Estimation of bivariate minimum information dependence models using the density-ratio framework

The minimum information dependence model is a flexible statistical model that can describe various dependence structures. A challenging problem on the model is how to effectively estimate the unknown parameters for given data. In this paper, an estimation method of the bivariate minimum information dependence model is constructed. The method is based on the maximum likelihood mutual information in the density-ratio estimation problem of machine learning. The statistical properties of the estimator are established. Illustrative examples on neural networks and canonical correlation analysis are provided.