Inductive Learning from Probability Distributions Using Maximum Likelihood Method and the Principle of Indifference

Abstract

This paper presents an algorithm for unsupervised inductive learning from discrete probability distributions. Few algorithms have directly dealt with probability distributions. The procedures are as follows: 1. Find a probability distribution corresponding to a proposition of classical logic using maximum liklihood method. 2. Transform the probability distribution to a proposition based on the principle of indifference. 3. Reduce the proposition. The principle of indifference states that a probability distribution is uniform when we have no information. Using this principle, the propositions of classical logic can be corresponded to some probability distributions. The algorithm is applied to a real data. The result shows that the algorithm works well. The result is also compared with a method of multivariate analysis.