题目：           Bayesian optimisation and Intrinsic Gaussian process on manifold

报告人：      Mu Niu (University of Glasgow)

时间地点：   2018.08.13  10:30am  N208

摘要：          In recent years it has become common to collect data that are restricted to a complex constrained space. For example, data may be collected in a spatial domain but restricted to a complex or intricately structured region corresponding to a geographic feature, such as a lake. Traditional smoothing or modelling methods that do not respect the intrinsic geometry of the space, and in particular the boundary constraints, may produce poor results. We propose a class of intrinsic Gaussian processes (in-GPs) for interpolation and regression on manifolds with a primary focus on complex constrained domains or irregular-shaped spaces arising as subsets or submanifolds of R^2, R^3 and beyond. in-GPs respect the potentially complex boundary or interior conditions as well as the intrinsic geometry of the spaces. The key novelty of the proposed approach is to utilise the relationship between heat kernels and the transition density of Brownian motion on manifolds for constructing and approximating valid and computationally feasible covariance kernels.

One of the application of Gaussian process is Bayesian optimisation. It is a sequential design strategy for global optimization of unknown functions or a black box function whose gradients are hard to compute. A cheap proxy function can be built from the Gaussian process prediction. We can make the proxy function exploit uncertainty to balance exploration against exploitation. Bayesian optimization has been widely used to optimize functions defined in Euclidean spaces. In our work, we propose an approach of Bayesian optimization on some interesting domains such as sphere, and Grassmannian.