Fast Kernel Distribution Function Estimation and fast kernel density estimation based on sparse Bayesian learning and regularization

In this paper, we develop a novel method of obtaining very sparse representation of Kernel Distribution Function Estimation (KDFE) and Kernel Density Estimation (KDE) exploiting Sparse Bayesian Regression (SBR) technique with the aidance of regularization by jittering. SBR introduces a parameterized sparsity-inducing prior on the unknown parameters of the linear model. After reviewing the existent methodologies of fast kernel density estimation, we adapt SBR to the problem of construction of sparse KDFE and KDE. Numerical results of preliminary simulation studies on synthetic data demonstrate the effectiveness of our algorithm which can achieve sparser representation of KDE than SVM-based algorithm and can produce more precise estimate than traditional full-sample KDE algorithm.