Gaussian Process Regression with Soft Inequality and Monotonicity Constraints
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.
Code (0)
등록된 구현이 없습니다.
Tasks
regressionSimilar Papers 제목 키워드 기반
Gaussian Process Modulated Cox Processes under Linear Inequality Constraints
Gaussian process (GP) modulated Cox processes are widely used to model point patterns. Existing approaches require a mapping (link function) between the unconstrained GP and the positive intensity function. This commonly…
Point ProcessesHigh-dimensional additive Gaussian processes under monotonicity constraints
We introduce an additive Gaussian process framework accounting for monotonicity constraints and scalable to high dimensions. Our contributions are threefold. First, we show that our framework enables to satisfy the const…
Dimensionality ReductionGaussian ProcessesVocal Bursts Intensity PredictionFinite-dimensional Gaussian approximation with linear inequality constraints
Introducing inequality constraints in Gaussian process (GP) models can lead to more realistic uncertainties in learning a great variety of real-world problems. We consider the finite-dimensional Gaussian approach from Ma…
parameter estimationUncertainty QuantificationApproximating Gaussian Process Emulators with Linear Inequality Constraints and Noisy Observations via MC and MCMC
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…
Gaussian ProcessesGaussian processes with linear operator inequality constraints
This paper presents an approach for constrained Gaussian Process (GP) regression where we assume that a set of linear transformations of the process are bounded. It is motivated by machine learning applications for high-…
Gaussian Processes