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GP-linalg

Randomized Algorithms for Gaussian Process Inference. Semester project, ANCHP Lab, EPFL.

About

Gaussian process inference engine based on GPyTorch (article, code). Theoretical analysis and numerical experiments can be found in the [report] of this repository. The engine relies on conjugate gradients and stochastic Lanczos quadrature, where partial pivoted Cholesky is used as a low rank approximation for preconditioning.

How-to

Getting started

One must first install the Python packages used in this project. The environment file is provided as environment.yaml, which also contains the Jupyter Lab package to view the notebook. The easiest method for installing is

  1. Install miniconda (a lightweight version of anaconda)
  2. Create the conda gpr (Gaussian Process Regression) environment that is later used to run the code:
conda env create -f environment.yml

One installation is complete, one must activate the environment:

user@host:/path$ conda activate gpr
(gpr) user@host:/path$ # gpr now appears, i.e. the environment is active

Regression Example

Run the script run_example.py to see the inference engine in action on a toy dataset. One should first activate the gpr environment and then run the script:

$ conda activate gpr
(gpr) $ python run_example.py

This prints the likelihood at each optimization step and produces a figure.

Project Structure

The user entry point is the GPModel class in models.py and the kernels in kernel.py .

File description

  • src folder contains
    • cg.py: mBCG algorithm
    • quadrature.py: Lanczos quadrature
    • chol.py: pivoted Cholesky algorithm
    • precond.py: routines for preconditioners of kernel matrices
    • kernel.py: squared exponential and Matern kernels
    • lanczos.py: Lanczos method for linear systems, used for debugging
    • inference.py: put pieces together to compute linear solve, logdet and trace term
    • model.py: compute likelihood and its gradient, perform optimization to fit hyperparameters
  • tests: unit tests for algorithms correctness

Numerical Experiments

All numerical experiments are gathered in the Jupyter notebook: notebook/Numerical Experiments.ipynb. In order to run it, cd into the root of this project and run:

user@host:/path$ conda activate gpr
(gpr) user@host:/path$ jupyter lab

This should open a browser tab with a jupyter server in which you can view and run the notebook. Make sure to run the cells in order.

Some cells perform heavy computations, those start with %%time and the running time appears under the cell. Those cells can be skipped as their results can be loaded in the following cells.