Related papers: Dimensionality determination: a thresholding doubl…

Sufficient dimension reduction (SDR) methods, which often rely on class precision matrices, are widely used in supervised statistical classification problems. However, when class-specific sample sizes are small relative to the original…

There are several ways to measure the compressibility of a random measure; they include general approaches such as using the rate-distortion curve, as well as more specific notions, such as the Renyi information dimension (RID). The RID…

This paper studies the inference about linear functionals of high-dimensional low-rank matrices. While most existing inference methods would require consistent estimation of the true rank, our procedure is robust to rank misspecification,…

Bayesian inverse problems use observed data to update a prior probability distribution for an unknown state or parameter of a scientific system to a posterior distribution conditioned on the data. In many applications, the unknown parameter…

A bottleneck of sufficient dimension reduction (SDR) in the modern era is that, among numerous methods, only the sliced inverse regression (SIR) is generally applicable under the high-dimensional settings. The higher-order inverse…

Recently, matrix-valued time series data have attracted significant attention in the literature with the recognition of threshold nonlinearity representing a significant advance. However, given the fact that a matrix is a two-array…

The evolution of local defects such as dislocations and cracks often determines the performance of engineering materials. For a proper description and understanding of these phenomena, one needs to descend to a very small scale, at which…

This paper proposes a new hybrid high-order discretization for the biharmonic problem and the corresponding eigenvalue problem. The discrete ansatz space includes degrees of freedom in $n-2$ dimensional submanifolds (e.g., nodal values in…

A plethora of dimensionality reduction techniques have emerged over the past decades, leaving researchers and analysts with a wide variety of choices for reducing their data, all the more so given some techniques come with additional…

Beta regression model is useful in the analysis of bounded continuous outcomes such as proportions. It is well known that for any regression model, the presence of multicollinearity leads to poor performance of the maximum likelihood…

Whereas most dimensionality reduction techniques (e.g. PCA, ICA, NMF) for multivariate data essentially rely on linear algebra to a certain extent, summarizing ranking data, viewed as realizations of a random permutation $\Sigma$ on a set…

Selecting the optimal resolution for discretizing high-dimensional data is a central problem in physics and data analysis, particularly in unsupervised settings where the underlying distribution is unknown. The Relevance-Resolution…

The regression discontinuity (RD) design is a popular approach to causal inference in non-randomized studies. This is because it can be used to identify and estimate causal effects under mild conditions. Specifically, for each subject, the…

It is of importance to develop statistical techniques to analyze high-dimensional data in the presence of both complex dependence and possible outliers in real-world applications such as imaging data analyses. We propose a new robust…

Most data sets comprise of measurements on continuous and categorical variables. In regression and classification Statistics literature, modeling high-dimensional mixed predictors has received limited attention. In this paper we study the…

This study debuts a new spline dimensional decomposition (SDD) for uncertainty quantification analysis of high-dimensional functions, including those endowed with high nonlinearity and nonsmoothness, if they exist, in a proficient manner.…

In the covariate shift learning scenario, the training and test covariate distributions differ, so that a predictor's average loss over the training and test distributions also differ. In this work, we explore the potential of extreme…

We study model selection by the Bayesian information criterion (BIC) in fixed-dimensional exploratory factor analysis over a fixed finite family of compact covariance classes. Our main result shows that the BIC is strongly consistent for…

Diverse planning is the problem of finding multiple plans for a given problem specification, which is at the core of many real-world applications. For example, diverse planning is a critical piece for the efficiency of plan recognition…

We consider a two-stage distributionally robust optimization (DRO) model with multimodal uncertainty, where both the mode probabilities and uncertainty distributions could be affected by the first-stage decisions. To address this setting,…