A Computational Approach to Log-Concave Density Estimation

Non-parametric density estimation with shape restrictions has witnessed a great deal of attention recently. We consider the maximum-likelihood problem of estimating a log-concave density from a given finite set of empirical data and present a computational approach to the resulting optimization problem. Our approach targets the ability to trade-off computational costs against estimation accuracy in order to alleviate the curse of dimensionality of density estimation in higher dimensions.