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The periodic Gaussian process (PGP) has been increasingly used to model periodic data due to its high accuracy. Yet, computing the likelihood of PGP has a high computational complexity of $\mathcal{O}\left(n^{3}\right)$ ($n$ is the data…
We consider the problem of estimating a sparse precision matrix of a multivariate Gaussian distribution, including the case where the dimension $p$ is large. Gaussian graphical models provide an important tool in describing conditional…
Time-series datasets are central in machine learning with applications in numerous fields of science and engineering, such as biomedicine, Earth observation, and network analysis. Extensive research exists on state-space models (SSMs),…
We propose Partial Correlation Screening (PCS) as a new row-by-row approach to estimating a large precision matrix $\Omega$. To estimate the $i$-th row of $\Omega$, $1 \leq i \leq p$, PCS uses a Screen step and a Clean step. In the Screen…
This paper proposes a penalized composite likelihood method for model selection in colored graphical Gaussian models. The method provides a sparse and symmetry-constrained estimator of the precision matrix, and thus conducts model selection…
In this paper, we investigate seemingly unrelated regression (SUR) models that allow the number of equations (N) to be large, and to be comparable to the number of the observations in each equation (T). It is well known in the literature…
This paper introduces Polynomial Graphical Lasso (PGL), a new approach to learning graph structures from nodal signals. Our key contribution lies in modeling the signals as Gaussian and stationary on the graph, enabling the development of a…
We propose a novel quasi-Newton method for solving the sparse inverse covariance estimation problem also known as the graphical least absolute shrinkage and selection operator (GLASSO). This problem is often solved using a second-order…
The sparse precision matrix plays an essential role in the Gaussian graphical model since a zero off-diagonal element indicates conditional independence of the corresponding two variables given others. In the Gaussian graphical model, many…
Many Machine Learning algorithms are formulated as regularized optimization problems, but their performance hinges on a regularization parameter that needs to be calibrated to each application at hand. In this paper, we propose a general…
In recent literature, the Gaussian Graphical model (GGM; Lauritzen, 1996),a network of partial correlation coefficients, has been used to capture potential dynamic relationships between observed variables. The GGM can be estimated using…
Gaussian graphical models are used for determining conditional relationships between variables. This is accomplished by identifying off-diagonal elements in the inverse-covariance matrix that are non-zero. When the ratio of variables (p) to…
Geostatistics is a branch of statistics concerned with stochastic processes over continuous domains, with Gaussian processes (GPs) providing a flexible and principled modelling framework. However, the high computational cost of simulating…
The graphical lasso is a widely used algorithm for fitting undirected Gaussian graphical models. However, for inference on functionals of edge values in the learned graph, standard tools lack formal statistical guarantees, such as control…
Gaussian graphical models provide a powerful framework for studying conditional dependencies in multivariate data, with widespread applications spanning biomedical, environmental sciences, and other data-rich scientific domains. While the…
Graphical lasso is one of the most used estimators for inferring genetic networks. Despite its diffusion, there are several fields in applied research where the limits of detection of modern measurement technologies make the use of this…
This paper considers the problem of estimating multiple related Gaussian graphical models from a $p$-dimensional dataset consisting of different classes. Our work is based upon the formulation of this problem as group graphical lasso. This…
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…
The estimation of a precision matrix is a crucial problem in various research fields, particularly when working with high dimensional data. In such settings, the most common approach is to use the penalized maximum likelihood. The…
Gaussian Graphical Models (GGMs) are popular tools for studying network structures. However, many modern applications such as gene network discovery and social interactions analysis often involve high-dimensional noisy data with outliers or…