Partitioning datasets based on equalities among parameters

When a phenomenon is described by a parametric model and multiple datasets are available, a key problem in statistics is to discover which datasets are characterized by the same parameter values. Equivalently, one is interested in partitioning the family of datasets into blocks collecting data that are described by the same parameters. Because of noise, different partitions can be consistent with the data, in the sense that they are accepted by generalized likelihood ratio tests with a given confidence level. Given the fact that testing all possible partitions is a computationally unaffordable task, we propose an algorithm for finding all acceptable partitions while avoiding to test unnecessary ones. The core of our method is an efficient procedure, based on partial order relations on partitions, for computing all partitions that verify an upper bound on a monotone function. The reduction of the computational burden brought about by the algorithm is analyzed both theoretically and experimentally. Applications to the identification of switched systems are also presented.