Heterogeneuous Change Point Inference

We propose a new estimator H-SMUCE (heterogeneous simultaneous multiscale change-point estimator) for the detection of multiple change-points of the signal in a heterogeneous gaussian regression model. A piecewise constant function is estimated by minimizing the number of change-points over the acceptance region of a multiscale test which locally adapts to possible changes in the variance. The multiscale test is a combination of likelihood ratio tests which are weighted by scale dependent critical values. We show that H-SMUCE controls over- and underestimation of the number of change-points at a given probability. Moreover, we obtain confidence sets for the location of the change-points and for the whole signal. All results are non-asymptotic and uniform over a large class of heterogeneous change-point models. H-SMUCE achieves the optimal detection rate and estimates the number of change-points consistently for vanishing signals, even when the number of change-points is unbounded. The estimator is computed by a fine tuned dynamic program and often performs almost linear in computation time. An R-package is available online. We compare the performance of H-SMUCE with several state of the art methods in simulations and analyse current recordings of a transmembrane protein in the bacterial outer membrane with pronounced heterogeneity for its states.