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Testing covariance structure is of importance in many areas of statistical analysis, such as microarray analysis and signal processing. Conventional tests for finite-dimensional covariance cannot be applied to high-dimensional data in…

Estimating the eigenvalues of a population covariance matrix from a sample covariance matrix is a problem of fundamental importance in multivariate statistics; the eigenvalues of covariance matrices play a key role in many widely…

We propose a novel method for multiple clustering that assumes a co-clustering structure (partitions in both rows and columns of the data matrix) in each view. The new method is applicable to high-dimensional data. It is based on a…

Accurate and precise covariance matrices will be important in enabling planned cosmological surveys to detect new physics. Standard methods imply either the need for many N-body simulations in order to obtain an accurate estimate, or a…

We explore the effect of finite population sampling in design problems with many variables cross-classified in many ways. In particular, we investigate designs where we wish to sample individuals belonging to different groups for which the…

Cosine similarity is an established similarity metric for computing associations on vectors, and it is commonly used to identify related samples from biological perturbational data. The distribution of cosine similarity changes with the…

Covariance matrix estimation is an important problem in multivariate data analysis, both from theoretical as well as applied points of view. Many simple and popular covariance matrix estimators are known to be severely affected by model…

We consider robust covariance estimation with group symmetry constraints. Non-Gaussian covariance estimation, e.g., Tyler scatter estimator and Multivariate Generalized Gaussian distribution methods, usually involve non-convex minimization…

It is a well-known fact that genetic sequences may contain sections with repeated units, called repeats, that differ in length over a population, with a length distribution of geometric type. A simple class of recombination models with…

Sample covariance matrices from multi-population typically exhibit several large spiked eigenvalues, which stem from differences between population means and are crucial for inference on the underlying data structure. This paper…

Many machine learning methods assume that the training and test data follow the same distribution. However, in the real world, this assumption is very often violated. In particular, the phenomenon that the marginal distribution of the data…

Categorical random variables are a common staple in machine learning methods and other applications across disciplines. Many times, correlation within categorical predictors exists, and has been noted to have an effect on various algorithm…

We study the problem of distribution to real-value regression, where one aims to regress a mapping $f$ that takes in a distribution input covariate $P\in \mathcal{I}$ (for a non-parametric family of distributions $\mathcal{I}$) and outputs…

The classical methods of multivariate analysis are based on the eigenvalues of one or two sample covariance matrices. In many applications of these methods, for example to high dimensional data, it is natural to consider alternative…

Extended geometric distribution is defined and its mixture is characterized by the property of having completely monotone probability sequence. Also, convolution equations and probability generating functions are used to characterize…

Computer Vision practitioners must thoroughly understand their model's performance, but conditional evaluation is complex and error-prone. In biometric verification, model performance over continuous covariates---real-number attributes of…

The wide availability of biological data at the genome-scale and across multiple variables has resulted in statistical questions regarding the enrichment or depletion of the number of discrete objects (e.g. genes) identified in individual…

Although several nonparametric tests are available for testing population identical distributions or equal means in multiple groups problem, the Van der Waerden test has asymptotically the same efficiency as the classical one-way analysis…

Several statistical models used in genome-wide prediction assume independence of marker allele substitution effects, but it is known that these effects might be correlated. In statistics, graphical models have been identified as a useful…

We propose two tests for the equality of covariance matrices between two high-dimensional populations. One test is on the whole variance--covariance matrices, and the other is on off-diagonal sub-matrices, which define the covariance…