Desirable Properties of Learning Function from Examples
Bodong Liang · International Journal of Control and Automation · 2014
In this paper, we argue that total three desirable properties should be satisfied so that a function to be learned or interpolated from a set of input-output examples can cross all the given examples with minimal oscillations among the examples.As long as the number of given examples exceeds the dimension of example and meanwhile none existing hyper-plane, in real vector space of example's dimension, passes through all the given examples exactly, we can construct one simple function learning solution, which is expressed as a sum of two terms: one is an example-influence term that consists of the outputs of a number of basis functions and another is a linear term, to allow all the three desirable properties to be satisfied exactly.Experiments show that the solution can simulate both continuous and discontinuous functions even with very sparse given examples.