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Gaussian graphical models are a popular tool to learn the dependence structure in the form of a graph among variables of interest. Bayesian methods have gained in popularity in the last two decades due to their ability to simultaneously…
Gaussian Graphical Models (GGMs) have wide-ranging applications in machine learning and the natural and social sciences. In most of the settings in which they are applied, the number of observed samples is much smaller than the dimension…
A conditional independence graph is a concise representation of pairwise conditional independence among many variables. Graphical Random Forests (GRaFo) are a novel method for estimating pairwise conditional independence relationships among…
Causal discovery methods are intrinsically constrained by the set of assumptions needed to ensure structure identifiability. Moreover additional restrictions are often imposed in order to simplify the inference task: this is the case for…
Stochastic inverse problems considered in this article consist of estimating the probability distributions of intrinsically random inputs of computer models. These estimations are based on observable outputs affected by model noise, and…
Gaussian graphical regressions have emerged as a powerful approach for regressing the precision matrix of a Gaussian graphical model on covariates, which, unlike traditional Gaussian graphical models, can help determine how graphs are…
Finding the parameters of a latent variable causal model is central to causal inference and causal identification. In this article, we show that existing graphical structures that are used in causal inference are not stable under…
We derive a method to reconstruct Gaussian signals from linear measurements with Gaussian noise. This new algorithm is intended for applications in astrophysics and other sciences. The starting point of our considerations is the principle…
This paper considers learning of the graphical structure of a $p$-dimensional random vector $X \in R^p$ using both parametric and non-parametric methods. Unlike the previous works which observe $x$ directly, we consider the indirect…
This work is concerned with the recovery of piecewise constant images from noisy linear measurements. We study the noise robustness of a variational reconstruction method, which is based on total (gradient) variation regularization. We show…
The pattern of zero entries in the inverse covariance matrix of a multivariate normal distribution corresponds to conditional independence restrictions between variables. Covariance selection aims at estimating those structural zeros from…
Linear structural equation models relate the components of a random vector using linear interdependencies and Gaussian noise. Each such model can be naturally associated with a mixed graph whose vertices correspond to the components of the…
We propose a Bayesian approximate inference method for learning the dependence structure of a Gaussian graphical model. Using pseudo-likelihood, we derive an analytical expression to approximate the marginal likelihood for an arbitrary…
Many important problems are characterized by the eigenvalues of a large matrix. For example, the difficulty of many optimization problems, such as those arising from the fitting of large models in statistics and machine learning, can be…
We consider learning Ising tree models when the observations from the nodes are corrupted by independent but non-identically distributed noise with unknown statistics. Katiyar et al. (2020) showed that although the exact tree structure…
We consider a structured estimation problem where an observed matrix is assumed to be generated as an $s$-sparse linear combination of $N$ given $n\times n$ positive-semidefinite matrices. Recovering the unknown $N$-dimensional and…
Gaussian graphical models represent the backbone of the statistical toolbox for analyzing continuous multivariate systems. However, due to the intrinsic properties of the multivariate normal distribution, use of this model family may hide…
Structural equation models are multivariate statistical models that are defined by specifying noisy functional relationships among random variables. We consider the classical case of linear relationships and additive Gaussian noise terms.…
We consider graphical models based on a recursive system of linear structural equations. This implies that there is an ordering, $\sigma$, of the variables such that each observed variable $Y_v$ is a linear function of a variable specific…
We address the problem of Bayesian structure learning for domains with hundreds of variables by employing non-parametric bootstrap, recursively. We propose a method that covers both model averaging and model selection in the same framework.…