Parsimonious Feature Extraction Methods: Extending Robust Probabilistic Projections with Generalized Skew-t
39 Pages Posted: 12 Nov 2020
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: Suggested Citation