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This paper studies the problem of estimating the covariance of a collection of vectors using only highly compressed measurements of each vector. An estimator based on back-projections of these compressive samples is proposed and analyzed. A…
Introducing inequality constraints in Gaussian process (GP) models can lead to more realistic uncertainties in learning a great variety of real-world problems. We consider the finite-dimensional Gaussian approach from Maatouk and Bay (2017)…
We present a multi-fidelity method for uncertainty quantification of parameter estimates in complex systems, leveraging generative models trained to sample the target conditional distribution. In the Bayesian inference setting, traditional…
We consider the topic of multivariate regression on manifold-valued output, that is, for a multivariate observation, its output response lies on a manifold. Moreover, we propose a new regression model to deal with the presence of grossly…
In numerous instances, the generalized exponential distribution can be used as an alternative to the most widely used non-regular family of distributions: Weibull, gamma, lognormal with three-parameters when analyzing lifetime or any skewed…
We introduce a doubly stochastic proximal gradient algorithm for optimizing a finite average of smooth convex functions, whose gradients depend on numerically expensive expectations. Our main motivation is the acceleration of the…
Distributed Gaussian process (DGP) is a popular approach to scale GP to big data which divides the training data into some subsets, performs local inference for each partition, and aggregates the results to acquire global prediction. To…
Data-driven Model Predictive Control (MPC), where the system model is learned from data with machine learning, has recently gained increasing interests in the control community. Gaussian Processes (GP), as a type of statistical models, are…
Multi-output Gaussian process (MGP) is commonly used as a transfer learning method to leverage information among multiple outputs. A key advantage of MGP is providing uncertainty quantification for prediction, which is highly important for…
The efficient modeling for disorder in a phenomena depends on the chosen score and objective functions. The main parameters in modeling are location, scale and shape. The exponential power distribution known as generalized Gaussian is…
Gaussian processes (GPs) are widely used as distributions of random effects in linear mixed models, which are fit using the restricted likelihood or the closely-related Bayesian analysis. This article addresses two problems. First, we…
This PhD Thesis presents an investigation into the analysis of financial returns using mixture models, focusing on mixtures of generalized normal distributions (MGND) and their extensions. The study addresses several critical issues…
An estimation problem of fundamental interest is that of phase synchronization, in which the goal is to recover a collection of phases using noisy measurements of relative phases. It is known that in the Gaussian noise setting, the maximum…
The Collective Graphical Model (CGM) models a population of independent and identically distributed individuals when only collective statistics (i.e., counts of individuals) are observed. Exact inference in CGMs is intractable, and previous…
The univariate generalized extreme value (GEV) distribution is the most commonly used tool for analyzing the properties of rare events. The ever greater utilization of Bayesian methods for extreme value analysis warrants detailed…
We consider the problem of computing a positive definite $p \times p$ inverse covariance matrix aka precision matrix $\theta=(\theta_{ij})$ which optimizes a regularized Gaussian maximum likelihood problem, with the elastic-net regularizer…
We consider a graphical model where a multivariate normal vector is associated with each node of the underlying graph and estimate the graphical structure. We minimize a loss function obtained by regressing the vector at each node on those…
Nowadays, more and more datasets are stored in a distributed way for the sake of memory storage or data privacy. The generalized eigenvalue problem (GEP) plays a vital role in a large family of high-dimensional statistical models. However,…
The multivariate version of the Mixed Tempered Stable is proposed. It is a generalization of the Normal Variance Mean Mixtures. Characteristics of this new distribution and its capacity in fitting tails and capturing dependence structure…
We consider a wide range of regularized stochastic minimization problems with two regularization terms, one of which is composed with a linear function. This optimization model abstracts a number of important applications in artificial…