TheAlgorithms
Add Gaussian Process Regression
Overview This implementation defines a Gaussian Process (GP) regression model in R using the kernlab package. GP is a non-parametric Bayesian regression algorithm that predicts continuous outputs while providing uncertainty estimates. It models a prior over functions via a kernel and updates the posterior distribution using observed data.
Features
Performs regression with uncertainty quantification for predictions. Supports small datasets effectively and works well with sparse data. Uses a kernel function (e.g., RBF) to define similarity between data points. Provides mean and variance (confidence) for each prediction. Handles non-linear relationships automatically through the kernel. Demonstrates predictions on synthetic or real regression datasets. Plotting functionality included for visualizing predictions against observations.
Complexity
Time Complexity: O(n³) due to kernel matrix inversion
Space Complexity: O(n²) for storing the kernel matrix
Demonstration
The included R script trains a GP model on a synthetic sine-wave dataset with noise. Predictions are made on test inputs, including plotting mean predictions. Replace x and y with other datasets for custom regression tasks. For large datasets, consider sparse GP approximations.
