  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.
