Robust Statistical Jump Models with Feature Selection

Abstract: A large area in statistics and machine learning is cluster analysis. This field of research concerns the design of algorithms that allow computers to automatically categorize a set of observations into different groups in a reasonable way, without any prior information about which observations belongs to which group. It is a part of the larger field of unsupervised learning within machine learning. Many of these algorithms are designed with a specific problem-task in mind. One example are so-called statistical jump models, developed by Bemporad et al. [2018] and further by Nystrup et al. [2021], that are developed to be used for (amongst other things, they are quite flexible models) the clustering of time-series data. In this thesis we have made a modification of these jump models that allows us to more freely chose how to measure distance between different observations. This opens up the possibility of designing more cluster algorithms for time series data that are more resilient to data containing many outliers, or doing clustering for categorical time series data.