Fast kernel density independent component analysis, Lecture

Abstract. We develop a super-fast kernel density estimation algorithm (FastKDE) and based on this a fast kernel independent component anal-ysis algorithm (KDICA). FastKDE calculates the kernel density estima-tor exactly and its computation only requires sorting n numbers plus roughly 2n evaluations of the exponential function, where n is the sam-ple size. KDICA converges as quickly as parametric ICA algorithms such as FastICA. By comparing with state-of-the-art ICA algorithms, simula-tion studies show that KDICA is promising for practical usages due to its computational efficiency as well as statistical efficiency. Some statistical properties of KDICA are analyzed