Performance bounds for coupled models

Two models are called “coupled” when a non empty set of the underlying parameters are related through a differentiable implicit function. The goal is to estimate the parameters of both models by merging all datasets, that is, by processing them jointly. In this context, we show that the parameter estimation accuracy under a general class of dataset distributions always improves when compared to an equivalent uncoupled model. We eventually illustrate our results with the fusion of multiple tensor data.