Motivated by the success of Bayesian optimisation algorithms in the Euclidean space, we propose a novel approach to construct Intrinsic Bayesian optimisation (In-BO) on manifolds with a primary focus on complex constrained domains or irregular-shaped spaces arising as submanifolds of R2, R3 and beyond. Data may be collected in a spatial domain but restricted to a complex or intricately structured region corresponding to a geographic feature, such as lakes. Traditional Bayesian Optimisation (Tra-BO) defined with a Radial basis function (RBF) kernel cannot accommodate these complex constrained conditions. The In-BO uses the Sparse Intrinsic Gaussian Processes (SIn-GP) surrogate model to take into account the geometric structure of the manifold. SInGPs are constructed using the heat kernel of the manifold which is estimated as the transition density of the Brownian Motion on manifolds. The efficiency of In-BO is demonstrated through simulation studies on a U-shaped domain, a Bitten torus, and a real dataset from the Aral sea. Its performance is compared to that of traditional BO, which is defined in Euclidean space.
翻译:以欧洲-克利德纳空间巴伊萨优化算法的成功为动力,我们提议了一种新颖的方法,在多处建造Intrinsic Bayesa Bayesian优化化(In-BO),主要侧重于复杂的受限制领域或作为R2、R3和R2、R3的子层外的异常形空间。数据可以在空间领域收集,但限于一个与地理特征(如湖泊等)相对的复杂或结构复杂的区域,如湖泊;传统的巴伊西亚优化(Tra-BOB),其定义是Radial基础函数(RBF)内核内核化(TRAF)内核化(Tra-BOB),无法适应这些复杂的受限制条件。在业内利用Sparse Instrinsic Gaussian进程(S-GP)的外形模型,以考虑该元体结构的几何结构。SInGP是使用这些元的热心箱建造的建筑,据测算出,这是BAR海中的转换密度。