Related papers: Regularized Estimation and Testing for High-Dimens…

We consider a class of infinite-dimensional optimization problems in which a distributed vector-valued variable should pointwise almost everywhere take values from a given finite set $\mathcal{M}\subset\mathbb{R}^m$. Such hybrid…

We propose a novel framework for learning stabilizable nonlinear dynamical systems for continuous control tasks in robotics. The key contribution is a control-theoretic regularizer for dynamics fitting rooted in the notion of…

This paper studies the high-dimensional mixed linear regression (MLR) where the output variable comes from one of the two linear regression models with an unknown mixing proportion and an unknown covariance structure of the random…

We derive an efficient stochastic algorithm for inverse problems that present an unknown linear forcing term and a set of nonlinear parameters to be recovered. It is assumed that the data is noisy and that the linear part of the problem is…

Recently there is a large amount of work devoted to the study of Markov chain stochastic gradient methods (MC-SGMs) which mainly focus on their convergence analysis for solving minimization problems. In this paper, we provide a…

The design of biological systems is hindered by uncertainty arising from both intrinsic stochasticity of biomolecular reactions and variability across laboratory or experimental conditions. In this work, we present a sequential framework to…

In multistage decision problems, it is often the case that an initial strategic decision (such as investment) is followed by many operational ones (operating the investment). Such initial strategic decision can be seen as a parameter…

The concept of Granger causality is increasingly being applied for the characterization of directional interactions in different applications. A multivariate framework for estimating Granger causality is essential in order to account for…

Mixed membership models are an extension of finite mixture models, where each observation can partially belong to more than one mixture component. A probabilistic framework for mixed membership models of high-dimensional continuous data is…

A multivariate quantile regression model with a factor structure is proposed to study data with many responses of interest. The factor structure is allowed to vary with the quantile levels, which makes our framework more flexible than the…

Theoretical guarantees are established for a standard estimator in a semi-parametric finite mixture model, where each component density is modeled as a product of univariate densities under a conditional independence assumption. The focus…

Matrix regression plays an important role in modern data analysis due to its ability to handle complex relationships involving both matrix and vector variables. We propose a class of regularized regression models capable of predicting both…

The objective of this study is to develop a good risk model for classifying business delinquency by simultaneously exploring several machine learning based methods including regularization, hyper-parameter optimization, and model ensembling…

Supervised learning with large-scale data usually leads to complex optimization problems, especially for classification tasks with multiple classes. Stochastic subgradient methods can enable efficient learning with a large number of samples…

As is the case for many curved exponential families, the computation of maximum likelihood estimates in a multivariate normal model with a Kronecker covariance structure is typically carried out with an iterative algorithm, specifically, a…

We introduce a new family of one factor distributions for high-dimensional binary data. The model provides an explicit probability for each event, thus avoiding the numeric approximations often made by existing methods. Model interpretation…

This paper studies the estimation of low-rank Markov chains from empirical trajectories. We propose a non-convex estimator based on rank-constrained likelihood maximization. Statistical upper bounds are provided for the Kullback-Leiber…

Time series of matrix-valued data are increasingly available in various areas including economics, finance, social science, among others. These data may shed light on the inter-dynamical relationships between two sets of attributes, for…

Model instability and poor prediction of long-term behavior are common problems when modeling dynamical systems using nonlinear "black-box" techniques. Direct optimization of the long-term predictions, often called simulation error…

Robust Markov decision processes (MDPs) aim to handle changing or partially known system dynamics. To solve them, one typically resorts to robust optimization methods. However, this significantly increases computational complexity and…