Monte Carlo Implementation of Gaussian Process Models for Bayesian Regression and Classification

Abstract

Gaussian processes are a natural way of defining prior distributions over functions of one or more input variables. In a simple nonparametric regression problem, where such a function gives the mean of a Gaussian distribution for an observed response, a Gaussian process model can easily be implemented using matrix computations that are feasible for datasets of up to about a thousand cases. Hyperparameters that define the covariance function of the Gaussian process can be sampled using Markov chain methods. Regression models where the noise has a t distribution and logistic or probit models for classification applications can be implemented by sampling as well for latent values underlying the observations. Software is now available that implements these methods using covariance functions with hierarchical parameterizations. Models defined in this way can discover high-level properties of the data, such as which inputs are relevant to predicting the response.

Cited by in corpus (54)

• Uncertainty Quantification in Machine Learning for Engineering Design and Health Prognostics: A Tutorial
• Student-t Processes as Alternatives to Gaussian Processes
• GPfit: An R package for Gaussian Process Model Fitting using a New Optimization Algorithm
• Online learning-based Model Predictive Control with Gaussian Process Models and Stability Guarantees
• Multivariate Gaussian and Student$-t$ Process Regression for Multi-output Prediction
• How priors of initial hyperparameters affect Gaussian process regression models
• Multi-Task Trust Transfer for Human-Robot Interaction
• Linear Multiple Low-Rank Kernel Based Stationary Gaussian Processes Regression for Time Series
• A Practical Introduction to Bayesian Estimation of Causal Effects: Parametric and Nonparametric Approaches
• Gaussian Process Regression with Heteroscedastic or Non-Gaussian Residuals
• Bayesian Modeling with Gaussian Processes using the GPstuff Toolbox
• Large Scale Variable Fidelity Surrogate Modeling
• Asynchronous Gibbs Sampling
• Practical Hilbert space approximate Bayesian Gaussian processes for probabilistic programming
• An analytic comparison of regularization methods for Gaussian Processes
• Multi-class Gaussian Process Classification with Noisy Inputs
• Exact Inference for Gaussian Process Regression in case of Big Data with the Cartesian Product Structure
• Stochastic stiffness identification and response estimation of Timoshenko beams via physics-informed Gaussian processes
• Quantifying out-of-station waiting time in oversaturated urban metro systems
• Bayesian Regression and Classification Using Gaussian Process Priors Indexed by Probability Density Functions
• Gaussian Process Regression with a Student-t Likelihood
• Practical Bayesian optimization in the presence of outliers
• On Approximate Inference for Generalized Gaussian Process Models
• Quantum Machine Learning using Gaussian Processes with Performant Quantum Kernels
• Additive Gaussian Process Regression
• How Bayesian Should Bayesian Optimisation Be?
• MCMC methods for Gaussian process models using fast approximations for the likelihood
• Bayesian Field Theory: Nonparametric Approaches to Density Estimation, Regression, Classification, and Inverse Quantum Problems
• Schrödinger PCA: On the Duality between Principal Component Analysis and Schrödinger Equation
• Cluster-Specific Predictions with Multi-Task Gaussian Processes
• Bayesian Reconstruction of Approximately Periodic Potentials at Finite Temperature
• How Deep Are Deep Gaussian Processes?
• Predicting the Output From a Stochastic Computer Model When a Deterministic Approximation is Available
• Probabilistic Programming with Gaussian Process Memoization
• Stein Variational Gaussian Processes
• Classification and categorical inputs with treed Gaussian process models
• Transitional annealed adaptive slice sampling for Gaussian process hyper-parameter estimation
• Models of Disease Spectra
• A Latent Gaussian Process Model with Application to Monitoring Clinical Trials
• Particle learning of Gaussian process models for sequential design and optimization
• Learning Integral Representations of Gaussian Processes
• Cases for the nugget in modeling computer experiments
• Statistical Modelling and Analysis of the Computer-Simulated Datasets
• Variable Selection Using Nearest Neighbor Gaussian Processes
• Quantifying Uncertainty in Stochastic Models with Parametric Variability
• Gaussian Processes and Limiting Linear Models
• Quantile Propagation for Wasserstein-Approximate Gaussian Processes
• Adaptive design and analysis of supercomputer experiments
• Fast matrix computations for functional additive models
• On MCMC for variationally sparse Gaussian processes: A pseudo-marginal approach
• Efficient Optimization of the Likelihood Function in Gaussian Process Modelling
• Gaussian Processes for Individualized Continuous Treatment Rule Estimation
• A Computationally Stable Approach to Gaussian Process Interpolation of Deterministic Computer Simulation Data
• Understanding Hormonal Crosstalk in Arabidopsis Root Development via Emulation and History Matching