laGP.jl

A Julia implementation of Local Approximate Gaussian Process (laGP) regression for scalable GP predictions on large datasets.

Overview

laGP.jl is a port of the R laGP package by Robert Gramacy. It provides efficient Gaussian Process regression by building local GP models at each prediction point using nearest neighbors and acquisition functions.

Key Features:

• Scalable GP predictions for large datasets via local approximation
• Both isotropic and separable (ARD) kernel implementations
• Active Learning Cohn (ALC) and MSPE acquisition functions
• Maximum likelihood estimation with Inverse-Gamma priors
• Dual implementation: legacy direct matrix operations and AbstractGPs.jl backend
• Multi-threaded prediction support

Installation

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

Quick Start

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
d_range = darg(X)
g_range = garg(Z)

# Create and fit GP
gp = new_gp(X, Z, d_range.start, g_range.start)
jmle_gp!(gp; drange=(d_range.min, d_range.max), grange=(g_range.min, g_range.max))

# Make predictions
X_test = rand(10, 2)
pred = pred_gp(gp, X_test)
println("Predictions: ", pred.mean)
println("Variances: ", pred.s2)

Local Approximate GP

For large datasets, use the local approximate GP functions:

using laGP

# Large training set
X_train = rand(10000, 2)
Z_train = sin.(2π * X_train[:, 1]) .* cos.(2π * X_train[:, 2])

# Test points
X_test = rand(100, 2)

# Get hyperparameter ranges
d_range = darg(X_train)
g_range = garg(Z_train)

# Local approximate GP predictions
result = agp(X_train, Z_train, X_test;
    start=6, endpt=50,
    d=(start=d_range.start, mle=false),
    g=(start=g_range.start, mle=false),
    method=:alc  # or :mspe, :nn
)

println("Mean predictions: ", result.mean)
println("Variance estimates: ", result.var)

Documentation

For full documentation, including tutorials and API reference, see the documentation.

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.

License

LGPL-3.0