论文标题
边界条件线性约束的高斯过程
Linearly Constrained Gaussian Processes with Boundary Conditions
论文作者
论文摘要
贝叶斯机器学习中的一个目标是将先验知识编码为先验分布，以有效地对数据进行建模。我们考虑来自线性部分微分方程系统的先验知识及其边界条件。我们在此类系统的解决方案集中构建具有实现的多输出高斯工艺先验，特别是只有这样的解决方案才能通过高斯过程回归来表示。该结构是通过Gröbner碱基完全算法的，并且不采用任何近似值。它通过回调组合了两个参数化的构建这些先验：第一个参数将微分方程系统的解决方案和第二个参数化的所有函数都遵循了边界条件。
One goal in Bayesian machine learning is to encode prior knowledge into prior distributions, to model data efficiently. We consider prior knowledge from systems of linear partial differential equations together with their boundary conditions. We construct multi-output Gaussian process priors with realizations in the solution set of such systems, in particular only such solutions can be represented by Gaussian process regression. The construction is fully algorithmic via Gröbner bases and it does not employ any approximation. It builds these priors combining two parametrizations via a pullback: the first parametrizes the solutions for the system of differential equations and the second parametrizes all functions adhering to the boundary conditions.
