Related papers: Testing High Dimensional Covariance Matrices, with…

This paper deals with the estimation of a high-dimensional covariance with a conditional sparsity structure and fast-diverging eigenvalues. By assuming sparse error covariance matrix in an approximate factor model, we allow for the presence…

Covariance and Hessian matrices have been analyzed separately in the literature for classification problems. However, integrating these matrices has the potential to enhance their combined power in improving classification performance. We…

Estimation of covariance matrices is a fundamental problem in multivariate statistics. Recently, growing efforts have focused on incorporating covariate effects into these matrices, facilitating subject-specific estimation. Despite these…

We develop tests for high-dimensional covariance matrices under a generalized elliptical model. Our tests are based on a central limit theorem (CLT) for linear spectral statistics of the sample covariance matrix based on self-normalized…

Schizophrenia (SZ) is a prevalent mental disorder characterized by cognitive, emotional, and behavioral changes. Symptoms of SZ include hallucinations, illusions, delusions, lack of motivation, and difficulties in concentration. Diagnosing…

In genetic studies, not only can the number of predictors obtained from microarray measurements be extremely large, there can also be multiple response variables. Motivated by such a situation, we consider semiparametric dimension reduction…

Factor and sparse models are two widely used methods to impose a low-dimensional structure in high-dimensions. However, they are seemingly mutually exclusive. We propose a lifting method that combines the merits of these two models in a…

Big data applications, such as medical imaging and genetics, typically generate datasets that consist of few observations n on many more variables p, a scenario that we denote as p>>n. Traditional data processing methods are often…

In this paper, we propose a new test for testing the equality of two population covariance matrices in the ultra-high dimensional setting that the dimension is much larger than the sizes of both of the two samples. Our proposed methodology…

This paper proposes a novel testing procedure for selecting a sparse set of covariates that explains a large dimensional panel. Our selection method provides correct false detection control while having higher power than existing…

Controlling false positives (Type I errors) through statistical hypothesis testing is a foundation of modern scientific data analysis. Existing causal structure discovery algorithms either do not provide Type I error control or cannot scale…

In this paper, we consider the problem of testing equality of the covariance matrices of L complex Gaussian multivariate time series of dimension $M$ . We study the special case where each of the L covariance matrices is modeled as a rank K…

Linear discriminant analysis (LDA) is a typical method for classification problems with large dimensions and small samples. There are various types of LDA methods that are based on the different types of estimators for the covariance…

Causal inference plays an important role in under standing the underlying mechanisation of the data generation process across various domains. It is challenging to estimate the average causal effect and individual causal effects from…

Due to their parsimony, separable covariance models have been popular in modeling matrix-variate data. However, the inference from such a model may be misleading if the population covariance matrix $\Sigma$ is actually non-separable,…

Self-supervised pre-training methods have brought remarkable breakthroughs in the understanding of text, image, and speech. Recent developments in genomics has also adopted these pre-training methods for genome understanding. However, they…

A fundamental approach in neuroscience research is to test hypotheses based on neuropsychological and behavioral measures, i.e., whether certain factors (e.g., related to life events) are associated with an outcome (e.g., depression). In…

The variance--covariance matrix plays a central role in the inferential theories of high-dimensional factor models in finance and economics. Popular regularization methods of directly exploiting sparsity are not directly applicable to many…

The boom of DL technology leads to massive DL models built and shared, which facilitates the acquisition and reuse of DL models. For a given task, we encounter multiple DL models available with the same functionality, which are considered…

Maximum eigenvalue detection (MED) is an important application of random matrix theory in spectrum sensing and signal detection. However, in small signal-to-noise ratio environment, the maximum eigenvalue of the representative signal is at…