Vahe Avagyan

Estimation of High-Dimensional Inverse Covariance Matrices: Methods and Applications 


Dr. Vahe Avagyan is an Assistant Professor at Wageningen University from the Netherlands.

Description of the Talk:

The estimation of the inverse covariance matrix (also known as precision matrix) is an important problem in various research fields and methodologies, especially in the current age of high-dimensional data abundance. In addition, the classical estimation methods are no longer stable and applicable in high dimensional settings, i.e., when the dimensionality has the same order as the sample size or is much larger.

This talk focuses on the estimation of precision matrices as well as their applications. Several recent developments in the estimation of large precision matrices are provided. In particular, estimation of the precision matrix using penalized generalized Sylvester matrix equations is provided. Its performance is demonstrated in the classification of breast cancer patients.

For most of the methodologies, the input sample covariance matrix potentially deteriorates the estimation of the precision matrices in the presence of outliers. The second part of this talk introduces robust alternatives for the input matrix, which are constructed by combining robust correlation estimators with robust variation measures. These approaches are used for studying the optimal portfolio allocations in the Shanghai Stock Exchange Composite Index.