A Mathematically Rigorous Foundation for Supervised Learning

Abstract

This paper consists of two parts, one theoretical, and one experimental. And while its primary focus is the development of a mathematically rigorous, theoretical foundation for the field of supervised learning, including a discussion of what constitutes a “solvable pattern recognition problem”, it will also provide some algorithmic detail for implementing the general classification method derived from the theory, a method based on classifier combination, and will discuss experimental results comparing its performance to other well-known methods on standard benchmark problems from the U.C. Irvine, and Statlog, collections. The practical consequences of this work are consistent with the mathematical predictions. Comparing our experimental results on 24 standard benchmark problems taken from the U.C. Irvine, and Statlog, collections, with those reported in the literature for other well-known methods, our method placed 1st on 19 problems, 2nd on 2 others, 4th on another, and 5th on the remaining 2.

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