Last week, I was again very busy with exams and doing experiments for a NIPS submission.
The latter is somehow related to my GSoC project, and I will implement it once the other stuff is done:
We developed a method for selecting optimal coefficients of a non-negative combination of kernels for the linear time (=large scale) MMD-two-sample test. The criterion that is optimised for is the ratio of the linear MMD ηk by its standard deviation σk, i.e.
k∗=argsupk∈Kηkσ−1k. That is equivalent to solving the quadratic program
min{βTˆQβ:βTˆη=1,β⪰0}
where the combination of kernels is given by
K:={k:k=d∑u=1βuku,d∑u=1βu≤D,βu≥0,∀u∈{1,…,d}}
ˆQ is a linear time estimate of the covariance of the MMD estimates and ˆη is a linear time estimate of the MMD using the above kernel combinations.
Apart from that, I implemented a method to approximate the null-distribution of the quadratic time MMD, which is based on the Eigenspectrum of the kernel matrix of the merged samples from the two distributions, based on [1]. It still needs to be compared against the MATLAB implementation. It comes with some minor helper functions around matrix algebra.
This week, I will finally have my last exam and then continue on the advanced methods for computing test thresholds.
[1]: Gretton, A., Fukumizu, K., & Harchaoui, Z. (2011). A fast, consistent kernel two-sample test.