Exploiting Hankel-Toeplitz Structures for Fast Computation of Kernel Precision Matrices
Authors: Frida Marie Viset, Anton Kullberg, Frederiek Wesel, Arno Solin
TMLR 2024 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We demonstrate the storage and computational savings of our structure exploiting scheme by means of three numerical experiments. The experiments demonstrate the practical efficiency of our scheme using the hgp. Our first experiment demonstrates the computational scaling of our scheme on a simulated 3D dataset. Secondly, we consider a magnetic field mapping example with data collected by an underwater vessel, as an application where the high-frequency content of the data requires a large amount of bfs to reconstruct the field. Thirdly, a precipitation dataset is used, mirroring an example in Solin & Särkkä (2020), improving the computational scaling in that particular application even further than the standard hgp. |
| Researcher Affiliation | Academia | Frida Viset EMAIL Delft Center for Systems and Control Delft University of Technology, The Netherlands Anton Kullberg EMAIL Department of Electrical Engineering Linköping University, Sweden Frederiek Wesel EMAIL Delft Center for Systems and Control Delft University of Technology, The Netherlands Arno Solin EMAIL Department of Computer Science Aalto University, Finland |
| Pseudocode | Yes | Algorithm 1 Sketch of an algorithm for Hilbert gp learning and inference. The original approach by Solin & Särkkä (2020) in red, our proposed approach in blue. |
| Open Source Code | Yes | A reference implementation built on top of GPJax is available at https://github.com/AOKullberg/hgp-hankel-structure. |
| Open Datasets | Yes | We consider a standard precipitation data set containing US annual precipitation summaries for year 1995 (d = 2 and N = 5776) (Vanhatalo & Vehtari, 2008). ... The data used were collected by MARMINE/NTNU research cruise funded by the Research Council of Norway (Norges Forskningsråd, NFR) Project No. 247626/O30 and associated industrial partners. Ocean Floor Geophysics provided magnetometer that was used for magnetic data acquisition and pre-processed the magnetic data. |
| Dataset Splits | Yes | The data was later split into a training set and test set, at a roughly 50% split. The nature of the data split is visualized in Fig. A8b. However, in practice, we selected the width of the test squares and the training squares smaller than the one displayed in the illustration and they are merely that big for visualization purposes. The illustration displays squares that are 0.01 latitudinal degrees wide and 0.03 longitudinal degrees tall, corresponding to approximately 1 km in Cartesian coordinates in this area. The split we actually used was squares which were 0.001 latitudinal degrees wide and 0.003 longitudinal degrees tall, corresponding to approximately 100 m in both directions in Cartesian coordinates in that area. |
| Hardware Specification | Yes | All timing experiments are run on an HP Elitebook 840 G5 laptop (Intel i7-8550U CPU, 16GB RAM). |
| Software Dependencies | No | The paper mentions software like GPJax (Pinder & Dodd, 2022) and Adam (Kingma & Adam, 2015) by citing their respective papers, but it does not specify explicit version numbers for these software packages or any other dependencies. |
| Experiment Setup | Yes | The hyperparameters of the kernel and likelihood were initialized as l = 1, σ2 SE = 10 and σe = 1, where l is the lengthscale, σ2 SE is the kernel variance and σe the noise standard deviation. ... The hyperparameters were initialized as l = 200 m, σ2 SE = 1 and σ2 y = 1. The resulting hyperparameters were l SE = 190, σ2 y = 0.0675, σ2 SE = 7.15. |