deep stochastic process
Appendix of Deep Stochastic Processes via Functional Markov Transition Operator A Proofs
A.1 Proof of proposition 4.1 (See page 4) A.2 Proof of proposition 4.2 (See page 4) MTOs in the form of Equation ( 9) are consistent and exchangeable. MTO s are consistent and exchangeable for the general form. These convex functions are then randomly shifted and rescaled to increase diversity. To circumvent memory issues, we use deep sets in this instance. Note that we do not share parameters among iterations.
Appendix of Deep Stochastic Processes via Functional Markov Transition Operator A Proofs
A.1 Proof of proposition 4.1 (See page 4) A.2 Proof of proposition 4.2 (See page 4) MTOs in the form of Equation ( 9) are consistent and exchangeable. MTO s are consistent and exchangeable for the general form. These convex functions are then randomly shifted and rescaled to increase diversity. To circumvent memory issues, we use deep sets in this instance. Note that we do not share parameters among iterations.
Deep Stochastic Processes via Functional Markov Transition Operators
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.