FastARD

A Julia implementation of Fast Automatic Relevance Determination (ARD) for sparse Bayesian regression with uncertainty quantification.

Key Features

• Automatic sparsity detection in high-dimensional regression problems
• Uncertainty quantification with well-calibrated confidence intervals
• Polynomial chaos expansion support for function approximation
• Method comparison against traditional numerical approaches
• Performance optimization with timing analysis and convergence monitoring

Quick Example

using FastARD
using Random, Statistics, LinearAlgebra

# Test on the Ishigami function
function ishigami(x; a=7.0, b=0.1)
    x1, x2, x3 = x[1], x[2], x[3]
    return sin(x1) + a * sin(x2)^2 + b * x3^4 * sin(x1)
end

# Generate test data
Random.seed!(123)
n_train = 300
X_train = 2π * rand(n_train, 3) .- π
y_train = [ishigami(X_train[i, :]) for i in 1:n_train]

# Create polynomial basis (35 terms for degree 4)
# ... (see examples for full implementation)

# Fit FastARD model
model = FastARDRegressor(verbose=true, compute_score=true)
fit!(model, Psi_train, y_train_noisy)

# Analyze sparsity
active_indices, active_coefs = get_active_coefficients(model)
println("Selected $(length(active_indices)) out of 35 basis functions")

# Get predictions with uncertainty
y_pred, y_std = predict_with_uncertainty(model, Psi_test)

Tested Applications

The package includes comprehensive tests demonstrating performance on the Ishigami function, a standard benchmark for:

• Sensitivity analysis and uncertainty quantification
• Polynomial chaos expansion with automatic basis selection
• Comparison against multiple advanced numerical methods
• Uncertainty calibration and coverage probability analysis

See examples/ishigami_comparison_test.jl for the complete tested implementation.

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Contributors