  We introduce Markov Neural Processes (MNPs), a new class of Stochastic
Processes (SPs) which are constructed by stacking sequences of neural
parameterised Markov transition operators in function space. We prove that
these Markov transition operators can preserve the exchangeability and
consistency of SPs. Therefore, the proposed iterative construction adds
substantial flexibility and expressivity to the original framework of Neural
Processes (NPs) without compromising consistency or adding restrictions. Our
experiments demonstrate clear advantages of MNPs over baseline models on a
variety of tasks.
