Related papers: On Approximate Nonlinear Gaussian Message Passing …

Signal processing on directed graphs (digraphs) is problematic, since the graph shift, and thus associated filters, are in general not diagonalizable. Furthermore, the Fourier transform in this case is now obtained from the Jordan…

In this paper, we focus on the matching recovery problem between a pair of correlated Gaussian Wigner matrices with a latent vertex correspondence. We are particularly interested in a robust version of this problem such that our observation…

In this article, we present a visual introduction to Gaussian Belief Propagation (GBP), an approximate probabilistic inference algorithm that operates by passing messages between the nodes of arbitrarily structured factor graphs. A special…

In this work we perform some mathematical analysis on non-negative matrix factorizations (NMF) and apply NMF to some imaging and inverse problems. We will propose a sparse low-rank approximation of big positive data and images in terms of…

Recently, several studies proposed non-linear transformations, such as a logarithmic or Gaussianization transformation, as efficient tools to recapture information about the (Gaussian) initial conditions. During non-linear evolution, part…

Graph neural networks have recently achieved great successes in predicting quantum mechanical properties of molecules. These models represent a molecule as a graph using only the distance between atoms (nodes). They do not, however,…

Approximate message passing algorithms proved to be extremely effective in reconstructing sparse signals from a small number of incoherent linear measurements. Extensive numerical experiments further showed that their dynamics is accurately…

Foundation models have achieved remarkable success across many domains, relying on pretraining over vast amounts of data. Graph-structured data often lacks the same scale as unstructured data, making the development of graph foundation…

Continuous-time state estimation is gaining in popularity due to its abilities to provide smooth solutions, handle asynchronous sensors, and interpolate between data points. While there are two main paradigms, parametric (e.g., temporal…

Graph Neural Networks (GNNs) have shown great power in various domains. However, their predictions may inherit societal biases on sensitive attributes, limiting their adoption in real-world applications. Although many efforts have been…

We consider the task of estimating a low-rank matrix from non-linear and noisy observations. We prove a strong universality result showing that Bayes-optimal performances are characterized by an equivalent Gaussian model with an effective…

Probabilistic graphical models are widely used to model complex systems under uncertainty. Traditionally, Gaussian directed graphical models are applied for analysis of large networks with continuous variables as they can provide…

The compute-and-forward framework permits each receiver in a Gaussian network to directly decode a linear combination of the transmitted messages. The resulting linear combinations can then be employed as an end-to-end communication…

Message passing neural networks have become a method of choice for learning on graphs, in particular the prediction of chemical properties and the acceleration of molecular dynamics studies. While they readily scale to large training data…

Gaussian Boson Sampling is a non-universal model for quantum computing inspired by the original formulation of the Boson Sampling problem. Nowadays, it represents a paradigmatic quantum platform to reach the quantum advantage regime in a…

We present nested sampling for factor graphs (NSFG), a novel nested sampling approach to approximate inference for posterior distributions expressed over factor-graphs. Performing such inference is a key step in simultaneous localization…

A Gaussian process (GP)-based methodology is proposed to emulate complex dynamical computer models (or simulators). The method relies on emulating the numerical flow map of the system over an initial (short) time step, where the flow map is…

Gaussian and quadratic approximations of message passing algorithms on graphs have attracted considerable recent attention due to their computational simplicity, analytic tractability, and wide applicability in optimization and statistical…

The perceived advantage of machine learning (ML) models is that they are flexible and can incorporate a large number of features. However, many of these are typically correlated or dependent, and incorporating all of them can hinder model…

We propose a Fourier-based learning algorithm for highly nonlinear multiclass classification. The algorithm is based on a smoothing technique to calculate the probability distribution of all classes. To obtain the probability distribution,…