Learning with consistency between inductive functions and kernels

Regularized Least Squares (RLS) algorithms have the ability to avoid over-fitting problems and to express solutions as kernel expansions. However, we observe that the current RLS algorithms cannot provide a satisfactory interpretation even on the penalty of a constant function. Based on the intuition that a good kernelbased inductive function should be consistent with both the data and the kernel, a novel learning scheme is proposed. The advantages of this scheme lie in its corresponding Representer Theorem, its strong interpretation ability about what kind of functions should not be penalized, and its promising accuracy improvements shown in a number of experiments. Furthermore, we provide a detailed technical description about heat kernels, which serves as an example for the readers to apply similar techniques for other kernels. Our work provides a preliminary step in a new direction to explore the varying consistency between inductive functions and kernels under various distributions.