Deep Stochastic Processes via Functional Markov Transition Operators

• URL: http://arxiv.org/abs/2305.15574v1
• Date: Wed, 24 May 2023 21:15:23 GMT
• Title: Deep Stochastic Processes via Functional Markov Transition Operators
• Authors: Jin Xu, Emilien Dupont, Kaspar M\"artens, Tom Rainforth, Yee Whye Teh
• Abstract summary: We introduce a new class of Processes (SPs) 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.
• Score: 59.55961312230447
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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