Maximum Entropy and Learning Theory

We derive the learning theory recently reported by Tishby, Levin, and Solla (TLS) directly from the principle of maximum entropy instead of statistical mechanics. The theory generally applies to any problem of modeling data. We analyze an elementary example for which we find the predictions consistent with intuition and conventional statistical results and we numerically examine the more realistic problem of training a competitive net to learn a one-dimensional probability density from samples. The TLS theory is useful for predicting average training behavior.