Before revision:  In this paper we propose a principled approach that allows to perform model selection for cross-impact models, showing that symmetriesand consistency requirements are particularly effective in reducing the universe of possible models to a much smaller set of viable candidates, thus mitigating the effect of noise on the properties of the inferred model.
After revision:  In this study we propose a principled approach that allows to perform model selection for cross-impact models, showing that symmetriesand consistency requirements are particularly effective in reducing the universe of possible models to a much smaller set of viable candidates, thus mitigating the effect of noise on the properties of the inferred model.