Stochastic Processes and Partial Differential Equations for problems in Statistics and Machine learning

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The project will investigate the application of continuous time stochastic processes for optimisation and sampling problems. The aim is to clarify links between optimisation and sampling and the long term behaviour of stochastic processes, such as accelerated or self interacting diffusions. We will consider the properties and performance of appropriate time discretisations when intended for contemporary applications from Statistics and Machine learning, such as learning parameters of deep neural networks, high dimensional regression or Bayesian variable selection.