Cherry-picking for complex data: robust structure discovery

Complex data often arise as a superposition of data generated from several simpler models. The traditional strategy for such cases is to use mixture modelling, but it can be problematic, especially in higher dimensions. This paper considers an alternative approach, emphasizing data exploration and robustness to model misspecification. The strategy is applied to problems in regression, cluster analysis and multidimensional scaling. The approach is illustrated through simulation and the analysis of several datasets.