Product of Experts is a machine learning

Machine learning

Machine learning, a branch of artificial intelligence, is a scientific discipline concerned with the design and development of algorithms that allow computers to evolve behaviors based on empirical data, such as from sensor data or databases...

 technique. It models a probability distribution by combining the output from several simpler distributions.
It was proposed by Geoff Hinton, along with an algorithm for training the parameters of such a system.

The core idea is to combine several probability distributions ("experts") by multiplying their density functions—making the PoE classification similar to an "and" operation. This allows each expert to make decisions on the basis of a few dimensions without having to cover the full dimensionality of a problem.

This is related to (but quite different from) a mixture model

Mixture model

In statistics, a mixture model is a probabilistic model for representing the presence of sub-populations within an overall population, without requiring that an observed data-set should identify the sub-population to which an individual observation belongs...

, where several probability distributions are combined via an "or" operation, which is a weighted sum of their density functions.