Non-separable Non-stationary random fields
Authors: Kangrui Wang, Oliver Hamelijnck, Theodoros Damoulas, Mark Steel
ICML 2020 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We demonstrate the capabilities of the resulting covariance functions within a Gaussian process (GP) framework and against other GP based approaches and compositions. Code is available at https://github.com/ohamelijnck/nsns_kernels and is implemented in GPFlow (Matthews et al., 2017). To demonstrate our SPMs we apply them on two synthetic datasets, on the well-studied Irish wind dataset and on the challenging setting of forecasting NO2 across London. We compare against nonstationary separable kernels (Paciorek & Schervish, 2004) denoted as GP( St Sp), and stationary nonseparable kernels (Fonseca & Steel, 2011a) denoted as GP(St Sp), Treed GPs (Gramacy & Lee, 2008) and a two-layer Deep Gaussian process (DGP) (Damianou & Lawrence, 2013) with the doubly stochastic framework (Salimbeni & Deisenroth, 2017). We denote SPM:nonstationary convolutions (SPM:NC) as GP( St Sp):NC and SPM:nonstationary mixings (SPM:NM) as GP( St Sp):NM. A summary of results is provided in Table. 1. |
| Researcher Affiliation | Academia | 1Data-centric Engineering, The Alan Turing Institute, London, UK 2Department of Statistics, University of Warwick, Coventry, UK 3Department of Computer Science, University of Warwick. Correspondence to: Kangrui Wang <Kwang@turing.ac.uk>, Theodoros Damoulas <T.Damoulas@warwick.ac.uk>. |
| Pseudocode | No | No pseudocode or algorithm blocks were found in the paper. |
| Open Source Code | Yes | Code is available at https://github.com/ohamelijnck/nsns_kernels and is implemented in GPFlow (Matthews et al., 2017). |
| Open Datasets | Yes | To demonstrate our SPMs we apply them on two synthetic datasets, on the well-studied Irish wind dataset and on the challenging setting of forecasting NO2 across London. We generate 7 data sets with increasing sample sizes using 10, 20, 30, 50, 100, 200 and 500 randomly selected observations. The Irish wind data consists of average daily wind speeds across 12 different locations in Ireland. We model NO2 across London using observations from 34 sensors from the London air quality network (LAQN). |
| Dataset Splits | Yes | We take the first two time slices as our training set and then predict on the remaining three. We train a GP using observations below the white dashed line and predict on the region above ([0.4, 1.0]). |
| Hardware Specification | No | No specific hardware details (e.g., GPU/CPU models, memory amounts, or detailed computer specifications) were provided for running the experiments. |
| Software Dependencies | No | The paper mentions 'implemented in GPFlow (Matthews et al., 2017)' but does not provide a specific version number for GPFlow or any other software dependencies. |
| Experiment Setup | Yes | We use single GPs for all covariance functions and to make comparisons with the DGP fair we optimize all models w.r.t to their variational lower bounds and use as many inducing points as input observations. We found that the single GP models were easy to fit and robust to initialization whereas the DGP has a tendency to explain the observations as noise; this required us to first hold the noise variance constant and release it half way through optimisation. |