Ensembles of change-point methods to estimate the change point in residual sequences

Abstract

Change-point methods (CPMs) are statistical tests design to assess whether a given sequence comes from an unique, stationary, data-generating process. CPMs eventually estimate the change-point location, i.e., the point where the data-generating process shifted. While there exists a large literature concerning CPMs meant for sequences of independent and identically distributed (i.i.d.) random variables, their use on time-dependent signals has not been properly investigated. In this case, a straightforward solution consists in computing at first the residuals between the observed signal and the output of a suitable approximation model, and then applying the CPM on the residual sequence. Unfortunately, in practical applications, such residuals are seldom i.i.d., and this may prevent the CPMs to operate properly. To counteract this problem, we introduce the ensemble of CPMs, which aggregates several estimates obtained from CPMs executed on different subsequences of residuals, obtained from random sampling. Experiments show that the ensemble of CPMs improves the change-point estimates when the residuals are not i.i.d., as it is often the case in real-world scenarios.