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Statistical inference of the high-dimensional regression coefficients is challenging because the uncertainty introduced by the model selection procedure is hard to account for. A critical question remains unsettled; that is, is it possible…
We consider high-dimensional binary classification by sparse logistic regression. We propose a model/feature selection procedure based on penalized maximum likelihood with a complexity penalty on the model size and derive the non-asymptotic…
This the text of a proceeding accepted for the 21st International Symposium on Mathematical Theory of Networks and Systems (MTNS 2014). We present some results of an ongoing research on the controllability problem of an abstract bilinear…
Data characterized by high dimensionality and sparsity are commonly used to describe real-world node interactions. Low-rank representation (LR) can map high-dimensional sparse (HDS) data to low-dimensional feature spaces and infer node…
We propose a finite-dimensional control-based method to approximate solution operators for evolutional partial differential equations (PDEs), particularly in high-dimensions. By employing a general reduced-order model, such as a deep neural…
We propose methodology for statistical inference for low-dimensional parameters of sparse precision matrices in a high-dimensional setting. Our method leads to a non-sparse estimator of the precision matrix whose entries have a Gaussian…
Model Predictive Control is an extremely effective control method for systems with input and state constraints. Model Predictive Control performance heavily depends on the accuracy of the open-loop prediction. For systems with uncertainty…
We consider the Chance Constrained Model Predictive Control problem for polynomial systems subject to disturbances. In this problem, we aim at finding optimal control input for given disturbed dynamical system to minimize a given cost…
We provide a general theory of the expectation-maximization (EM) algorithm for inferring high dimensional latent variable models. In particular, we make two contributions: (i) For parameter estimation, we propose a novel high dimensional EM…
As its name suggests, sufficient dimension reduction (SDR) targets to estimate a subspace from data that contains all information sufficient to explain a dependent variable. Ample approaches exist to SDR, some of the most recent of which…
This paper develops a unified methodology for probabilistic analysis and optimal control design for jump diffusion processes defined by polynomials. For such systems, the evolution of the moments of the state can be described via a system…
This paper deals with a distributed implementation of minimax adaptive control algorithm for networked dynamical systems modeled by a finite set of linear models. To hedge against the uncertainty arising out of finite number of possible…
We propose methodology for estimation of sparse precision matrices and statistical inference for their low-dimensional parameters in a high-dimensional setting where the number of parameters $p$ can be much larger than the sample size. We…
In distributed statistical learning, $N$ samples are split across $m$ machines and a learner wishes to use minimal communication to learn as well as if the examples were on a single machine. This model has received substantial interest in…
This article presents proposals for the design of reduced-order controllers for high-dimensional dynamical systems. The objective is to develop efficient control strategies that ensure stability and robustness with reduced computational…
Distributionally robust control is a well-studied framework for optimal decision making under uncertainty, with the objective of minimizing an expected cost function over control actions, assuming the most adverse probability distribution…
We present an exact dimensional reduction for high-dimensional dynamical systems composed of $N$ identical dynamical units governed by quasi-linear ordinary differential equations (ODEs) of order $M$. In these systems, each unit follows a…
In this paper, we investigate the architecture of an optimal controller that maximizes the convergence speed of a consensus protocol with single-integrator dynamics. Under the assumption that communication delays increase with the number of…
We consider the problem of controlling the group behavior of a large number of dynamic systems that are constantly interacting with each other. These systems are assumed to have identical dynamics (e.g., birds flock, robot swarm) and their…
Learning or identifying dynamics from a sequence of high-dimensional observations is a difficult challenge in many domains, including reinforcement learning and control. The problem has recently been studied from a generative perspective…