Related papers: PC algorithm for Gaussian copula graphical models
Testing independence among a number of (ultra) high-dimensional random samples is a fundamental and challenging problem. By arranging $n$ identically distributed $p$-dimensional random vectors into a $p \times n$ data matrix, we investigate…
One of the main challenges in current systems neuroscience is the analysis of high-dimensional neuronal and behavioral data that are characterized by different statistics and timescales of the recorded variables. We propose a parametric…
Gaussian graphical model is a graphical representation of the dependence structure for a Gaussian random vector. It is recognized as a powerful tool in different applied fields such as bioinformatics, error-control codes, speech language,…
Genetical genomics experiments have now been routinely conducted to measure both the genetic markers and gene expression data on the same subjects. The gene expression levels are often treated as quantitative traits and are subject to…
Estimating causal interactions in complex dynamical systems is an important problem encountered in many fields of current science. While a theoretical solution for detecting the causal interactions has been previously formulated in the…
Max-linear Bayesian networks (MLBNs) are a relatively recent class of structural equation models which arise when the random variables involved have heavy-tailed distributions. Unlike most directed graphical models, MLBNs are typically not…
Physical phenomena are observed in many fields (sciences and engineering) and are often studied by time-consuming computer codes. These codes are analyzed with statistical models, often called emulators. In many situations, the physical…
Gaussian Graphical models (GGM) are widely used to estimate the network structures in many applications ranging from biology to finance. In practice, data is often corrupted by latent confounders which biases inference of the underlying…
Due to their flexibility, Gaussian processes (GPs) have been widely used in nonparametric function estimation. A prior information about the underlying function is often available. For instance, the physical system (computer model output)…
Gaussian process (GP) models are widely used to emulate propagation uncertainty in computer experiments. GP emulation sits comfortably within an analytically tractable Bayesian framework. Apart from propagating uncertainty of the input…
With the significant advancement in quantum computation in the past couple of decades, the exploration of machine-learning subroutines using quantum strategies has become increasingly popular. Gaussian process regression is a widely used…
Gaussian process is a theoretically appealing model for nonparametric analysis, but its computational cumbersomeness hinders its use in large scale and the existing reduced-rank solutions are usually heuristic. In this work, we propose a…
Gaussian process emulators of computationally expensive computer codes provide fast statistical approximations to model physical processes. The training of these surrogates depends on the set of design points chosen to run the simulator.…
It is well known that the dependence structure for jointly Gaussian variables can be fully captured using correlations, and that the conditional dependence structure in the same way can be described using partial correlations. The partial…
Principal component analysis (PCA) is a widespread technique for data analysis that relies on the covariance-correlation matrix of the analyzed data. However to properly work with high-dimensional data, PCA poses severe mathematical…
The partial correlation graphical LASSO (PCGLASSO) is a penalised likelihood method for Gaussian graphical models which provides scale invariant sparse estimation of the precision matrix and improves upon the popular graphical LASSO method.…
The graphical structure of Probabilistic Graphical Models (PGMs) encodes the conditional independence (CI) relations that hold in the modeled distribution. Graph algorithms, such as d-separation, use this structure to infer additional…
In this contribution we deal with the problem of learning an undirected graph which encodes the conditional dependence relationship between variables of a complex system, given a set of observations of this system. This is a very central…
Non-parametric reconstruction methods, such as Gaussian process (GP) regression, provide a model-independent way of estimating an underlying function and its uncertainty from noisy data. We demonstrate how GP-reconstruction can be used as a…
Linear non-Gaussian causal models postulate that each random variable is a linear function of parent variables and non-Gaussian exogenous error terms. We study identification of the linear coefficients when such models contain latent…