Multiresolution Kernel Approximation for Gaussian Process Regression
Authors: Yi Ding, Risi Kondor, Jonathan Eskreis-Winkler
NeurIPS 2017 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We compare MKA to five other methods: 1. Full: the full GP regression using Cholesky factorization [1]. ... Qualitative results. We show the qualitative behavior of each method on the 1D toy dataset from [34]. ... Real data. We tested the efficacy of GP regression on real-world datasets. The data are normalized to mean zero and variance one. We randomly selected 10% of each dataset to be used as a test set. On the other 90% we did five-fold cross validation to learn the length scale and noise parameter for each method and the regression results were averaged over repeating this setting five times. All experiments were ran on a 3.4GHz 8 core machine with 8GB of memory. Two distinct error measures are used to assess performance: (a) standardized mean square error (SMSE), ... and (2) mean negative log probability (MNLP) ... From Table 1, we are competitive in both error measures when the number of pseudo-inputs (dcore) is small... |
| Researcher Affiliation | Academia | Department of Computer Science, Department of Statistics The University of Chicago, Chicago, IL, 60637 {dingy,risi,eskreiswinkler}@uchicago.edu |
| Pseudocode | Yes | The pseudocode of the full algorithm is in the Supplementary Material. |
| Open Source Code | No | The paper mentions implementation details like "Our algorithm MKA was implemented in C++ with the Matlab interface" but does not state that the source code for the described methodology is publicly available or provide a link. |
| Open Datasets | Yes | Qualitative results. We show the qualitative behavior of each method on the 1D toy dataset from [34]. ... Real data. We tested the efficacy of GP regression on real-world datasets. The data are normalized to mean zero and variance one. We randomly selected 10% of each dataset to be used as a test set. On the other 90% we did five-fold cross validation to learn the length scale and noise parameter for each method and the regression results were averaged over repeating this setting five times. All experiments were ran on a 3.4GHz 8 core machine with 8GB of memory. ... Table 1: Regression Results with k to be # pseudo-inputs/dcore : SMSE(MNLP) Method k Full SOR FITC PITC MEKA MKA housing 16... rupture 16... wine 32... pageblocks 32... comp Act 32... pendigit 64... |
| Dataset Splits | Yes | On the other 90% we did five-fold cross validation to learn the length scale and noise parameter for each method and the regression results were averaged over repeating this setting five times. |
| Hardware Specification | Yes | All experiments were ran on a 3.4GHz 8 core machine with 8GB of memory. |
| Software Dependencies | No | The paper mentions using "custom Matlab implementations" and that "Our algorithm MKA was implemented in C++ with the Matlab interface." However, no specific version numbers for Matlab, C++, or any libraries are provided. |
| Experiment Setup | Yes | We sampled the ground truth from a Gaussian processes with length scale ℓ= 0.5 and number of pseudo-inputs (dcore) is 10. We applied cross-validation to select the parameters for each method to fit the data. ... The Gaussian kernel is used for all experiments with one length scale for all input dimensions. ... On the other 90% we did five-fold cross validation to learn the length scale and noise parameter for each method and the regression results were averaged over repeating this setting five times. |