Machine Learning Coffee Seminar: Esa Ollila, Aalto University "High-dimensional Covariance Matrix Estimation With Applications in Finance and Genomic Studies"

High-dimensional Covariance Matrix Estimation With Applications in Finance and Genomic Studies

Esa Ollila
Professor of Electrical Engineering, Aalto University

We consider the problem of estimating a high-dimensional (HD) covariance matrix when the sample size is smaller, or not much larger, than the dimensionality of the data, which could potentially be very large. We develop a regularized sample covariance matrix (RSCM) estimator that is optimal (in minimum mean squared error sense) when the data is sampled from an unspecified elliptically symmetric distribution. The proposed covariance estimator is then used in portfolio optimization problems in finance and microarray data analysis (MDA). In portfolio optimization problem we use our estimator for optimally allocating the total wealth to a large number of assets, where optimality means that the risk (i.e., variance of portfolio returns) is minimized. Microarray technology is a powerful approach for genomics research that allows monitoring the expression levels of tens of thousands of genes simultaneously. We develop a compressive regularized discriminant analysis (CRDA) method based on our covariance estimator and illustrate its effectiveness in MDA. Our analysis results on real stock market data and microarray data illustrate that the proposed approach is able to outperform the current benchmark methods.

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