An Information Geometric Approach to Increase Representational Power in Unsupervised Learning

Abstract

Machine learning models increase their representational power by increasing the number of parameters in the model. The number of parameters in the model can be increased by introducing hidden nodes, higher-order interaction effects or by introducing new features into the model. In this thesis we study different approaches to increase the representational power in unsupervised machine learning models. We investigate the use of incidence algebra and information geometry to develop novel machine learning models to include higher-order interactions effects into the model. Incidence algebra provides a natural formulation for combinatorics by expressing it as a generative function and information geometry provides many theoretical guarantees in the model by projecting the problem onto a dually flat Riemannian structure for optimization. Combining the two techniques together formulates the information geometric formulation of the binary log-linear model. We first use the information geometric formulation of the binary log-linear model to formulate the higher-order Boltzmann machine (HBM) to compare the different behaviours when using hidden nodes and higher-order feature interactions to increase the representational power of the model. We then apply the concepts learnt from this study to include higher-order interaction terms in Blind Source Separation (BSS) and to create an efficient approach to estimate higher order functions in Poisson process. Lastly, we explore the possibility to use Bayesian non-parametrics to automatically reduce the number of higher-order interactions effects included in the model.