Computationally-efficient initialisation of GPs: The generalised variogram method
Authors: Felipe Tobar, Elsa Cazelles, Taco de Wolff
TMLR 2023 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | 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. |
| Researcher Affiliation | Academia | Felipe Tobar EMAIL Initiative for Data & AI Universidad de Chile Elsa Cazelles EMAIL CNRS, IRIT Université de Toulouse Taco de Wolff tacodewolff@gmail.com Inria Chile |
| Pseudocode | Yes | Algorithm 1 GVM Spectral loss W2 & ({Sθ}θ Θ is location-scale) Require: ti, yi, i = 1, . . . , n Require: location-scale PSD family {Sθ}θ Θ (e.g., Gaussians) Define a grid over frequency space g = {ξ0, ξ1, . . . , ξk} Compute ˆSn = ˆSn(g), from eq. (6), over the chosen frequency grid Compute Qn the quantile function of ˆSn Compute θ n given by eq. (12) with Q := Qn |
| Open Source Code | Yes | The code for GVM is available at https://github.com/GAMES-UChile/Generalised-Variogram-Method, a minimal working example of the code is presented in Appendix D. |
| Open Datasets | Yes | We used a real-world audio signal from the Free Spoken Digit Dataset4. GVM was implemented with the metrics L1 and L2 both in the spectral and temporal domain to learn a sample from the above dataset, which was 4300 samples long. In this experiment, GVM was implemented to find the initial conditions of a GP with SM kernel (4, 8, 12 and 16 components) to a real-world 1800-point heart-rate signal from the MIT-BIH database5. |
| Dataset Splits | No | The paper mentions generating |
| Hardware Specification | No | No specific hardware details (e.g., CPU/GPU models, memory, or specific cloud instances) are provided for the experiments conducted by the authors. |
| Software Dependencies | No | The benchmarks were implemented on MOGPTK (de Wolffet al., 2021). The paper also shows Python code in Appendix D, but no specific version numbers for Python or any other libraries are provided. |
| Experiment Setup | Yes | We considered a GP with a 2-component spectral mixture kernel K(t) = P2 i=1 σ2 i exp( γiτ 2) cos(2πµiτ) + σ2 noiseδτ with hyperparameters σ1 = 2, γ1 = 10 4, µ1 = 2 10 2, σ2 = 2,γ2 = 10 4, µ2 = 3 10 2, σnoise = 1. We considered the L2 metric (spectral) minimised with Powell and then passed the hyperparameters to an ML routine for 1500 iterations (using Adam with learning rate = 0.1). |