Various Formulations for Learning the Kernel and Structured Sparsity

I will review an approach to learning the kernel, which consists in minimizing a convex objective function over a prescribed set of kernel matrices. I will establish some important properties of this problem and present a reformulation of it from a feature space perspective. A well studied example covered by this setting is multiple kernel learning, in which the set of kernels is the convex hull of a finite set of basic kernels. I will discuss extensions of this setting to more complex kernel families, which involve additional constraints and a continuous parametrization. Some of these examples are motivated by multi-task learning and structured sparsity, which I will describe in some detail during the talk.