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Tree-based ensemble methods, as Random Forests and Gradient Boosted Trees, have been successfully used for regression in many applications and research studies. Furthermore, these methods have been extended in order to deal with uncertainty…
We consider the problem of recovering the true causal structure among a set of variables, generated by a linear acyclic structural equation model (SEM) with the error terms being independent, not necessarily Gaussian, and having equal…
Variational auto-encoders (VAEs) are a popular and powerful deep generative model. Previous works on VAEs have assumed a factorized likelihood model, whereby the output uncertainty of each pixel is assumed to be independent. This…
We consider the problem of recovering the causal structure underlying observations from different experimental conditions when the targets of the interventions in each experiment are unknown. We assume a linear structural causal model with…
We provide a complete description of possible covariance matrices consistent with a Gaussian latent tree model for any tree. We then present techniques for utilising these constraints to assess whether observed data is compatible with that…
We introduce a novel class of graphical models, termed profile graphical models, that represent, within a single graph, how an external factor influences the dependence structure of a multivariate set of variables. This class is quite…
We consider the problem of recovering a structured signal $\mathbf{x} \in \mathbb{R}^{n}$ from noisy linear observations $\mathbf{y} =\mathbf{M} \mathbf{x}+\mathbf{w}$. The measurement matrix is modeled as $\mathbf{M} =…
The covariance structure of multivariate functional data can be highly complex, especially if the multivariate dimension is large, making extensions of statistical methods for standard multivariate data to the functional data setting…
This paper considers the objective comparison of stochastic models to solve inverse problems, more specifically image restoration. Most often, model comparison is addressed in a supervised manner, that can be time-consuming and partly…
We consider the challenging problem of statistical inference for exponential-family random graph models based on a single observation of a random graph with complex dependence. To facilitate statistical inference, we consider random graphs…
Probabilistic graphical models offer a powerful framework to account for the dependence structure between variables, which is represented as a graph. However, the dependence between variables may render inference tasks intractable. In this…
Graphical models are widely used in scienti fic and engineering research to represent conditional independence structures between random variables. In many controlled experiments, environmental changes or external stimuli can often alter…
We study the problem of causal structure learning from data using optimal transport (OT). Specifically, we first provide a constraint-based method which builds upon lower-triangular monotone parametric transport maps to design conditional…
This paper presents a unified geometric framework for the statistical analysis of a general ill-posed linear inverse model which includes as special cases noisy compressed sensing, sign vector recovery, trace regression, orthogonal matrix…
We present a Bayesian perspective on quantifying the uncertainty of graph signals estimated or reconstructed from imperfect observations. We show that many conventional methods of graph signal estimation, reconstruction and imputation, can…
We construct a tree-based dependence structure for the representation of binomial, Poisson and Gaussian random vectors having a given covariance matrix, using sums of independent random variables. This construction allows us to characterize…
Time series graphical models have recently received considerable attention for characterizing (conditional) dependence structures in multivariate time series. In many applications, the multivariate series exhibit variable-partitioned…
Graphs serve as generic tools to encode the underlying relational structure of data. Often this graph is not given, and so the task of inferring it from nodal observations becomes important. Traditional approaches formulate a convex inverse…
Real-world signals typically span across multiple dimensions, that is, they naturally reside on multi-way data structures referred to as tensors. In contrast to standard ``flat-view'' multivariate matrix models which are agnostic to data…
The estimation of linear causal models (also known as structural equation models) from data is a well-known problem which has received much attention in the past. Most previous work has, however, made an explicit or implicit assumption of…