Efficient And Accurate Multivariate Class Conditional Densities Using Copula

Univariate densities can be modeled accurately and efficiently using nonparametric kernel density estimators, which unfortunately cannot be easily extended to the multivariate case. As an alternative, Gaussian mixture model is used to approximate underlying multivariate distributions, especially because its estimation is relatively straight forward through EM algorithm. However, the multivariate Gaussian mixture model imposes a particular form on the marginal, a Gaussian mixture model. This is a strong assumption on the marginal and is violated in many practical applications.We propose a simple generative classification model based on the copula model that takes advantage of the accuracy of the nonparametric univariate density estimator and the multivariate dependencies captured in the Gaussian mixture model, thus alleviating the aforementioned limitations. We compare the performance of our models with previous classification benchmarks from UCI repository and show that for the same number of parameters the proposed models consistently outperforms Gaussian mixture models. We find that these generative models perform as well or better than Support Vector Machine (SVM).