The Kummer Beta Normal: A New Useful-Skew Model

Abstract

Probabilistic topic models have become a standard in modern machine learning to deal with a wide range of applications. Representing data by dimensional reduction of mixture proportion extracted from topic models is not only richer in semantics interpretation, but could also be informative for classification tasks. In this paper, we describe the Topic Model Kernel (TMK), a topicbased kernel for Support Vector Machine classification on data being processed by probabilistic topic models. The applicability of our proposed kernel is demonstrated in several classification tasks with real world datasets. TMK outperforms existing kernels on the distributional features and give comparative results on nonprobabilistic data types.

Compositional Data Modeling through Dirichlet Innovations

“…In the univariate case, the Kummer-beta distribution is seen as an extension of the beta distribution (see the studies of [14][15][16]), it then follows that the multivariate Kummer-beta (refer as to Kummer-Dirichlet hereafter) distribution is also considered as an extension of the Dirichlet distribution (see [17]). Authors such as [14][15][16]18] have applied the generating technique to the Kummer-beta distribution, by coupling the cdf of different baseline distributions with the pdf of the Kummer-beta distribution. The development of generated distributions using the Kummer-beta distribution, has introduced distributions that add more flexibility in modeling data sets that are in the (0, 1) domain (see [19] for an example).…”