Public defence in Signal Processing Technology, M.Sc.(Tech.) Elias Raninen
M.Sc.(Tech.) Elias Raninen will defend the thesis "Contributions to the Theory and Estimation of High-dimensional Covariance Matrices" on 27 May 2022 at 12 (EET) in Aalto University School of Electrical Engineering, Department of Signal Processing and Acoustics, in lecture hall T1, Konemiehentie 2, Espoo.
Dr. Xavier Mestre, Telecommunications Technological Center of Catalonia (CTTC), Spain
Dr. Florent Bouchard, CentraleSupélec, University of Paris-Saclay, France
Custos: Prof. Esa Ollila, Aalto University School of Electrical Engineering, Department of Signal Processing and Acoustics
Thesis available for public display at: https://aaltodoc.aalto.fi/doc_public/eonly/riiputus/
Doctoral theses in the School of Electrical Engineering: https://aaltodoc.aalto.fi/handle/123456789/53
In modern data analysis problems, the number of variables (dimension) can be very large relative to the number of observations (samples). Such high-dimensional problems have become increasingly common in many fields such as finance, biology, and communications. Many statistical signal processing and machine learning techniques depend on estimates of the degree of associations (i.e., covariances) between the variables but their reliable estimation is increasingly difficult from high-dimensional data. Using the conventional sample estimates, namely the sample covariances and the related sample covariance matrix often leads to unsatisfactory performance when sample lengths are not orders of magnitude larger than the data dimensionality.
This thesis addresses this problem and develops new theory and methods for high-dimensional covariance matrix estimation. New theoretical results for the sample covariance matrix and the spatial sign covariance matrix are derived when sampling from real and complex elliptically symmetric distributions. The thesis also proposes novel data-adaptive and computationally efficient covariance matrix estimators for single- and multi-class settings using regularization to improve the finite sample accuracy measured by the mean squared error. The proposed new regularized covariance matrix estimators are applied in diverse learning problems, including portfolio optimization in quantitative finance and classification problems of high-dimensional data sets.
Contact information of doctoral candidate