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

Overview

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

Owner
Aristeidis (Ares) Panos
I am a postdoctoral researcher in the Department of Statistics at the University of Warwick.
Aristeidis (Ares) Panos
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