Adding inequality constraints (e.g. boundedness, monotonicity, convexity) into Gaussian processes (GPs) can lead to more realistic stochastic emulators. Due to the truncated Gaussianity of the posterior, its distribution has to be approximated. In this work, we consider Monte Carlo (MC) and Markov chain Monte Carlo (MCMC). However, strictly interpolating the observations may entail expensive computations due to highly restrictive sample spaces. Having (constrained) GP emulators when data are actually noisy is also of interest. We introduce a noise term for the relaxation of the interpolation conditions, and we develop the corresponding approximation of GP emulators under linear inequality constraints. We show with various toy examples that the performance of MC and MCMC samplers improves when considering noisy observations. Finally, on a 5D monotonic example, we show that our framework still provides high effective sample rates with reasonable running times.
翻译:将不平等限制(如界限、单一度、混凝土等)添加到Gaussian进程(GPs)中,可能会导致更现实的随机模拟器。由于后表层的孔径短,其分布必须大致接近。在这项工作中,我们认为Monte Carlo(MC)和Markov链Monte Carlo(MC MC ) 。然而,严格地将观测结果进行内插可能会由于高度限制性的抽样空间而导致昂贵的计算。在数据确实吵闹时采用(受限制的)GP 模拟器也令人感兴趣。我们引入了一个噪音术语来缓解内插条件,我们在线性不平等的限制下对GP模拟器进行相应的近似。我们用许多微小的例子显示,在考虑扰动观察时,MC和MCMC取样器的性能会改善。最后,在5D的单一式观察中,我们显示我们的框架仍然在合理的运行时间提供高有效采样率。