Parsimonious Feature Extraction Methods: Extending Robust Probabilistic Projections with Generalized Skew-t

39 Pages Posted: 12 Nov 2020

See all articles by Dorota Toczydlowska

Dorota Toczydlowska

School of Mathematical and Physical Sciences, University of Technology Sydney; The Department of Statistical Science, University College London

Gareth Peters

University of California Santa Barbara; University of California, Santa Barbara

Pavel V. Shevchenko

Macquarie University - Department of Actuarial Studies and Business Analytics

Date Written: September 24, 2020

Abstract

We propose a novel generalization to the Student-t Probabilistic Principal Component methodology which: (1) accounts for an asymmetric distribution of the observation data; (2) is a framework for grouped and generalized multiple-degree-of-freedom structures, which provides a more flexible approach to modelling groups of marginal tail dependence in the observation data; and (3) separates the tail effect of the error terms and factors. The new feature extraction methods are derived in an incomplete data setting to efficiently handle the presence of missing values in the observation vector. We discuss various special cases of the algorithm being a result of simplified assumptions on the process generating the data. The applicability of the new framework is illustrated on a data set that consists of cryptocurrencies with the highest market capitalization.

Keywords: Probabilistic PCA; Feature Extraction; EM Algorithm; Robust Orthogonal Projections; Asymmetric T-Copulas; Skew T-Copula; Grouped T-Copula; Missing Data; Tail Dependence; Dependence Modelling; Cryptocurrencies

JEL Classification: C13;C38;C51

Suggested Citation

Toczydlowska, Dorota and Peters, Gareth and Shevchenko, Pavel V., Parsimonious Feature Extraction Methods: Extending Robust Probabilistic Projections with Generalized Skew-t (September 24, 2020). Available at SSRN: https://ssrn.com/abstract=3678383 or http://dx.doi.org/10.2139/ssrn.3678383

Dorota Toczydlowska (Contact Author)

School of Mathematical and Physical Sciences, University of Technology Sydney ( email )

15 Broadway, Ultimo
PO Box 123
Sydney, NSW 2007
Australia

The Department of Statistical Science, University College London ( email )

London

Gareth Peters

University of California Santa Barbara ( email )

Santa Barbara, CA 93106
United States

University of California, Santa Barbara ( email )

Pavel V. Shevchenko

Macquarie University - Department of Actuarial Studies and Business Analytics ( email )

Australia

HOME PAGE: http://www.mq.edu.au/research/centre-for-risk-analytics/pavel-shevchenko

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