Content

This repository includes the code used in paper:

Mojmir Mutny & Andreas Krause, "Efficient High Dimensional Bayesian Optimization with Additivity and Quadrature Fourier Features", NIPS 2018

For paper see here. Namely, we implement finite basis approximation to Gaussian processes. The main contribution of this paper is implementation of the method embed(x) which coincides with \Phi(x) in product approximation:

`k(x,y) = \Phi(x)^\top \Phi(y)`

Installation

First clone the repository:

git clone https://github.com/Mojusko/QFF.git

Inside the project directory, run

pip install -e .

The -e option installs the package in "editable" mode, where pip links to your local copy of the repository, instead of copying the files to the your site-packages directory. That way, a simple git pull will update the package. The project requires Python 3.6, and the dependencies should be installed with the package.

Updates

21/12/2019 - More efficient basis

Usage - Implements Phi(x)

from embedding import *
x = torch.random(100,1) ## 100 random points in 1D
emb = HermiteEmbedding(gamma=0.5, m=100, d=1, groups=None, approx = "hermite") # Squared exponential with lenghtscale 0.5 with 100 basis functions 
Phi = emb.embed(x)

Demonstration

• RFF of Rahimi & Recht (2007)
• Quasi-RFF Avron et. al. (2014)
• Orthogonal RFF - Felix et. al. (2016)
• QFF - Mutny & Krause (2018)