Contribution On the Estimation of the Copulas Parameters

Abstract

he task of modeling high dimensional datasets has become increasingly difficult and challenging due to the large amount of redundancy present in the data. This redundancy often leads to the presence of noise and inaccurate data modeling and analysis results. While numerous statistical methods have been proposed to address this problem, many of them involve multiple operations and have high time complexity, often resulting in poor classification performance. To deal with that, in this thesis, three Dimensionality Reduction based on the inter-correlation between the huge data attributes are proposed, where this correlation is modeled using the theory of Copulas. The first two Dimensionality Reduction techniques aim to reduce redundancy by selecting only relevant attributes. While the third proposed technique is a feature extraction process that combines Principal Component Analysis PCA and the bivariate Copulas. All these techniques are performed using real-world datasets and compared against powerful Dimensionality Reduction methods in term of reduction, information capturing and models accuracy of the obtained reduced data to evaluate the effectiveness of each technique.