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In many environmental applications involving spatially-referenced data, limitations on the number and locations of observations motivate the need for practical and efficient models for spatial interpolation, or kriging. A key component of…

As technology advanced, collecting data via automatic collection devices become popular, thus we commonly face data sets with lengthy variables, especially when these data sets are collected without specific research goals beforehand. It…

A semi-parametric, non-linear regression model in the presence of latent variables is introduced. These latent variables can correspond to unmodeled phenomena or unmeasured agents in a complex networked system. This new formulation allows…

We develop a new method for multivariate scalar on multidimensional distribution regression. Traditional approaches typically analyze isolated univariate scalar outcomes or consider unidimensional distributional representations as…

We propose a robust inferential procedure for assessing uncertainties of parameter estimation in high-dimensional linear models, where the dimension $p$ can grow exponentially fast with the sample size $n$. Our method combines the…

There is increasing interest in modeling high-dimensional longitudinal outcomes in applications such as developmental neuroimaging research. Growth curve model offers a useful tool to capture both the mean growth pattern across individuals,…

A new sparse semiparametric model is proposed, which incorporates the influence of two functional random variables in a scalar response in a flexible and interpretable manner. One of the functional covariates is included through a…

Motivated by normalizing DNA microarray data and by predicting the interest rates, we explore nonparametric estimation of additive models with highly correlated covariates. We introduce two novel approaches for estimating the additive…

The paper considers linear regression problems where the number of predictor variables is possibly larger than the sample size. The basic motivation of the study is to combine the points of view of model selection and functional regression…

The increased availability of massive data sets provides a unique opportunity to discover subtle patterns in their distributions, but also imposes overwhelming computational challenges. To fully utilize the information contained in big…

This thesis responds to the challenges of using a large number, such as thousands, of features in regression and classification problems. There are two situations where such high dimensional features arise. One is when high dimensional…

We propose a model selection approach for covariance estimation of a multi-dimensional stochastic process. Under very general assumptions, observing i.i.d replications of the process at fixed observation points, we construct an estimator of…

We address the problem of constructing varying-coefficient models based on basis expansions along with the technique of regularization. A crucial point in our modeling procedure is the selection of smoothing parameters in the regularization…

In this paper, we develop a systematic theory for high dimensional analysis of variance in multivariate linear regression, where the dimension and the number of coefficients can both grow with the sample size. We propose a new \emph{U}~type…

A ubiquitous feature of data of our era is their extra-large sizes and dimensions. Analyzing such high-dimensional data poses significant challenges, since the feature dimension is often much larger than the sample size. This thesis…

We propose a recurrent neural network for a "model-free" simulation of a dynamical system with unknown parameters without prior knowledge. The deep learning model aims to jointly learn the nonlinear time marching operator and the effects of…

Logistic regression is key method for modeling the probability of a binary outcome based on a collection of covariates. However, the classical formulation of logistic regression relies on the independent sampling assumption, which is often…

This paper proposes a new method for estimating high-dimensional binary choice models. We consider a semiparametric model that places no distributional assumptions on the error term, allows for heteroskedastic errors, and permits endogenous…

Variational inference is an alternative estimation technique for Bayesian models. Recent work shows that variational methods provide consistent estimation via efficient, deterministic algorithms. Other tools, such as model selection using…

Variable selection plays a fundamental role in high-dimensional data analysis. Various methods have been developed for variable selection in recent years. Well-known examples are forward stepwise regression (FSR) and least angle regression…