Change Point Detection for Time Dependent Counts Using Extended MDL and Genetic Algorithms

This article introduces an extension for change point detection based on the Minimum Description Length (MDL) methodology. Unlike traditional approaches, this proposal accommodates observations that are not necessarily independent or identically distributed. Specifically, we consider a scenario where the counting process comprises observations from a Non-homogeneous Poisson process (NHPP) with a potentially non-linear time-dependent rate. The analysis can be applied to the counts for events such as the number of times that an environmental variable exceeded a threshold. The change point identification allows extracting relevant information on the trends for the observations within each segment and the events that may trigger the changes. The proposed MDL framework allows us to estimate the number and location of change points and incorporates a penalization mechanism to mitigate bias towards single regimen models. The methodology addressed the problem as a bilevel optimization problem. The first problem involves optimizing the parameters of NHPP given the change points and has continuous nature. The second one consists of optimizing the change points assignation from all possible options and is combinatorial. Due to the complexity of this parametric space, we use a genetic algorithm associated with a generational spread metric to ensure minimal change between iterations. We introduce a statistical hypothesis t-test as a stopping criterion. Experimental results using synthetic data demonstrate that the proposed method offers more precise estimates for both the number and localization of change points compared to more traditional approaches.