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We consider the consistency properties of a regularised estimator for the simultaneous identification of both changepoints and graphical dependency structure in multivariate time-series. Traditionally, estimation of Gaussian Graphical…
In this paper, we aim to give a theoretical approximation for the penalty level of $\ell_{1}$-regularization problems. This can save much time in practice compared with the traditional methods, such as cross-validation. To achieve this…
Non-concave penalized maximum likelihood methods, such as the Bridge, the SCAD, and the MCP, are widely used because they not only do parameter estimation and variable selection simultaneously but also have a high efficiency as compared to…
We address the image restoration problem under Poisson noise corruption. The Kullback-Leibler divergence, which is typically adopted in the variational framework as data fidelity term in this case, is coupled with the second-order Total…
Linear inverse problems are ubiquitous. Often the measurements do not follow a Gaussian distribution. Additionally, a model matrix with a large condition number can complicate the problem further by making it ill-posed. In this case, the…
In a first part, we present a mathematical analysis of a general methodology of a probabilistic learning inference that allows for estimating a posterior probability model for a stochastic boundary value problem from a prior probability…
We consider the problem of estimating a time-varying sparse precision matrix, which is assumed to evolve in a piece-wise constant manner. Building upon the Group Fused LASSO and LASSO penalty functions, we estimate both the network…
This paper is devoted to the estimation of a partial graphical model with a structural Bayesian penalization. Precisely, we are interested in the linear regression setting where the estimation is made through the direct links between…
We emphasize that it is possible to improve the principle of unbiased risk estimation for model selection by addressing excess risk deviations in the design of penalization procedures. Indeed, we propose a modification of Akaike's…
In this paper we study algorithms to find a Gaussian approximation to a target measure defined on a Hilbert space of functions; the target measure itself is defined via its density with respect to a reference Gaussian measure. We employ the…
In parametric estimation of covariance function of Gaussian processes, it is often the case that the true covariance function does not belong to the parametric set used for estimation. This situation is called the misspecified case. In this…
Regularization is often used in high-dimensional regression settings to generate a sparse model, which can save tremendous computing resources and identify predictors that are most strongly associated with the response. When the predictors…
Graphical models describe associations between variables through the notion of conditional independence. Gaussian graphical models are a widely used class of such models where the relationships are formalized by non-null entries of the…
Graphical Gaussian models are popular tools for the estimation of (undirected) gene association networks from microarray data. A key issue when the number of variables greatly exceeds the number of samples is the estimation of the matrix of…
Classic Bayesian methods with complex models are frequently infeasible due to an intractable likelihood. Simulation-based inference methods, such as Approximate Bayesian Computing (ABC), calculate posteriors without accessing a likelihood…
We consider estimation of undirected Gaussian graphical models and inverse covariances in high-dimensional scenarios by penalizing the corresponding precision matrix. While single $L_1$ (Graphical Lasso) and $L_2$ (Graphical Ridge)…
This work addresses the problem of graph learning from data following a Gaussian Graphical Model (GGM) with a time-varying mean. Graphical Lasso (GL), the standard method for estimating sparse precision matrices, assumes that the observed…
In the gravitational-wave analysis of pulsar-timing-array datasets, parameter estimation is usually performed using Markov Chain Monte Carlo methods to explore posterior probability densities. We introduce an alternative procedure that…
Generalized cross validation (GCV) is one of the most important approaches used to estimate parameters in the context of inverse problems and regularization techniques. A notable example is the determination of the smoothness parameter in…
Bayesian inference for graphical models has received much attention in the literature in recent years. It is well known that when the graph G is decomposable, Bayesian inference is significantly more tractable than in the general…