Accession Number : AD0708062

Title :   LEARNING WITH A PROBABILISTIC TEACHER.

Descriptive Note : Technical rept.,

Corporate Author : HARVARD UNIV CAMBRIDGE MASS DIV OF ENGINEERING AND APPLIED PHYSICS

Personal Author(s) : Agrawala,Ashok K.

Report Date : MAY 1970

Pagination or Media Count : 119

Abstract : Estimation or learning problems arise in practical systems in many ways. Depending on the learning information available, the estimation problem may be supervised or unsupervised. Bayesian estimation may be used for both these problems. The Bayesian solution of a supervised learning problem is reasonably simple while the unsupervised Bayesian learning is enormously complex. A practical way of solving an unsupervised learning problem is to convert it into a supervised learning problem by labelling the observation before using it for learning. Decision directed learning scheme uses the result of a decision process as the label. The computations for this scheme are feasible but the resulting estimates do not converge to the correct value. A learning scheme, 'learning with a probabilistic teacher,' is proposed in which a label is generated as a random variable from an appropriate probability density function. This scheme leads to a feasible solution to an unsupervised learning problem and assures the convergence of the estimate to the correct value. The average mean square error of the resulting estimate is twice the mean square error of the 'learning with a teacher' estimate. This learning scheme can also be used to estimate the state of a Gauss Markov sequence when the observation process has additive as well as multiplicative noise. (Author)

Descriptors :   (*DECISION THEORY, *STATISTICAL ANALYSIS), LEARNING MACHINES, PATTERN RECOGNITION, PROBABILITY DENSITY FUNCTIONS, ADAPTIVE SYSTEMS

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE