On the identifiability of mixtures-of-experts

In mixtures-of-experts (ME) models, "experts" of generalized linear models are combined, according to a set of local weights called the "gating function". The invariant transformations of the ME probability density functions include the permutations of the expert labels and the translations of the parameters in the gating functions. Under certain conditions, we show that the ME systems are identifiable if the experts are ordered and the gating parameters are initialized. The conditions are validated for Poisson, gamma, normal and binomial experts.