Related papers: Dealing with collinearity in large-scale linear sy…

This paper proposes a novel uncertainty quantification framework for computationally demanding systems characterized by a large vector of non-Gaussian uncertainties. It combines state-of-the-art techniques in advanced Monte Carlo sampling…

Principal component regression uses principal components as regressors. It is particularly useful in prediction settings with high-dimensional covariates. The existing literature treating of Bayesian approaches is relatively sparse. We…

We develop a method to carry out MAP estimation for a class of Bayesian regression models in which coefficients are assigned with Gaussian-based spike and slab priors. The objective function in the corresponding optimization problem has a…

This paper develops a sequential-linearization feedback optimization framework for driving nonlinear dynamical systems to an optimal steady state. A fundamental challenge in feedback optimization is the requirement of accurate first-order…

Dynamical system state estimation and parameter calibration problems are ubiquitous across science and engineering. Bayesian approaches to the problem are the gold standard as they allow for the quantification of uncertainties and enable…

The goal of robust motion planning consists of designing open-loop controls which optimally steer a system to a specific target region while mitigating uncertainties and disturbances which affect the dynamics. Recently, stochastic optimal…

This thesis develops exact analytical tools to study strongly correlated stochastic systems, with a focus on extreme value statistics, gap statistics, and full counting statistics in multi-particle processes. A central contribution is the…

A typical problem in causal modeling is the instability of model structure learning, i.e., small changes in finite data can result in completely different optimal models. The present work introduces a novel causal modeling algorithm for…

We develop a new efficient methodology for Bayesian global sensitivity analysis for large-scale multivariate data. The focus is on computationally demanding models with correlated variables. A multivariate Gaussian process is used as a…

We propose an extension of the input-output feedback linearization for a class of multivariate systems that are not input-output linearizable in a classical manner. The key observation is that the usual input-output linearization problem…

We study feedback stabilization of continuous-time linear systems under finite data-rate constraints in the presence of unknown disturbances. A communication and control strategy based on sampled and quantized state measurements is…

We apply a recently developed measure of multiscale complexity to the Gaussian model consisting of continuous spins with bilinear interactions for a variety of interaction matrix structures. We find two universal behaviors of the complexity…

This paper addresses the positive synchronization of interconnected systems on undirected graphs. For homogeneous positive systems, a static feedback protocol design is proposed, based on the Linear Regulator problem. The solution to the…

Discovering the underlying dynamics of complex systems from data is an important practical topic. Constrained optimization algorithms are widely utilized and lead to many successes. Yet, such purely data-driven methods may bring about…

We present a Bayesian approach for modeling multivariate, dependent functional data. To account for the three dominant structural features in the data--functional, time dependent, and multivariate components--we extend hierarchical dynamic…

Current methods for regularization in machine learning require quite specific model assumptions (e.g. a kernel shape) that are not derived from prior knowledge about the application, but must be imposed merely to make the method work. We…

We consider the problem of jointly estimating multiple related zero-mean Gaussian distributions from data. We propose to jointly estimate these covariance matrices using Laplacian regularized stratified model fitting, which includes loss…

The Bayesian approach to inverse problems typically relies on posterior sampling approaches, such as Markov chain Monte Carlo, for which the generation of each sample requires one or more evaluations of the parameter-to-observable map or…

Using Kalman techniques, it is possible to perform optimal estimation in linear Gaussian state-space models. We address here the case where the noise probability density functions are of unknown functional form. A flexible Bayesian…

This paper introduces a Bayesian framework that combines Markov chain Monte Carlo (MCMC) sampling, dimensionality reduction, and neural density estimation to efficiently handle inverse problems that (i) must be solved multiple times, and…