Validation of fusion through linear programming

We develop a method to bound the out-of-sample error of a hypothesis function formed by combining the outputs of a collection of basis functions. First, uniform error bounds are calculated for the basis functions. Then a linear program is used to infer a bound for the hypothesis function from the basis function bounds. The resulting hypothesis function bound is not based on the size of the class of prospective hypothesis functions. Instead, the bound is based on the number of basis functions and on similarities between the basis functions and the hypothesis function. Hence, the linear program produces stronger bounds than direct validation over the hypothesis function class when the number of basis functions is small, when the class of hypothesis functions is complex, and when the hypothesis functions of interest are similar to the basis functions