Title: A generalisation of independence in statistical models for categorical distribution

Authors: Yu Fujimoto; Noboru Murata

Addresses: Aoyama Gakuin University, 5-10-1 Fuchinobe, Chuo, Sagamihara, Kanagawa 252-5258, Japan. ' Waseda University, 3-4-1 Ohkubo, Shinjuku, Tokyo 169-8555, Japan

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.

Keywords: independent models; naive models; Bayes models; Thomas Bayes; generalised independence; copulas; Bregman divergence; statistical models; categorical distribution; statistical independence; generalised multiplication; monotonic increases; inverse functions; estimation methods; empirical distributions; marginal distributions; simplicity; calculations; robust properties; benchmark datasets; data mining; data modelling; data management; intelligent data analysis.

DOI: 10.1504/IJDMMM.2012.046809

International Journal of Data Mining, Modelling and Management, 2012 Vol.4 No.2, pp.172 - 187

Received: 08 May 2021
Accepted: 12 May 2021

Published online: 09 May 2012 *

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