Defines diffusion processes on implicit data manifolds via proximity-graph approximations to the infinitesimal generator and carré-du-champ operator, proves convergence in law to the continuous manifold process, and provides an Euler-Maruyama integrator validated on synthetic and MNIST manifolds.
Theory and a lgorithms for diffusion processes on Riemannian manifolds
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A new TaSP-CM integrator achieves strong order-1 convergence for SDEs on SO(n) and SE(n) under both commutative and non-commutative noise.
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Diffusion Processes on Implicit Manifolds
Defines diffusion processes on implicit data manifolds via proximity-graph approximations to the infinitesimal generator and carré-du-champ operator, proves convergence in law to the continuous manifold process, and provides an Euler-Maruyama integrator validated on synthetic and MNIST manifolds.
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Geometric Milstein Scheme for Stochastic Differential Equations on SO(n) and SE(n)
A new TaSP-CM integrator achieves strong order-1 convergence for SDEs on SO(n) and SE(n) under both commutative and non-commutative noise.