Automated Proving Properties of Expectation-Maximization Algorithm using Symbolic Tools

In many analyses based on estimating the parameters of probability distribution functions, the algorithms are developed for unknown probabilities. Some algorithms are derived starting from previous solutions and algorithms. One very popular algorithm is the EM (Expectation-Maximization) algorithm. The EM algorithm is a starting point for developing other advanced algorithms. Features of EM and other algorithms are observed with the traditional numerical approach. In this paper, we present a new approach of analysing the EM algorithm using computer algebra tools (Mathematica). We automatically derive properties of the algorithm. The knowledge embedded in symbolic expressions was used to simulate an example system and EM algorithm to generate the implementation code and to understand the nature of the error produced by selecting the total number of observed elements.