Gherardo Varando

University of Valencia | UV · Laboratorio de Procesado de Imagenes (LPI)

Bayesian networks are widely used to learn and reason about the dependence structure of discrete variables. However, they are only capable of formally encoding symmetric conditional independence, which in practice is often too strict to hold. Asymmetry-labeled DAGs have been recently proposed to both extend the class of Bayesian networks by relaxin...

Several structural learning algorithms for staged tree models, an asymmetric extension of Bayesian networks, have been defined. However, they do not scale efficiently as the number of variables considered increases. Here we introduce the first scalable structural learning algorithm for staged trees, which searches over a space of models where only...

stagedtrees is an R package which includes several algorithms for learning the structure of staged trees and chain event graphs from data. Score-based and clustering-based algorithms are implemented, as well as various functionalities to plot the models and perform inference. The capabilities of stagedtrees are illustrated using mainly two datasets...

Bayesian networks faithfully represent the symmetric conditional independences existing between the components of a random vector. Staged trees are an extension of Bayesian networks for categorical random vectors whose graph represents non-symmetric conditional independences via vertex coloring. However, since they are based on a tree representatio...

Bayesian networks are a widely-used class of probabilistic graphical models capable of representing symmetric conditional independence between variables of interest using the topology of the underlying graph. They can be seen as a special case of the much more general class of models called staged trees, which can represent any type of non-symmetri...

Tackling climate change needs to understand the complex phenomena occurring on the Planet. Discovering teleconnection patterns is an essential part of the endeavor. Events like El Niño Southern Oscillation (ENSO) impact essential climate variables at large distances, and influence the underlying Earth system dynamics. However, their automatic ident...

Causal discovery algorithms aims at untangling complex causal relationships using observational data only. Here, we introduce new causal discovery algorithms based on staged tree models, which can represent complex and non-symmetric causal effects. To demonstrate the efficacy of our algorithms, we introduce a new distance, inspired by the widely us...

Generative models for classification use the joint probability distribution of the class variable and the features to construct a decision rule. Among generative models, Bayesian networks and naive Bayes classifiers are the most commonly used and provide a clear graphical representation of the relationship among all variables. However, these have t...

The sparse Cholesky parametrization of the inverse covariance matrix is directly related to Gaussian Bayesian networks. Its counterpart, the covariance Cholesky factorization model, has a natural interpretation as a hidden variable model for ordered signal data. Despite this, it has received little attention so far, with few notable exceptions. To...

Structure learning methods for covariance and concentration graphs are often validated on synthetic models, usually obtained by randomly generating: (i) an undirected graph, and (ii) a compatible symmetric positive definite (SPD) matrix. In order to ensure positive definiteness in (ii), a dominant diagonal is usually imposed. In this work we invest...

We explore if it is possible to learn a directed acyclic graph (DAG) from data without imposing explicitly the acyclicity constraint. In particular, for Gaussian distributions, we frame structural learning as a sparse matrix factorization problem and we empirically show that solving an $\ell_1$-penalized optimization yields to good recovery of the...

The sparse Cholesky parametrization of the inverse covariance matrix can be interpreted as a Gaussian Bayesian network; however its counterpart, the covariance Cholesky factor, has received, with few notable exceptions, little attention so far, despite having a natural interpretation as a hidden variable model for ordered signal data. To fill this...

The linear Lyapunov equation of a covariance matrix parametrizes the equilibrium covariance matrix of a stochastic process. This parametrization can be interpreted as a new graphical model class, and we show how the model class behaves under marginalization and introduce a method for structure learning via $\ell_1$-penalized loss minimization. Our...

stagedtrees is an R package which includes several algorithms for learning the structure of staged trees and chain event graphs from data. Score-based and distance-based algorithms are implemented, as well as various functionalities to plot the models and perform inference. The capabilities of stagedtrees are illustrated using mainly two datasets b...

In this article, we describe the algorithms for causal structure learning from time series data that won the Causality 4 Climate competition at the Conference on Neural Information Processing Systems 2019 (NeurIPS). We examine how our combination of established ideas achieves competitive performance on semi-realistic and realistic time series data...

Structure learning methods for covariance and concentration graphs are often validated on synthetic models, usually obtained by randomly generating: (i) an undirected graph, and (ii) a compatible symmetric positive definite (SPD) matrix. In order to ensure positive definiteness in (ii), a dominant diagonal is usually imposed. In this work we invest...

We propose a novel Metropolis-Hastings algorithm to sample uniformly from the space of correlation matrices. Existing methods in the literature are based on elaborated representations of a correlation matrix, or on complex parametrizations of it. By contrast, our method is intuitive and simple, based the classical Cholesky factorization of a positi...

We show that, for generative classifiers, conditional independence corresponds to linear constraints for the induced discrimination functions. Discrimination functions of undirected Markov network classifiers can thus be characterized by sets of linear constraints. These constraints are represented by a second order finite difference operator over...

We propose a novel Metropolis-Hastings algorithm to sample uniformly from the space of correlation matrices. Existing methods in the literature are based on elaborated representations of a correlation matrix, or on complex parametrizations of it. By contrast, our method is intuitive and simple, based the classical Cholesky factorization of a positi...

Structure learning methods for covariance and concentration graphs are often validated on synthetic models, usually obtained by randomly generating: (i) an undirected graph, and (ii) a compatible symmetric positive definite (SPD) matrix. In order to ensure positive definiteness in (ii), a dominant diagonal is usually imposed. However, the link stre...

The development of 3D visualization and reconstruction methods to analyse microscopic structures at different levels of resolutions is of great importance to define brain microorganization and connectivity. MultiMap is a new tool that allows the visualization, 3D segmentation and quantification of fluorescent structures selectively in the neuropil...

Bayesian network classifiers are a powerful machine learning tool. In order to evaluate the expressive power of these models, we compute families of polynomials that sign-represent decision functions induced by Bayesian network classifiers. We prove that those families are linear combinations of products of Lagrange basis polynomials. In absence of...

In recent years, a plethora of approaches have been proposed to deal with the increasingly challenging task of multi-output regression. This study provides a survey on state-of-the-art multi-output regression methods, that are categorized as problem transformation and algorithm adaptation methods. In addition, we present the mostly used performance...

Multi-label classification problems require each instance to be assigned a subset of a defined set of labels. This problem is equivalent to finding a multi-valued decision function that predicts a vector of binary classes. In this paper we study the decision boundaries of two widely used approaches for building multi-label classifiers, when Bayesia...

Mixtures of polynomials (MoPs) are a nonparametric density estimation technique especially designed for hybrid Bayesian networks with continuous and discrete variables. Algorithms to learn one- and multidimensional (marginal) MoPs from data have recently been proposed. In this paper, we introduce two methods for learning MoP approximations of condi...

Bayesian network classifiers are widely used in machine learning because they intuitively represent causal relations. Multi-label classification problems require each instance to be assigned a subset of a defined set of h labels. This problem is equivalent to finding a multi-valued decision function that predicts a vector of h binary classes. In th...