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Change-point regression robustified to smooth artefacts

Piecewise constant regression is undeniable the most common form of change-point regression. While the assumption of a piecewise constant signal is reasonable in many applications, there are import examples where such an assumption is at least questionable. We will introduce two examples (and methodology to analyse them): genome sequencing to detect copy number variations and ion channel recordings. The latter are experiments to measure the conductance of a single ion channel over time. We will see that such experiments can be better modelled by a piecewise constant function plus a smooth function. Existing methods are not using such a model explicitly. Contrarily, they assume a piecewise smooth signal, either explicitly or a decomposition into piecewise constant plus smooth functions is stated but not used for detecting change-points, instead only the smooth function is re-estimated in a second step. To use the decomposition explicitly, a modified fused lasso combined with smoothing techniques is proposed. Simulations show that this leads often to a better detection power. Moreover, the new methodology is very flexible. Kernel regression, smoothing splines and other methodologies can be used for smoothing. Secondly, extensions to multivariate and to filtered datasets are straightforward. We will give an outlook how these extensions can be used to analyse genome sequencing data and ion channel recordings, respectively.