Mercer Gaussian Process (MGP) and Fourier Gaussian Process (FGP) Regression

We provide the code used in our paper "How Good are Low-Rank Approximations in Gaussian Process Regression?" to run experiments on the real-world datasets. The code includes implementation of Mercer GP (using dimensionality reduction) and Fourier GP. We also include the GPFlow code to run SGPR model.

Requirements

TensorFlow - version 2.1.0
TensorFlow Probability - version 0.9.0
GPflow - version 2.0.0 or newer
silence-tensorflow - version 1.1.1 (optional)

Flags

• batch_size: Batch size for MGP (due to the included shallow neural network) (integer - default=2048)
• num_epochs: Display loss function value every FLAGS.display_freq epochs (integer - default=100)
• num_splits: Number of random data splits used - number of experiments run for a model (integer - default=1)
• display_freq: Display loss function value every display_freq epochs (integer - default=10)
• rank: Rank r for MGP, FGP, SGPR (integer - default=10)
• d_mgp: Number of output dimensions for MGP's projection (integer - default=5)
• dataset: Dataset name (string - available names=[elevators, protein, sarcos, 3droad] - default=elevators)

Source code

The following files can be found in the src directory :

• models.py: implementation of MGP and FGP
• helper.py: various utility functions
• hermite_coeff.npy: a numpy array containing the Hermite polynomial coefficients needed for the DMGP model
• run_experiments.py: code for running models MGP, FGP, and SGPR on the real-world datasets used in the paper

Examples

You can run the code with the configuration of your choice using the following command

# Train MGP, FGP, SGPR models over the Protein dataset and repeat experiments 5 times
# Set the number of epochs equal to 500 
# Print the values of the log-marginal likelihood every 5 epochs.
# The rank of the kernel approximation is chosen to be 50

python src/run_experiments.py --dataset=protein --display_freq=5 --num_splits=5 --rank=50