Multivariate rank outlyingness and correlation effects

Low rank Multivariate regression

We consider in this paper the multivariate regression problem, when the target regression matrix A is close to a low rank matrix. Our primary interest is in on the practical case where the variance of the noise is unknown. Our main contribution is to propose in this setting a criterion to select among a family of low rank estimators and prove a non-asymptotic oracle inequality for the resulting...

Nonparametric multivariate rank tests and their unbiasedness

JANA JUREČKOVÁ1 and JAN KALINA2 1Department of Probability and Statistics, Charles University in Prague, Sokolovská 83, CZ-186 75 Prague 8, Czech Republic. E-mail: [email protected] 2EUROMISE Center, Department of Medical Informatics, Institute of Computer Science of the Academy of Sciences of CR, v.v.i., Pod Vodárenskou věží 2, CZ-182 07 Prague 8, Czech Republic. E-mail: kalina@euromi...

Spearman Rank Correlation Coefficient

Multivariate Maximal Correlation Analysis

Correlation analysis is one of the key elements of statistics, and has various applications in data analysis. Whereas most existing measures can only detect pairwise correlations between two dimensions, modern analysis aims at detecting correlations in multi-dimensional spaces. We propose MAC, a novel multivariate correlation measure designed for discovering multidimensional patterns. It belong...

Unbiased Multivariate Correlation Analysis

Correlation measures are a key element of statistics and machine learning, and essential for a wide range of data analysis tasks. Most existing correlation measures are for pairwise relationships, but real-world data can also exhibit complex multivariate correlations, involving three or more variables. We argue that multivariate correlation measures should be comparable, interpretable, scalable...