laGP.jl

Local Approximate Gaussian Process Regression for Julia

Overview

laGP.jl is a Julia implementation of Local Approximate Gaussian Process (laGP) regression, ported from the R laGP package by Robert Gramacy. It enables scalable GP predictions for large datasets by building local GP models at each prediction point.

Key Features

• Scalable Predictions: Handle datasets with thousands of observations by building local GP models
• AbstractGPs.jl Backend: Built on the JuliaGaussianProcesses ecosystem for robust GP computations
• Isotropic & Separable Kernels: Single lengthscale or per-dimension ARD lengthscales
• Acquisition Functions: ALC (Active Learning Cohn) and MSPE for intelligent point selection
• MLE with Priors: Maximum likelihood estimation with Inverse-Gamma priors (MAP)
• Multi-threaded: Parallel predictions across test points

Installation

using Pkg
Pkg.add(url="https://github.com/joshualeond/laGP.jl")

Quick Example

using laGP
using Random

Random.seed!(42)

# Generate training data
n = 100
X = rand(n, 2)
Z = sin.(2π * X[:, 1]) .* cos.(2π * X[:, 2]) + 0.1 * randn(n)

# Estimate hyperparameters from data
d_range = darg(X)
g_range = garg(Z)

# Create GP with initial parameters
gp = new_gp(X, Z, d_range.start, g_range.start)

# Optimize hyperparameters via joint MLE
jmle_gp!(gp; drange=(d_range.min, d_range.max), grange=(g_range.min, g_range.max))

println("Optimized lengthscale: ", gp.d)
println("Optimized nugget: ", gp.g)

# Make predictions
X_test = rand(10, 2)
pred = pred_gp(gp, X_test)

println("Predictions: ", pred.mean)
println("Variances: ", pred.s2)

Design Matrix Convention

All design matrices use rows as observations:

• X is n × m where n is number of points and m is dimensionality
• This matches the R laGP convention

Contents

• Getting Started
• • Creating a GP Model
  • Hyperparameter Estimation
  • Making Predictions
  • Local Approximate GP
  • Acquisition Methods
  • Next Steps
• Theory
• • Gaussian Process Basics
  • Kernel Parameterization
  • Concentrated Likelihood
  • Inverse-Gamma Priors
  • Local Approximate GP
  • Prediction Variance Scaling
  • Data-Adaptive Hyperparameter Ranges
  • References
• Local Approximate GP Demo
• • Overview
  • Setup
  • Test Function
  • Generate Training Data
  • Create Test Grid
  • Full GP Model
  • Local Approximate GP
  • Compare Results
  • Local Design Visualization
  • Key Observations
  • Next Steps
• Posterior Sampling Example
• • Overview
  • Setup
  • Generate Training Data
  • Fit Isotropic GP
  • Full Posterior Prediction
  • Draw Posterior Samples
  • Visualization (with CairoMakie)
  • Key Concepts
  • Credible Intervals
• Wing Weight Surrogate Example
• • Overview
  • Setup
  • Wing Weight Simulator
  • Generate Training Data
  • Fit Isotropic GP
  • Fit Separable GP
  • Compare on 2D Slice
  • Main Effects Analysis
  • Visualization (with CairoMakie)
  • Key Findings
  • Surrogate Benefits
• Satellite Drag Modeling Example
• • Overview
  • Background
  • Setup
  • Load Data
  • Normalize Data
  • Fit Separable GPs
  • Atmospheric Mixture
  • Lengthscale Analysis
  • Main Effects (for Helium)
  • Visualization (with CairoMakie)
  • Key Findings
• API Reference
• • Types
  • Core GP Functions (Isotropic)
  • Core GP Functions (Separable)
  • MLE Functions (Isotropic)
  • MLE Functions (Separable)
  • Acquisition Functions
  • Local GP Functions (Isotropic)
  • Local GP Functions (Separable)
  • Index

References

• Gramacy, R. B. (2016). laGP: Large-Scale Spatial Modeling via Local Approximate Gaussian Processes in R. Journal of Statistical Software, 72(1), 1-46.
• Gramacy, R. B. (2020). Surrogates: Gaussian Process Modeling, Design and Optimization for the Applied Sciences. Chapman Hall/CRC.