Deep Stochastic Processes via Functional Markov Transition Operators
This work addresses the need for more flexible and expressive models in machine learning for tasks involving stochastic processes, representing an incremental improvement over existing Neural Processes.
The paper tackles the problem of enhancing flexibility and expressivity in Stochastic Processes by introducing Markov Neural Processes (MNPs), which use neural parameterized Markov transition operators, and demonstrates clear advantages over baseline models in experiments.
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.