Gaussian process (GP) regression is a non-parametric, Bayesian framework to approximate complex models. Standard GP regression can lead to an unbounded model in which some points can take infeasible values. We introduce a new GP method that enforces the physical constraints in a probabilistic manner. This GP model is trained by the quantum-inspired Hamiltonian Monte Carlo (QHMC). QHMC is an efficient way to sample from a broad class of distributions. Unlike the standard Hamiltonian Monte Carlo algorithm in which a particle has a fixed mass, QHMC allows a particle to have a random mass matrix with a probability distribution. Introducing the QHMC method to the inequality and monotonicity constrained GP regression in the probabilistic sense, our approach improves the accuracy and reduces the variance in the resulting GP model. According to our experiments on several datasets, the proposed approach serves as an efficient method as it accelerates the sampling process while maintaining the accuracy, and it is applicable to high dimensional problems.

翻译：高斯过程回归是一种非参数、贝叶斯框架，用于近似复杂模型。标准高斯过程回归可能导致无界模型，其中某些点可能取不可行值。我们提出了一种新的高斯过程方法，以概率方式强制执行物理约束。该高斯过程模型通过量子启发式哈密顿蒙特卡洛（QHMC）进行训练。QHMC是一种高效的方法，可从广泛的分布类别中进行采样。与标准哈密顿蒙特卡洛算法中粒子具有固定质量不同，QHMC允许粒子具有概率分布的随机质量矩阵。将QHMC方法引入概率意义下带不等式和单调性约束的高斯过程回归，我们的方法提高了精度并降低了所得高斯过程模型中的方差。根据我们在多个数据集上的实验，所提出的方法是一种高效方法，因为它加速了采样过程同时保持了精度，并且适用于高维问题。