State Space Gaussian Processes with Non-Gaussian Likelihood
Authors: Hannes Nickisch, Arno Solin, Alexander Grigorevskiy
ICML 2018 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | The experiments focus on showing that the state space formulation delivers the exactness of the full na ıve solution, but with appealing computational benefits, and wide applicability over GP regression and classification tasks. Sec. 3.1 assesses the effects of the fast approximations of Ai and Qi. Sec. 3.2 demonstrates the unprecedented computational speed, and Sec. 3.3 presents a comparison study including 12 likelihood/inference combinations. Finally, two large-scale real-data examples are presented and solved on a standard laptop in a matter of minutes. |
| Researcher Affiliation | Collaboration | 1Digital Imaging, Philips Research, Hamburg, Germany 2Department of Computer Science, Aalto University, Espoo, Finland 3Silo.AI, Helsinki, Finland. |
| Pseudocode | Yes | Algorithm 1 Predictions and log marginal likelihood log Z for Gaussian process regression (Alg. 2.1 in Rasmussen & Williams (2006)). Complexity is O(n3) for the Cholesky decomposition, and O(n2) for solving triangular systems. ... Algorithm 2 Kalman (forward) filtering. For ADF, (W, b) are not required as inputs. Note, b = Wr. ... Algorithm 3 Rauch Tung Striebel (backward) smoothing. |
| Open Source Code | Yes | Code for the paper is available as part of the GPML toolbox version 4.2 (Rasmussen & Nickisch, 2010). |
| Open Datasets | Yes | We consider hourly observations of log electricity consumption (H ebrail & B erard, 2012) for one household (in log k W) over a time-period of 1,442 days (n = 34,154, with 434 missing observations). ... The data consists of dates of incidents that were scraped form (Wikipedia, 2018), and it covers 1210 incidents over the time-span of 1919 2017. |
| Dataset Splits | Yes | We evaluate our approach by 10-fold cross-validation over complete days, in this experiment with fixed hyperparameters, and obtain a predictive RMSE of 0.98 0.02 and NLPD of 1.47 0.01. |
| Hardware Specification | Yes | The results (including results in following sections) were run on an Apple Mac Book Pro (2.3 GHz Intel Core i5, 16 Gb RAM) laptop in Mathworks Matlab 2017b. |
| Software Dependencies | Yes | The results (including results in following sections) were run on an Apple Mac Book Pro (2.3 GHz Intel Core i5, 16 Gb RAM) laptop in Mathworks Matlab 2017b. All methods were implemented in the GPML Toolbox framework... |
| Experiment Setup | Yes | For each generated dataset we considered GP regression (in the form of Sec. 2.5) with a Gaussian likelihood and Mat ern (ν = 5/2) covariance function. Initially, all the matrices Ai and Qi were computed exactly. The results were compared to the approximate results of those matrices with various number of interpolation grid points K. ... For inference we use direct KL minimization (Sec. 2.8). We evaluate our approach by 10-fold cross-validation over complete days, in this experiment with fixed hyperparameters... All hyperparameters (except the period length) were optimized w.r.t. marginal likelihood, such that we first obtained a ball-park estimate of the parameters using one-month binning, and then continued optimizing with the full data set. |