Fast Kernel Independent Component Analysis

We develop a super-fast kernel density estimation algorithm (FastKDE) and based on this a fast kernel independent component analysis algorithm (KDICA). FastKDE calculates the kernel density estimator exactly and its computation only requires sorting $n$ numbers plus roughly $2n$ evaluations of the exponential function, where $n$ is the sample size. KDICA converges as quickly as parametric ICA algorithms such as FastICA. By comparing with state-of-the-art ICA algorithms, simulation 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.