On unsupervised estimation algorithms

There are several approaches to unsupervised estimation that have application to problems of communications, control, and pattern recognition. This paper presents properties of several different digitally implemented algorithms suitable for unsupervised estimation. One result is the rate of convergence in mean square of the Bayes solution for a discretized parameter space. A regression function that is the expected value of the natural logarithm of the mixture probability density function naturally arises from the Bayes approach. This regression function can be used to devise unsupervised estimation algorithms of the stochastic approximation form. Also, the asymptotic solution and rates of convergence in mean square of a class of minimum-integral-square-difference algorithms are determined. Two other estimators that use a "net" on the parameter space are also presented.