Gaussian Process Regression

Gaussian process regression is a Bayesian nonparametric method that models the outcome as a smooth random function with a covariance kernel, giving predictions together with uncertainty.

가우스 과정 회귀는 결과를 공분산 커널로 정의된 매끄러운 확률 함수로 모형화해 예측값과 그 불확실성을 함께 주는 베이지안 비모수 회귀 방법입니다.

Can I predict material strength from a few process variables with a flexible smooth model and see which variables matter?

공정 변수 몇 개로 재료 강도를 유연하고 매끄러운 모형으로 예측하고, 어떤 변수가 중요한지도 알 수 있을까요?

Fit a Gaussian process with an RBF kernel that has one length scale per standardized predictor plus a white-noise term, choosing hyperparameters by maximizing the marginal likelihood. Judge predictive accuracy with cross-validated R², and read short length scales as variables the response changes with quickly.

When to use Gaussian Process Regression

• The relationship is smooth but its form is unknown
• The sample is small to moderate, roughly up to a few thousand rows
• You want predictive uncertainty or a surrogate model for experiments

When to use something else

• You have tens of thousands of rows; use gradient boosting or a sparse approximation
• You need interpretable coefficients for inference; use linear regression or a generalized additive model

Assumptions and requirements

• The chosen kernel reflects the smoothness of the true function
• Noise is homoscedastic and Gaussian
• Predictors are on comparable scales after standardization
• Above 2,000 rows a random subsample is fitted, because the cost grows with n³

What the analysis reports

• Optimized signal variance, length scales and noise variance
• Log marginal likelihood
• k-fold cross-validated R²
• Cross-validated predictions versus observed values

How to report it

A Gaussian process regression with an ARD RBF plus white-noise kernel (N = [value], [value] predictors) achieved a 5-fold cross-validated R² of [value] (SD = [value]); estimated length scales were [value] for [variable] and [value] for [variable].

Related methods

• Support Vector Machine (SVM and SVR)
• Generalized Additive Models (GAM)
• Bayesian Linear Regression

Run Gaussian Process Regression on Quorant