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Biclustering has gained interest in gene expression data analysis due to its ability to identify groups of samples that exhibit similar behaviour in specific subsets of genes (or vice versa), in contrast to traditional clustering methods…

This paper studies inference for the mean vector of a high-dimensional $U$-statistic. In the era of Big Data, the dimension $d$ of the $U$-statistic and the sample size $n$ of the observations tend to be both large, and the computation of…

We propose an empirical Bayes estimator based on Dirichlet process mixture model for estimating the sparse normalized mean difference, which could be directly applied to the high dimensional linear classification. In theory, we build a…

This paper provides a framework for estimating the mean and variance of a high-dimensional normal density. The main setting considered is a fixed number of vector following a high-dimensional normal distribution with unknown mean and…

Machine learning (ML) research has yielded powerful tools for training accurate prediction models despite complex multivariate associations (e.g. interactions and heterogeneity). In fields such as medicine, improved interpretability of ML…

Machine learning models are being used extensively in many important areas, but there is no guarantee a model will always perform well or as its developers intended. Understanding the correctness of a model is crucial to prevent potential…

Sparse modelling or model selection with categorical data is challenging even for a moderate number of variables, because one parameter is roughly needed to encode one category or level. The Group Lasso is a well known efficient algorithm…

We present a novel coupled two-way clustering approach to gene microarray data analysis. The main idea is to identify subsets of the genes and samples, such that when one of these is used to cluster the other, stable and significant…

Several approaches have been proposed in the literature for clustering multivariate ordinal data. These methods typically treat missing values as absent information, rather than recognizing them as valuable for profiling population…

Bayes linear analysis and approximate Bayesian computation (ABC) are techniques commonly used in the Bayesian analysis of complex models. In this article we connect these ideas by demonstrating that regression-adjustment ABC algorithms…

The availability of large labeled datasets is the key component for the success of deep learning. However, annotating labels on large datasets is generally time-consuming and expensive. Active learning is a research area that addresses the…

This paper investigates the high-dimensional linear regression with highly correlated covariates. In this setup, the traditional sparsity assumption on the regression coefficients often fails to hold, and consequently many model selection…

Comparative meta-analyses of groups of subjects by integrating multiple observational studies rely on estimated propensity scores (PSs) to mitigate covariate imbalances. However, PS estimation grapples with the theoretical and practical…

In regression problems where covariates can be naturally grouped, the group Lasso is an attractive method for variable selection since it respects the grouping structure in the data. We study the selection and estimation properties of the…

In many social, economical, biological and medical studies, one objective is to classify a subject into one of several classes based on a set of variables observed from the subject. Because the probability distribution of the variables is…

The structural information in high-dimensional transposable data allows us to write the data recorded for each subject in a matrix such that both the rows and the columns correspond to variables of interest. One important problem is to test…

Mammography remains the most prevalent imaging tool for early breast cancer screening. The language used to describe abnormalities in mammographic reports is based on the breast Imaging Reporting and Data System (BI-RADS). Assigning a…

The demand of computational resources for the modeling process increases as the scale of the datasets does, since traditional approaches for regression involve inverting huge data matrices. The main problem relies on the large data size,…

Dimension reduction techniques have long been an important topic in statistics, and active subspaces (AS) have received much attention this past decade in the computer experiments literature. The most common approach towards estimating the…

Automatic cubatures approximate multidimensional integrals to user-specified error tolerances. For high dimensional problems, it makes sense to fix the sampling density but determine the sample size, $n$, automatically. Bayesian cubature…