Change-point detection in regression models via the max-EM algorithm

The problem of breakpoint detection is considered within a regression modeling framework. A novel method, the max-EM algorithm, is introduced, combining a constrained Hidden Markov Model with the Classification-EM algorithm. This algorithm has linear complexity and provides accurate detection of breakpoints and estimation of parameters. A theoretical result is derived, showing that the likelihood of the data, as a function of the regression parameters and the breakpoints location, increases at each step of the algorithm. Two initialization methods for the breakpoints location are also presented to address local maxima issues. Finally, a statistical test in the one breakpoint situation is developed. Simulation experiments based on linear, logistic, Poisson and Accelerated Failure Time regression models show that the final method that includes the initialization procedure and the max-EM algorithm has a strong performance both in terms of parameters estimation and breakpoints detection. The statistical test is also evaluated and exhibits a correct rejection rate under the null hypothesis and a strong power under various alternatives. Two real dataset are analyzed, the UCI bike sharing and the health disease data, where the interest of the method to detect heterogeneity in the distribution of the data is illustrated.