MAP hypothesis in Bayesian concept learning

Machine learning is applied to many fields. Bayesian reasoning is essential to machine learning, because it supports quantitative method for measuring confidence level of multiple hypotheses. This paper studies concept learning through using Bayesian theory. We first prove that every consistent hypothesis is maximum a posterior hypothesis (MAP hypothesis) under some proper assumption; then, under three different zero-mean noise distributions (Laplace distribution, uniform distribution, and normal distribution), we obtain the MAP hypothesis of output about one kind of machine learning problem.