Machine Learning and Statistical MAP Methods

For machine learning of an input-output function f from examples, we show it is possible to define an a priori probability density function on the hypothesis space to represent knowledge of the probability distribution of f , even when the hypothesis space H is large (i.e., nonparametric). This allows extension of maximum a posteriori (MAP) estimation methods nonparametric function estimation. Among other things, the resulting MAPN (MAP for nonparametric machine learning) procedure easily reproduces spline and radial basis function solutions of