Facies Classification with Copula Entropy

Facies are the type of rocks with similar characteristics given by geologists and facies classification is of very significance in geological tasks, such as formation evaluation, reservoir characterization. As the geological data accumulates, there are growing interests in facies classification with machine learning methods [1, 2, 3, 4, 5, 6, 7, 8, 9]. There are two issues with the existing works on facies classification. First, the machine learning models are built without variable selection or with only very primary method, such as cross-validation, which makes the classifiers with useless variable as inputs and therefore with low performance. Second, most of the models for facies classification are block-box, such as deep learning [5, 10, 11], Boostings or SVMs[7], which are un-interpretable to geologists. Variable selection is a common task that selects a subset from all the available variables for machine learning models. By this, the accuracy of the predictive models built with the selected variables can be improved compared with those built without selection. The traditional method for variable selection are mainly based on likelihoods, such as AIC, BIC, or accuracy, such as LASSO [12], or correlation, such as HSIC [13], distance correlation [14], and copula entropy [15]. Copula Entropy (CE) is a recently proposed rigorous mathematical concept for measuring multivariate statistical independence and is proved to be equivalent to mutual information in information theory [16].