KernelMatmul: Scaling Gaussian Processes to Large Time Series
Authors: Tilman Hoffbauer, Holger H. Hoos, Jakob Bossek
AAAI 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We thoroughly benchmark our new method against multiple baselines to demonstrate its benefits and limitations, both in efficiency and accuracy. Our work includes a benchmark of multiple approaches to kernel matrix multiplication performance (including Ke Ops (Charlier et al. 2021)). This benchmark demonstrates improved performance of Kernel Matmul on many configurations (Section 5.1). An investigation of the residuals (Section 5.2) showcases the low error introduced by our sparsity approximation. Additionally, we provide a comparison (Section 5.3) to other approximation schemes, such as variational inference (Wu, Pleiss, and Cunningham 2022) and structured kernel interpolation (Wilson and Nickisch 2015). |
| Researcher Affiliation | Academia | 1Chair for AI Methodology, RWTH Aachen University, Germany 2Leiden Institute of Advanced Computer Science, Leiden University, The Netherlands 3University of British Columbia, Canada 4Chair for Machine Learning and Optimisation, Paderborn University, Germany |
| Pseudocode | No | The paper describes mathematical formulas and implementation details but does not contain a clearly labeled pseudocode block or algorithm section. |
| Open Source Code | Yes | Implementation https://github.com/Turakar/kernel-matmul Experiments https://github.com/Turakar/kernel-matmul-benchmark |
| Open Datasets | Yes | It was executed on three datasets from the Monash Forecasting Repository: London Smart Meters, Solar and Traffic (Godahewa et al. 2021). |
| Dataset Splits | Yes | We use the splits into training, validation and test data provided by the the Monash Forecasting Repository. |
| Hardware Specification | Yes | All experiments were run on an NVIDIA H100 GPU with CUDA 12.1 on Linux. |
| Software Dependencies | Yes | All experiments were run on an NVIDIA H100 GPU with CUDA 12.1 on Linux. |
| Experiment Setup | Yes | For each dataset, we compiled a list of 11 randomly selected subsets of 20 series each. Then, we performed individual hyperparameter optimizations (HPOs) for each subset and method. Every HPO is performed with SMAC3 (Lindauer et al. 2022) in a multi-instance setting for 4 hours wall time. The best configuration of each HPO is then evaluated on all series in the test dataset by retraining on the training and validation data of that series. ... Kernel Matmul-based CG inference (ϵ = 10 5) ... For this dataset, we constructed a perfectly matching spectral kernel (i.e., ν = 1) with α = 0.01. ... The predictions for this second comparison were generated with GPy Torch default settings, i.e., a CG tolerance of 0.01. ... SKI used as many grid points as there are samples in the training set, while VNNGP used 64 neighbours per sample. |