Last week was a mixed one. Next to new examples, tests, bugfixes, and helper methods, the biggest implementation is an automatic kernel selection algorithm for the linear time MMD. This is one thing that I worked on during my Master project at UCL.
It selects optimal optimal kernel weights for kernel of the family
\[
\mathcal{K}:=\{k : k=\sum_{u=1}^d\beta_uk_u,\sum_{u=1}^d\beta_u\leq D,\beta_u\geq0, \forall u\in\{1,…,d\}\}
\]
by solving the convex program
\[
\min \{ \beta^T\hat{Q}\beta : \beta^T \hat{\eta}=1, \beta\succeq0\}
\]
where \(\hat{Q}\) is a linear time estimate of the covariance of the MMD estimates and \(\hat{\eta}\) is a linear time estimate of the MMD.

I already described this a few weeks ago, when the method was developed. It is now integrated into SHOGUN. Efficient kernel selection, yeah 🙂 It uses a convex solver called libqp, which is by Vojtech Franc, one of the mentors of this year’s GSoC. Still, I need to think of a nice way of embedding it into SHOGUN’s model selection framework, which isn’t as straight-forward as it first seems.

This week, bug-hunting continues with a bug that gives wrong results during cross-validation on multi-class machines. Afterwards, I will try to polish my code so far a bit, especially documentation (and tutorial); and continue on more examples/demo for the new framework for statistical testing.