Data segmentation algorithms: Univariate mean change and beyond

Data segmentation a.k.a. multiple change point analysis has received considerable attention due to its importance in time series and signal processing, with applications a variety of fields including natural social sciences, medicine, engineering finance. The first part reviews the existing literature on canonical data problem which aims at detecting localising points mean univariate series. An overview popular methodologies is provided their computational complexity theoretical properties. In particular, discussion focuses separation rate relating are detectable by given procedure, localisation quantifying precision corresponding estimators, distinction made whether homogeneous or multiscale viewpoint been adopted derivation. It further highlighted that latter provides most general setting for investigating optimality algorithms. Arguably, framework propose new algorithms study efficiency last decades. second this survey motivates attaining an in-depth understanding strengths weaknesses simpler, setting, as stepping stone development more complex problems. This illustrated range examples showcasing connections between distributional changes those mean. Extensions towards high-dimensional problems also discussed where it demonstrated challenges arising from high dimensionality orthogonal dealing points.