Notice: The reproducibility variables underlying each score are classified using an automated LLM-based pipeline, validated against a manually labeled dataset. LLM-based classification introduces uncertainty and potential bias; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in [1].
On the Equivalence between Kernel Quadrature Rules and Random Feature Expansions
Authors: Francis Bach
JMLR 2017 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | In this section, we consider simple illustrative quadrature experiments4 with X = [0, 1] and kernels k(x, y) = 1+P m=1 1 m2s cos 2πm(x y), with various values of s and distributions dρ which are Beta random variable with the two parameters equal to a = b, hence symmetric around 1/2. We report results comparing different Sobolev spaces for testing functions to integrate (parameterized by s) and learning quadrature weights (parameterized by t) in Figure 1, where we compute errors averaged over 1000 draws. |
| Researcher Affiliation | Academia | Francis Bach EMAIL INRIA Sierra Project-team D epartement d Informatique de l Ecole Normale Sup erieure (UMR CNRS/ENS/INRIA) 2, rue Simone Iff 75012 Paris, France |
| Pseudocode | No | The paper describes methods and algorithms in paragraph text, for example, in Section 4.2 regarding the algorithm to estimate the optimized distribution, but it does not contain any explicitly labeled pseudocode or algorithm blocks. |
| Open Source Code | Yes | Matlab code for all 5 figures may be downloaded from http://www.di.ens.fr/~fbach/quadrature.html. |
| Open Datasets | No | The paper describes using synthetic data based on mathematical distributions: "we consider simple illustrative quadrature experiments4 with X = [0, 1] and kernels k(x, y) = 1+P m=1 1 m2s cos 2πm(x y), with various values of s and distributions dρ which are Beta random variable with the two parameters equal to a = b, hence symmetric around 1/2." This is not a publicly available dataset in the conventional sense. |
| Dataset Splits | No | The paper describes illustrative simulations and experiments with mathematical functions and distributions, but it does not use or specify any training, validation, or test dataset splits. The evaluation involves computing errors averaged over draws or plotting densities. |
| Hardware Specification | No | The paper does not provide any specific hardware details such as GPU/CPU models, processor types, or memory amounts used for running the experiments. |
| Software Dependencies | No | The paper mentions that the code is in Matlab ("Matlab code for all 5 figures"), but it does not specify any version numbers for Matlab or any other software libraries used. |
| Experiment Setup | Yes | In this section, we consider simple illustrative quadrature experiments4 with X = [0, 1] and kernels k(x, y) = 1+P m=1 1 m2s cos 2πm(x y), with various values of s and distributions dρ which are Beta random variable with the two parameters equal to a = b, hence symmetric around 1/2. We report results comparing different Sobolev spaces for testing functions to integrate (parameterized by s) and learning quadrature weights (parameterized by t) in Figure 1, where we compute errors averaged over 1000 draws. We did not use regularization to compute quadrature weights α. |