||The task of parameter/function estimation has been at the center of scientific attention for a long time and it comes under different names such as filtering, prediction, beamforming, curve fitting, classification, regression. Conventionally, the task has been treated as an optimization task of an appropriately adopted loss function. However, in most of the cases, the choice of the loss function is mainly dictated by its mathematically tractability and not on a physical reasoning related to the specific problem at hand. The task is further complicated when a-priori information, in the form of constraints, becomes available. The presence of constraints in estimation tasks is recently gaining in importance, due to the revival of interest in robust learning schemes.
In this talk, the estimation task is treated in the context of set theoretic estimation arguments. Instead of a single optimal point we are searching for a set of solutions that are in agreement with the available information, which is provided to us in the form of a set of training points and a set of constraints.
The goal of this talk is to present a general tool for parameter/function estimation, both for classification as well as regression tasks, in a time adaptive setting in (infinite dimensional) Reproducing Kernel Hilbert spaces (RKHS). The general framework is that of convex set theory via the powerful and elegant tool of projections.