Automated proving properties of expectation-maximization algorithm using symbolic tools

In many analysis based on estimation the parameters of probability distribution functions, the algorithms are developing 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 analysis EM algorithm using symbolic processing (specific Mathematica). We automatically derive properties of the algorithm. The knowledge embedded in the symbolic expressions was used to simulate an example system and EM algorithm to generate the implementation code of some critical parts of analysis.