Rates of Convergence for Sparse Variational Gaussian Process Regression
Authors: David Burt, Carl Edward Rasmussen, Mark Van Der Wilk
ICML 2019 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Figure 1. Increasing N with fixed M increases the expected KL divergence. t/2σ2 n is a lower bound for the expected value over the KL divergence when y is generated according to our prior model. Figure 3. Rates of convergence as M increases on fixed dataset of size N = 1000, with a SE-kernel with ℓ= .6, v = 1, σn = 1 and x N(0, 1) and y sampled from the prior. Figure 4. We increase N and take M = C log(N) for a onedimensional SE-kernel and normally distributed inputs. The KL divergence decays rapidly, as predicted by Corollary 2. |
| Researcher Affiliation | Collaboration | 1University of Cambridge, Cambridge, UK 2PROWLER.io, Cambridge, UK. |
| Pseudocode | No | The paper does not contain any structured pseudocode or algorithm blocks. |
| Open Source Code | No | The paper mentions "Open source implementations of approximate k-DPPs are available (e.g. [Gautier et al., 2018])." and provides a link to DPPy in the acknowledgements, which is a tool for k-DPPs. However, it does not state that the code for the specific methodology described in *this* paper is open-source or provide a link to it. |
| Open Datasets | No | Figure 3. Rates of convergence as M increases on fixed dataset of size N = 1000, with a SE-kernel with ℓ= .6, v = 1, σn = 1 and x N(0, 1) and y sampled from the prior. The paper uses synthetic data generated according to a specified distribution, not a publicly available dataset. |
| Dataset Splits | No | The paper does not explicitly provide training/test/validation dataset splits. It discusses theoretical bounds and illustrates them with simulated data rather than evaluating on partitioned empirical datasets. |
| Hardware Specification | No | The paper does not describe any specific hardware used for running its experiments or simulations. |
| Software Dependencies | No | The paper does not provide specific version numbers for any software dependencies used in its implementation or experiments. |
| Experiment Setup | Yes | Figure 3. Rates of convergence as M increases on fixed dataset of size N = 1000, with a SE-kernel with ℓ= .6, v = 1, σn = 1 and x N(0, 1) and y sampled from the prior. Figure 4. We increase N and take M = C log(N) for a onedimensional SE-kernel and normally distributed inputs. |