A maximum entropy kernel density estimator with applications to function interpolation and texture segmentation
Nikhil Balakrishnan, Dan Schonfeld · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2006
In this paper, we develop a new algorithm to estimate an unknown probability density function given a finite data sample using a tree shaped kernel density estimator. The algorithm formulates an integrated squared error based cost function which minimizes the quadratic divergence between the kernel density and the Parzen density estimate. The cost function reduces to a quadratic programming problem which is minimized within the maximum entropy framework. The maximum entropy principle acts as a regularizer which yields a smooth solution. A smooth density estimate enables better generalization to unseen data and offers distinct advantages in high dimensions and cases where there is limited data. We demonstrate applications of the hierarchical kernel density estimator for function interpolation and texture segmentation problems. When applied to function interpolation, the kernel density estimator improves performance considerably in situations where the posterior conditional density of the dependent variable is multimodal. The kernel density estimator allows flexible non parametric modeling of textures which improves performance in texture segmentation algorithms. We demonstrate performance on a text labeling problem which shows performance of the algorithm in high dimensions. The hierarchical nature of the density estimator enables multiresolution solutions depending on the complexity of the data. The algorithm is fast and has at most quadratic scaling in the number of kernels.