Related papers: A New Algorithm for Maximum Likelihood Estimation …
Maximum Likelihood Estimation of continuous variable models can be very challenging in high dimensions, due to potentially complex probability distributions. The existence of multiple interdependencies among variables can make it very…
A covariance graph is an undirected graph associated with a multivariate probability distribution of a given random vector where each vertex represents each of the different components of the random vector and where the absence of an edge…
A concentration graph associated with a random vector is an undirected graph where each vertex corresponds to one random variable in the vector. The absence of an edge between any pair of vertices (or variables) is equivalent to full…
Seemingly unrelated regressions are statistical regression models based on the Gaussian distribution. They are popular in econometrics but also arise in graphical modeling of multivariate dependencies. In maximum likelihood estimation, the…
Bayesian methods for learning Gaussian graphical models offer a principled framework for quantifying model uncertainty and incorporating prior knowledge. However, their scalability is constrained by the computational cost of jointly…
Graphical model selection is a seemingly impossible task when many pairs of variables are never jointly observed; this requires inference of conditional dependencies with no observations of corresponding marginal dependencies. This…
Probabilistic independence can dramatically simplify the task of eliciting, representing, and computing with probabilities in large domains. A key technique in achieving these benefits is the idea of graphical modeling. We survey existing…
Maximum likelihood estimation is a common method of estimating the parameters of the probability distribution from a given sample. This paper aims to introduce the maximum likelihood estimation in the framework of sublinear expectation. We…
Undirected graphs are often used to describe high dimensional distributions. Under sparsity conditions, the graph can be estimated using $\ell_1$-penalization methods. We propose and study the following method. We combine a multiple…
Logistic regression is a fundamental and widely used statistical method for modeling binary outcomes based on covariates. However, the presence of missing data, particularly in settings involving hybrid covariates (a mix of discrete and…
Graphical models are commonly used tools for modeling multivariate random variables. While there exist many convenient multivariate distributions such as Gaussian distribution for continuous data, mixed data with the presence of discrete…
Directed acyclic graphs provide a fundamental tool for representing directed dependence structures in multivariate network data, and are widely used to model financial and economic networks. However, accurate and interpretable estimation…
We study Bayesian inference methods for solving linear inverse problems, focusing on hierarchical formulations where the prior or the likelihood function depend on unspecified hyperparameters. In practice, these hyperparameters are often…
Estimations of physical parameters using data usually involve non-uniform experimental efficiencies. In this article, a method of maximum likelihood fit is introduced using the efficiency as a weight, while the probability distribution…
Functional Gaussian graphical models (GGM) used for analyzing multivariate functional data customarily estimate an unknown graphical model representing the conditional relationships between the functional variables. However, in many…
Maximum likelihood estimation is effective for identifying dynamical systems, but applying it to large networks becomes computationally prohibitive. This paper introduces a maximum likelihood estimation method that enables identification of…
We present a stepwise approach to estimate high dimensional Gaussian graphical models. We exploit the relation between the partial correlation coefficients and the distribution of the prediction errors, and parametrize the model in terms of…
We introduce priors and algorithms to perform Bayesian inference in Gaussian models defined by acyclic directed mixed graphs. Such a class of graphs, composed of directed and bi-directed edges, is a representation of conditional…
Mechanistic network models specify the mechanisms by which networks grow and change, allowing researchers to investigate complex systems using both simulation and analytical techniques. Unfortunately, it is difficult to write likelihoods…
Likelihood based-learning of graphical models faces challenges of computational-complexity and robustness to model mis-specification. This paper studies methods that fit parameters directly to maximize a measure of the accuracy of predicted…