In search of truth, simplicity is needed. There exist heavy-weighted libraries, but as you know, we need to go bare bone sometimes. Here is a minimal implementation of Gaussian process regression in PyTorch.

The implementation generally follows Algorithm 2.1 in Gaussian Process for Machine Learning (Rassmussen and Williams, 2006).

• Author: Sangwoong Yoon, Hyeokjun Kwon

• Gaussian process regression with squared exponential kernel.
• Hyperparameter optimization via marginal likelihood maximization using Pytorch built-in autograd functionality. (See demo.ipynb)
• Unittesting using Pytest.

• 2022-01-01: Bugfix in predictive variance computation
• 2023-01-03: Implement binary Laplace Gaussian process regression

• Numpy
• PyTorch
• PyTest
• Matplotlib (for demo)

from gp import GP

# generate data
X = torch.randn(100,1)
y = torch.sin(X * 2 * np.pi /4). + torch.randn(100, 1) * 0.1
grid = torch.linspace(-5, 5, 200)[:,None]

# run GP
gp = GP()  # you may specify initial hyperparameters using keyword arguments
gp.fit(X, y)
mu, var = gp.forward(grid)

from gp import GP

# generate data
X = torch.randn(100,1)
f = torch.sin(X * 3 * np.pi / 4)
y = (f > 0.).int() * 2 - 1
grid = torch.linspace(-5, 5, 200)[:,None]

# run GP
gp = BinaryLaplaceGPC()  # you may specify initial hyperparameters using keyword arguments
gp.fit(X, y)
mu, var, pi = gp.forward(grid)

$ pytest

• GPyTorch: A full-featured Gaussian process package based on PyTorch.