for signal estimation in noisy matrix models.
problem Signal estimation in rectangular spiked matrix models with rotationally invariant noise.
method Orthogonal Approximate Message Passing (OAMP) algorithm for signal estimation.
result Optimal OAMP algorithm minimizes mean-squared error and achieves Bayes-optimal performance.
Recent efforts on combining deep models with probabilistic graphical models are promising in providing flexible models that are also easy to interpret. We propose a variational message-passing algorithm for variational inference in such models. We make three contributions. First, we propose structured inference network…
Crowdsourcing is a strategy to categorize data through the contribution of many individuals. A wide range of theoretical and algorithmic contributions are based on the model of Dawid and Skene [1]. Recently it was shown in [2,3] that, in certain regimes, belief propagation is asymptotically optimal for data generated f…
We propose a framework for the derivation and evaluation of distributed iterative algorithms for receiver cooperation in interference-limited wireless systems. Our approach views the processing within and collaboration between receivers as the solution to an inference problem in the probabilistic model of the whole sys…
New graph coarsening method preserves GNN message-passing signals.
problem Preserving GNN message-passing on coarsened graphs.
method Proposed a new oriented message-passing operation for coarsened graphs.
result Improved node classification results compared to naive methods.
For the problem of multi-class linear classification and feature selection, we propose approximate message passing approaches to sparse multinomial logistic regression (MLR). First, we propose two algorithms based on the Hybrid Generalized Approximate Message Passing (HyGAMP) framework: one finds the maximum a posterio…
Study on convergence of graph neural networks on random graphs.
problem Convergence of message passing graph neural networks on large random graphs.
method Extended convergence results to a broad class of aggregation functions using McDiarmid inequality.
result Non-asymptotic bounds for convergence quantified with high probability.
Iterative information processing, either based on heuristics or analytical frameworks, has been shown to be a very powerful tool for the design of efficient, yet feasible, wireless receiver architectures. Within this context, algorithms performing message-passing on a probabilistic graph, such as the sum-product (SP) a…
PushNet efficiently and adaptively pushes messages in neural networks, improving performance.
problem Inefficient and inflexible synchronous message passing in neural networks.
method Asynchronous message passing with adaptive receptive fields and multiple scale correlations.
result PushNet outperforms competitors in semi-supervised node classification on multiple datasets.
MACE uses higher-order messages to create fast, accurate force fields.
problem Creating fast and accurate force fields in computational chemistry and materials science.
method Introducing MACE, an equivariant MPNN model that uses four-body messages.
result MACE reduces the required number of message passing iterations to just two, achieving state-of-the-art accuracy.
We study the misclassification error for community detection in general heterogeneous stochastic block models (SBM) with noisy or partial label information. We establish a connection between the misclassification rate and the notion of minimum energy on the local neighborhood of the SBM. We develop an optimally weighte…
MPLP learns neural network weights by treating operations as message-passing agents.
problem Training neural networks using gradient-based methods.
method MPLP abstracts neural network operations as message-passing agents, updating internal states and passing messages.
result MPLP outperforms traditional gradient-based methods on simple feed-forward neural networks.
Unified tutorial on AMP for high-dimensional problems.
problem Structured high-dimensional statistical problems.
method Statistical perspective of AMP and its applications.
result Unified and strengthened results in AMP literature.
DimeNet uses directional message passing to improve molecular predictions.
problem Lack of directional information in graph neural networks for molecules.
method Directional message passing, rotationally equivariant embeddings, spherical functions.
result DimeNet outperforms previous GNNs by 76% on MD17 and 31% on QM9.
A fundamental computation for statistical inference and accurate decision-making is to compute the marginal probabilities or most probable states of task-relevant variables. Probabilistic graphical models can efficiently represent the structure of such complex data, but performing these inferences is generally difficul…
New algorithms improve rank one signal estimation from noisy data.
problem Estimating a rank one signal matrix from corrupted data with rotationally invariant noise.
method Developed approximate message-passing algorithms exploiting eigenvalues and iterates denoisers.
result Achieves optimal asymptotic estimation error among iterative algorithms.
Maximum a posteriori (MAP) inference is a fundamental computational paradigm for statistical inference. In the setting of graphical models, MAP inference entails solving a combinatorial optimization problem to find the most likely configuration of the discrete-valued model. Linear programming (LP) relaxations in the Sh…
Proposes a new method for predicting missing relations in knowledge graphs.
problem Predicting missing relations between entities in knowledge graphs.
method Relational message passing method considering only edge features without entity IDs.
result PathCon method outperforms state-of-the-art methods significantly.
Introduces P-tensors for generalized higher-order message passing in graph neural networks.
problem Expanding the expressive power of graph neural networks through higher-order structures.
method Introduces P-tensors to define the most general form of permutation equivariant message passing.
result Achieves state-of-the-art performance on molecular datasets.
Improved algorithm for network alignment with binary diffing application.
problem Network alignment problem and binary diffing.
method Inspired by Bayati et al. [2], the algorithm uses message passing with modifications for speed and convergence.
result Our model outperforms state-of-the-art solvers in experiments.
Paper interprets contrastive learning dynamics using message passing.
problem Lack of rigorous understanding of contrastive learning dynamics.
method Casts contrastive objective into message passing scheme on augmentation graph.
result The learning dynamics of contrastive learning can be theoretically characterized.
Agent uses message passing to optimize robot navigation, balancing exploration and exploitation.
problem Optimizing robot navigation in continuous-valued spaces with uncertainty.
method Autoregressive active inference agent using message passing on a factor graph.
result Agent modulates action based on predictive uncertainty, leading to better model of dynamics.
New method explains GNNs using power iteration clustering.
problem Mysterious mechanism of message passing in GNNs.
method Subspace power iteration clustering (SPIC) models.
result Message passing in GNNs can be understood through power iteration.
We introduce an iterative optimization scheme for convex objectives consisting of a linear loss and a non-separable penalty, based on the expectation-consistent approximation and the vector approximate message-passing (VAMP) algorithm. Specifically, the penalties we approach are convex on a linear transformation of the…
Active sampling algorithm improves accuracy of inferred scores from pairwise comparisons.
problem Inference of accurate scores from time-consuming pairwise comparisons.
method Approximate message passing and expected information gain maximization.
result ASAP offers the highest accuracy of inferred scores compared to existing methods.