Categorical Nature of Major Factor Selection via Information Theoretic Measurements

• Published in: Entropy (Basel, Switzerland) Vol. 23; no. 12; p. 1684
• Main Authors: Chen, Ting-Li, Chou, Elizabeth P, Fushing, Hsieh
• Format: Journal Article
• Language: English
• Published: Switzerland MDPI AG 15-12-2021; MDPI
• Subjects: Big Data; CEDA; Cole, Gerrit; Collections; conditional entropy; conditional mutual information; Contingency; Criteria; Data analysis; heterogeneity; information gain; Information theory; Professional baseball; Qualitative analysis; New York; United States > US; CEDA; conditional mutual information; information gain; conditional entropy; heterogeneity
• ISSN: 1099-4300; 1099-4300
• DOI: 10.3390/e23121684

Without assuming any functional or distributional structure, we select collections of major factors embedded within response-versus-covariate (Re-Co) dynamics via selection criteria [C1: confirmable] and [C2: irrepaceable], which are based on information theoretic measurements. The two criteria are constructed based on the computing paradigm called Categorical Exploratory Data Analysis (CEDA) and linked to Wiener-Granger causality. All the information theoretical measurements, including conditional mutual information and entropy, are evaluated through the contingency table platform, which primarily rests on the categorical nature within all involved features of any data types: quantitative or qualitative. Our selection task identifies one chief collection, together with several secondary collections of major factors of various orders underlying the targeted Re-Co dynamics. Each selected collection is checked with algorithmically computed reliability against the finite sample phenomenon, and so is each member's major factor individually. The developments of our selection protocol are illustrated in detail through two experimental examples: a simple one and a complex one. We then apply this protocol on two data sets pertaining to two somewhat related but distinct pitching dynamics of two pitch types: slider and fastball. In particular, we refer to a specific Major League Baseball (MLB) pitcher and we consider data of multiple seasons.