On Numerical Stability and Statistical Consistency of the Balanced Minimum Evolution Problem

Catanzaro, Daniele;Frohn, Martin;Pesenti, Raffaele
(2021) , 5 pages

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The Balanced Minimum Evolution Problem (BMEP) is affected by numerical instabilities that may preclude its use on practical instances. In this article, we investigate the impact of rescaling the objective function of the problem to overcome numerical instabilities and we show how this strategy may affect the statistical consistency of the optimal solution. In particular, we show that the numerical instabilities at the core of the BMEP cannot be overcome by any kind of rescaling of the objective function. As an extension of this negative result, we also characterize the class of the input distance matrices that may give rise to numerical instabilities for large scale instances.
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Catanzaro, D., Frohn, M., & Pesenti, R. (2021). On Numerical Stability and Statistical Consistency of the Balanced Minimum Evolution Problem (LIDAM Discussion Paper CORE 2021/26). https://hdl.handle.net/2078.5/108222