Finding dependencies in data with information-theoretic methods

Davor Sluga (2017) Finding dependencies in data with information-theoretic methods. PhD thesis.

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Abstract

The selection of features that are relevant for a classification or a regression problem is very important in many domains which involve high-dimensional data. It improves the performance and generalization capabilities of regression and classification methods and facilitates the interpretation of the data about a system. To assess feature relevance, some kind of criterion function must be used. Information measures are an obvious candidate because they arise from the goal of feature selection: we wish to obtain a set of features that contain the most information about a system. Information-theoretic feature selection methods usually need to estimate the probability distributions of the data in order to assess feature relevance, this often proves to be problematic. In this thesis we propose a novel feature selection method (QMIFS) based on quadratic mutual information which has its roots in Cauchy--Schwarz divergence and Renyi entropy. The method uses the direct estimation of quadratic mutual information from data samples using Gaussian kernel functions, and can detect second order non-linear relations. Feature selection on large data sets can be infeasible due to long execution times. We reduce the computational complexity of the method through incomplete Cholesky decomposition of the input data and derive an appropriate estimator of the criterion function. The effectiveness of the proposed method is demonstrated through an extensive comparison with mutual information feature selection (MIFS), minimum redundancy maximum relevance (MRMR), and joint mutual information (JMI) on classification and regression problem domains. The experiments show that proposed method performs comparably to the other methods when applied to classification problems, except it is considerably faster. In the case of regression, it compares favourably to the others, but is slower. If the data includes hundreds or even thousands of features, sequential algorithms for feature selection may no longer suffice. Nowadays massively parallel systems such as graphics processing units offer the computational power to make analysis of high-dimensional data feasible. We modified the proposed method to make use of the powerful hardware of graphics processing units. We achieve considerable improvements in the execution times, making it viable for usage on large data sets.

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