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Inverse problems, i.e., estimating parameters of physical models from experimental data, are ubiquitous in science and engineering. The Bayesian formulation is the gold standard because it alleviates ill-posedness issues and quantifies…

Multi-scale representations deeply learned via convolutional neural networks have shown tremendous importance for various pixel-level prediction problems. In this paper we present a novel approach that advances the state of the art on…

We present a new family of models that is based on graphs that may have undirected, directed and bidirected edges. We name these new models marginal AMP (MAMP) chain graphs because each of them is Markov equivalent to some AMP chain graph…

Model selection and learning the structure of graphical models from the data sample constitutes an important field of probabilistic graphical model research, as in most of the situations the structure is unknown and has to be learnt from…

We propose a new modeling approach that is a generalization of generative and discriminative models. The core idea is to use an implicit parameterization of a joint probability distribution by specifying only the conditional distributions.…

We introduce the Graph Mixture Density Networks, a new family of machine learning models that can fit multimodal output distributions conditioned on graphs of arbitrary topology. By combining ideas from mixture models and graph…

We consider n agents located on the vertices of a connected graph. Each agent v receives a signal X_v(0)~N(s, 1) where s is an unknown quantity. A natural iterative way of estimating s is to perform the following procedure. At iteration t +…

Graphical models or networks describe the statistical dependence among multiple variables and are widely used in biology (e.g., gene regulatory networks). Under appropriate assumptions, directed edges may represent causal relationships. A…

Generative models lack rigorous statistical guarantees for their outputs and are therefore unreliable in safety-critical applications. In this work, we propose Sequential Conformal Prediction for Generative Models (SCOPE-Gen), a sequential…

In this study, we present a multi-class graphical Bayesian predictive classifier that incorporates the uncertainty in the model selection into the standard Bayesian formalism. For each class, the dependence structure underlying the observed…

Link prediction aims to reveal missing edges in a graph. We address this task with a Gaussian process that is transformed using simplified graph convolutions to better leverage the inductive bias of the domain. To scale the Gaussian process…

Whittle-Mat\'ern fields are a recently introduced class of Gaussian processes on metric graphs, which are specified as solutions to a fractional-order stochastic differential equation. Unlike earlier covariance-based approaches for…

Graphs are ubiquitous in modelling relational structures. Recent endeavours in machine learning for graph-structured data have led to many architectures and learning algorithms. However, the graph used by these algorithms is often…

This paper introduces two new probabilistic graphical models for reconstruction of genetic regulatory networks using DNA microarray data. One is an Independence Graph (IG) model with either a forward or a backward search algorithm and the…

Graph-based collaborative filtering methods have prevailing performance for recommender systems since they can capture high-order information between users and items, in which the graphs are constructed from the observed user-item…

Graphical models are used to describe the conditional independence relations in multivariate data. They have been used for a variety of problems, including log-linear models (Liu and Massam, 2006), network analysis (Holland and Leinhardt,…

In this study, we introduce a sophisticated generative conditional strategy designed to impute missing values within datasets, an area of considerable importance in statistical analysis. Specifically, we initially elucidate the theoretical…

We study conditional independence relationships for random networks and their interplay with exchangeability. We show that, for finitely exchangeable network models, the empirical subgraph densities are maximum likelihood estimates of their…

Directed acyclic graphs provide a fundamental tool for representing directed dependence structures in multivariate network data, and are widely used to model financial and economic networks. However, accurate and interpretable estimation…

Network models are useful tools for modelling complex associations. If a Gaussian graphical model is assumed, conditional independence is determined by the non-zero entries of the inverse covariance (precision) matrix of the data. The…