Great engineering. Since the article asks about analytical tips for performance improvement: looks like you should be able to substantially get the complexity d

Great engineering. Since the article asks about analytical tips for performance improvement: looks like you should be able to substantially get the complexity down using something like least angle regression (ie what's used by efficient implementations of Lasso shrinkage estimators). Or basically any approach where you successively add the most highly correlated variable to your set instead of checking all size-k subsets.