We study approaches for compressing the empirical measure in the context of finite dimensional reproducing kernel Hilbert spaces (RKHSs). In this context, the empirical measure is contained within a natural convex set and can be approximated using convex optimization methods.
We derive a closed-form solution for this relaxed optimization problem and complement the result with a study of the dependencies between the newly generated features and the sensitive ones.
We study the recovering bandits problem, a variant of the stochastic multi-armed bandit problem where the expected reward of each arm varies according to some unknown function of the time since the arm was last played.
In the RKHS regression context, we choose our non-adaptive estimators to be clipped least-squares estimators constrained to lie in a ball in an RKHS.
Statistics Theory Statistics Theory
Furthermore, copulas place a wide range of dependence structures at the disposal and can be used to analyze higher order interactions.