# Computationally-efficient initialisation of GPs: The generalised variogram method

arXiv: https://arxiv.org/abs/2210.05394 · HTML: https://mlsanity.com/paper/2210.05394/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 39 references that are in the map.
- First posted on arXiv 11 Oct 2022.

## Builds on (most cited first, 13 of 13)

- [Gaussian Processes for Big Data](https://mlsanity.com/paper/1309.6835/) (2013)
- [Doubly Stochastic Variational Inference for Deep Gaussian Processes](https://mlsanity.com/paper/1705.08933/) (2017)
- [Gaussian Process Kernels for Pattern Discovery and Extrapolation](https://mlsanity.com/paper/1302.4245/) (2013)
- [Exact Gaussian Processes on a Million Data Points](https://mlsanity.com/paper/1903.08114/) (2019)
- [Rates of Convergence for Sparse Variational Gaussian Process Regression](https://mlsanity.com/paper/1903.03571/) (2019)
- [Procrustes Metrics on Covariance Operators and Optimal Transportation of Gaussian Processes](https://mlsanity.com/paper/1801.01990/) (2018)
- [The Wasserstein-Fourier Distance for Stationary Time Series](https://mlsanity.com/paper/1912.05509/) (2019)
- [A Gaussian Process Regression Model for Distribution Inputs](https://mlsanity.com/paper/1701.09055/) (2017)
- [MOGPTK: The Multi-Output Gaussian Process Toolkit](https://mlsanity.com/paper/2002.03471/) (2020)
- [Bayesian Nonparametric Spectral Estimation](https://mlsanity.com/paper/1809.02196/) (2018)
- [Hierarchical Gaussian Processes with Wasserstein-2 Kernels](https://mlsanity.com/paper/2010.14877/) (2020)
- [Learning non-Gaussian Time Series using the Box-Cox Gaussian Process](https://mlsanity.com/paper/1803.07102/) (2018)
- [Audio Transport: A Generalized Portamento via Optimal Transport](https://mlsanity.com/paper/1906.06763/) (2019)

## Abstract (arXiv)

We present a computationally-efficient strategy to initialise the hyperparameters of a Gaussian process (GP) avoiding the computation of the likelihood function. Our strategy can be used as a pretraining stage to find initial conditions for maximum-likelihood (ML) training, or as a standalone method to compute hyperparameters values to be plugged in directly into the GP model. Motivated by the fact that training a GP via ML is equivalent (on average) to minimising the KL-divergence between the true and learnt model, we set to explore different metrics/divergences among GPs that are computationally inexpensive and provide hyperparameter values that are close to those found via ML. In practice, we identify the GP hyperparameters by projecting the empirical covariance or (Fourier) power spectrum onto a parametric family, thus proposing and studying various measures of discrepancy operating on the temporal and frequency domains. Our contribution extends the variogram method developed by the geostatistics literature and, accordingly, it is referred to as the generalised variogram method (GVM). In addition to the theoretical presentation of GVM, we provide experimental validation in terms of accuracy, consistency with ML and computational complexity for different kernels using synthetic and real-world data.