Modelling high-dimensional data by combining simple experts

It is possible to combine multiple non-linear probabilistic models of the same data by multiplying the probability distributions together and then renormalizing. A "product of experts" is a very efficient way to model data that simultaneously satisfies many different constraints. It is difficult to fit a product of experts to data using maximum likelihood because the gradient of the log likelihood is intractable, but there is an efficient way of optimizing a different objective function and this produces good models of high-dimensional data.