A generalisation of independence in statistical models for categorical distribution. (1st January 2012)

• Record Type: Journal Article
• Authors: Fujimoto, Yu; Murata, Noboru
• Is Part Of: International journal of data mining, modelling and management. Volume 4:Number 2(2012)
• Page Start: 172
• Page End: 187
• Publication Date: 2012-01-01
• Subjects: independent model -- naive Bayes model -- generalised independence -- copula -- Bregman divergence; Data mining -- Periodicals; Information science -- Periodicals; Databases -- Periodicals; 005.7
• Languages: English
• ISSNs: 1759-1163

Abstract

In this paper, generalised statistical independence in statistical models for categorical distributions is proposed from the viewpoint of generalised multiplication characterised by a monotonically increasing function and its inverse function, and it is implemented in naive Bayes models. This paper also proposes an idea of their estimation method which directly uses empirical marginal distributions to retain simplicity of calculation. This method is interpreted as an optimisation of a rough approximation of the Bregman divergence so that it is expected to have a kind of robust property. Effectiveness of proposed models is shown by numerical experiments on some benchmark datasets.