Using validation by inference to select a hypothesis function

Uniform error bounds for a set of basis functions over a set of data inputs can be used to infer uniform error bounds for large classes of hypothesis functions. This paper presents a method to identify a hypothesis function with minimum error bound among functions composed of convex combinations of basis function outputs. Test results comparing the hypothesis function with minimum error bound to the basis function with minimum error bound show that, on average, the hypothesis function achieves lower error as well as a lower error bound.