Title: Robust regularised precision matrix estimation
Authors: Garth Tarr - University of Sydney (Australia) [presenting]
Abstract: There is a great need for robust techniques in data mining and machine learning contexts where many standard techniques such as principal component analysis and linear discriminant analysis are inherently susceptible to outliers. Furthermore, standard robust procedures assume that less than half the observation rows of a data matrix are contaminated, which may not be a realistic assumption when the number of observed features is large. We consider the problem of estimating covariance and precision matrices under cellwise contamination. Specifically, the use of a robust pairwise covariance matrix as an input to various regularisation routines, such as the graphical lasso, QUIC or CLIME. We review a number of approaches that can be used to ensure the input covariance matrix is positive semidefinite. The result is a potentially sparse precision matrix that is resilient to moderate levels of cellwise contamination and scales well to higher dimensions. We consider the selection of an appropriate value for the tuning parameter that controls the level of sparsity and potential applications involving financial data and bioinformatics.