My main interest is in using kernel methods to reveal properties of probability distributions, for instance disovering whether two random variables are independent, or testing whether two samples are from the same distribution. One application area for these techniques is in discovering patterns of activity in the brain, and discovering how the brain responds to visual stimuli.
Downloadable code:
Fast Kernel ICA
Kernel ICA uses kernel measures of statistical independence to separate linearly mixed sources. We have made this process much faster
by using an approximate Newton-like method on the special orthogonal group to perform the optimisation.
Matlab code is available
here.
Kernel Two-Sample Test
We propose a kernel method to perform a statistical test of whether two samples are from different distributions. This test can be applied to high dimensional data, as well as to non-vectorial data such as graphs; indeed, it can be used wherever kernels provide a similarity measure.
Matlab code is available
here.
Kernel Independence Test
We propose a statistical test of whether two random variables are independent. As with the two-sample test above, the independence test relies on kernels, and can be used for high dimensional and non-vectorial data (e.g. strings).
Matlab code is available
here.
