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We create a mixed-integer optimization (MIO) approach for doing cluster-awareregression, i.e. linear regression that takes into account the inherentclustered structure of the data. We compare to the linear mixed effectsregression (LMEM) which is the most used current method, and design simulationexperiments to show superior performance to LMEM in terms of both predictiveand inferential metrics in silico. Furthermore, we show how our method isformulated in a very interpretable way; LMEM cannot generalize and makecluster-informed predictions when the cluster of new data points is unknown,but we solve this problem by training an interpretable classification tree thatcan help decide cluster effects for new data points, and demonstrate the powerof this generalizability on a real protein expression dataset.

A distribution-free mixed-integer optimization approach to hierarchical modelling of clustered and longitudinal data