46 citations · 284 across the 22 of their papers we have counts for
22 papers
Universal Time-Uniform Trajectory Approximation for Random Dynamical Systems with Recurrent Neural Networks
Adrian N. Bishop
The capability of recurrent neural networks to approximate trajectories of a random dynamical system, with random inputs, on non-compact domains, and over an indefinite or infinite…
Recurrent Neural Networks and Universal Approximation of Bayesian Filters
Adrian N. Bishop, Edwin V. Bonilla
We consider the Bayesian optimal filtering problem: i.e. estimating some conditional statistics of a latent time-series signal from an observation sequence. Classical approaches of…
Modeling and Detecting Communities in Node Attributed Networks
Ren Ren, Jinliang Shao, Adrian N. Bishop +1
As a fundamental structure in real-world networks, in addition to graph topology, communities can also be reflected by abundant node attributes. In attributed community detection,…
On the Mathematical Theory of Ensemble (Linear-Gaussian) Kalman-Bucy Filtering
Adrian N. Bishop, Pierre Del Moral
The purpose of this review is to present a comprehensive overview of the theory of ensemble Kalman-Bucy filtering for continuous-time, linear-Gaussian signal and observation models…
Backward Nonlinear Smoothing Diffusions
Brian D. O. Anderson, Adrian N. Bishop, Pierre Del Moral +1
We present a backward diffusion flow (i.e. a backward-in-time stochastic differential equation) whose marginal distribution at any (earlier) time is equal to the smoothing distribu…
A Multilevel Approach for Stochastic Nonlinear Optimal Control
Ajay Jasra, Jeremy Heng, Yaxian Xu +1
We consider a class of finite time horizon nonlinear stochastic optimal control problem, where the control acts additively on the dynamics and the control cost is quadratic. This f…