Expectation maximization algorithm over Fourier series (EMoFS)

Abstract

The application of expectation maximization (EM) algorithm for the univariate problems in the literature suffers mainly from the requirement of the prior information on parametrized probability distribution function (pdf) and its family. For the highly dynamic environments, however, there is a high potential of mismatch between the domain characteristics and the pre-assumed distribution. The observed data may have been drawn based on an unknown pdf, which can additionally be combination of discontinuous functions with different types. For such cases, it is very likely that an arbitrary selection of a mixture distribution would yield worse performance. Even if the domain characteristics are captured correctly, i.e. the pdf family is known, another complexity may arise due to the fact that a tractable and a closed form cannot always be obtained. Addressing these two problems, we present the EM over Fourier Series (EMoFS) approach for univariate problems to be solved with EM. Our solution produces the true pdf approximately; thus sidesteps the necessity of a prior assumption. Additionally it guarantees a tractable and closed form for E-step. We verify and evaluate our model via comparison with state of the art solutions, theoretical experiments and real world problems.