Probability density estimation using incomplete data

An unsupervised method of learning probability density function parameters in the framework of mixture densities from incomplete data is developed. Unsupervised learning can be considered as learning from observations as they are received. In real-world processes, there are many imperfections in the observations. The Expectation-Maximization algorithm is used to iteratively find the maximum likelihood estimate of the missing values and the parameters of the probability density function. Reliability of the Expectation-Maximization algorithm and its convergence properties during the learning process from incomplete data are presented. Three examples of learning mixture probability density function parameters from an incomplete data set are presented and the boundaries of properly estimating the mixture probability density function parameters as the percentage of missing data increases are examined.