Cascade of Phase Transitions for Multi-Scale Clustering

Following these steps, we aim at showing how the latter formulation can be useful to understand and analyse Many optimisation and inference problems have been the outcome of GMMs. In particular, we exploit the shown to have an equivalent formulation in statistical cascade of phase transitions occurring during annealing physics [1, 2] that allowed a brand-new look at some longstanding procedures of the EM algorithm to build a hierarchical problems and improved the understanding of multi-scale description of a dataset. By defining an overlap complex systems [3, 4]. In particular, the identification of between the ground truth and the inferred partitions, the phase diagram of a model can bring interesting new we show on artificial datasets how it can be interpreted insights such as knowing if a given information can be as an order parameter whose value follows the sequence retrieved depending on the model's parameters and the of phase transitions.