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Variable selection for models including interactions between explanatory variables often needs to obey certain hierarchical constraints. The weak or strong structural hierarchy requires that the existence of an interaction term implies at…
Multi-task learning is increasingly used to investigate the association structure between multiple responses and a single set of predictor variables in many applications. In the era of big data, the coexistence of incomplete outcomes, large…
With the advent of ubiquitous monitoring and measurement protocols, studies have started to focus more and more on complex, multivariate and heterogeneous datasets. In such studies, multivariate response variables are drawn from a…
We develop a new method for selecting the penalty parameter for $\ell_{1}$-penalized M-estimators in high dimensions, which we refer to as bootstrapping after cross-validation. We derive rates of convergence for the corresponding…
The amount of graph-structured data has recently experienced an enormous growth in many applications. To transform such data into useful information, fast analytics algorithms and software tools are necessary. One common graph analytics…
Datasets containing both categorical and continuous variables are frequently encountered in many areas, and with the rapid development of modern measurement technologies, the dimensions of these variables can be very high. Despite the…
Including a large number of predictors in the imputation model underlying a multiple imputation (MI) procedure is one of the most challenging tasks imputers face. A variety of high-dimensional MI techniques can help, but there has been…
We consider the problem of jointly modeling and clustering populations of tensors by introducing a high-dimensional tensor mixture model with heterogeneous covariances. To effectively tackle the high dimensionality of tensor objects, we…
Network structure is growing popular for capturing the intrinsic relationship between large-scale variables. In the paper we propose to improve the estimation accuracy for large-dimensional factor model when a network structure between…
The divide and conquer method is a common strategy for handling massive data. In this article, we study the divide and conquer method for cubic-rate estimators under the massive data framework. We develop a general theory for establishing…
We consider nonlinear mixed effects models including high-dimensional covariates to model individual parameters variability. The objective is to identify relevant covariates among a large set under sparsity assumption and to estimate model…
Missing data are frequently encountered in high-dimensional problems, but they are usually difficult to deal with using standard algorithms, such as the expectation-maximization (EM) algorithm and its variants. To tackle this difficulty,…
This paper develops a novel hybrid approach for estimating the mixture model of $t$-factor analyzers (MtFA) that employs multivariate $t$-distribution and factor model to cluster and characterize grouped data. The traditional estimation…
Standard approaches to decision-making under uncertainty focus on sequential exploration of the space of decisions. However, \textit{simultaneously} proposing a batch of decisions, which leverages available resources for parallel…
When multitudes of features can plausibly be associated with a response, both privacy considerations and model parsimony suggest grouping them to increase the predictive power of a regression model. Specifically, the identification of…
The literature on clustering for continuous data is rich and wide; differently, that one developed for categorical data is still limited. In some cases, the problem is made more difficult by the presence of noise variables/dimensions that…
We investigate the parameter estimation of regression models with fixed group effects, when the group variable is missing while group related variables are available. This problem involves clustering to infer the missing group variable…
Neural networks are usually not the tool of choice for nonparametric high-dimensional problems where the number of input features is much larger than the number of observations. Though neural networks can approximate complex multivariate…
We consider the task of meta-analysis in high-dimensional settings in which the data sources are similar but non-identical. To borrow strength across such heterogeneous datasets, we introduce a global parameter that emphasizes…
Mixed-effect models are very popular for analyzing data with a hierarchical structure, e.g. repeated observations within subjects in a longitudinal design, patients nested within centers in a multicenter design. However, recently, due to…