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 Coakley et alK. L. Coakley, T. Snelleman, H. Hoos, and O. E. Gundersen, "The embrace of open science: An analysis of a decade of AI research and 56 800 conference papers," Under Review, 2026..
Convergence guarantees for kernel-based quadrature rules in misspecified settings
Authors: Motonobu Kanagawa, Bharath K. Sriperumbudur, Kenji Fukumizu
NeurIPS 2016 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | For the algorithm by Bach [2], we conducted simulation experiments to support this observation, by using code available from http://www.di.ens.fr/~fbach/quadrature.html. The setting is what we have described with d = 1, and weights are obtained without regularization as in [2]. The result is shown in Figure 1, where r (= α) denotes the assumed smoothness, and s (= αθ) is the (unknown) smoothness of an integrand. The straight lines are (asymptotic) upper-bounds in Theorem 1 (slope s and intercept fitted for n 24), and the corresponding solid lines are numerical results (both in log-log scales). Averages over 100 runs are shown. The result indeed shows the adaptability of the quadrature rule by Bach for the less smooth functions (i.e. s = 1, 2, 3). |
| Researcher Affiliation | Academia | The Institute of Statistical Mathematics, Tokyo 190-8562, Japan Department of Statistics, Pennsylvania State University, University Park, PA 16802, USA |
| Pseudocode | No | The paper describes algorithms (e.g., QMC, Bach's algorithm) but does not present any of them in a structured pseudocode block or algorithm box. |
| Open Source Code | No | The paper mentions using "code available from http://www.di.ens.fr/~fbach/quadrature.html" for Bach's algorithm, which is a third-party code. It does not state that the authors are releasing their own source code for the methodology described in this paper. |
| Open Datasets | No | The paper describes generating data for simulations (e.g., "d = 1", "uniform distribution") rather than using a named public dataset or providing access information for a custom dataset. There is no mention of dataset availability. |
| Dataset Splits | No | The paper describes simulation experiments but does not provide specific training, validation, or test dataset splits. The data is generated based on the theoretical setting rather than being split from a pre-existing dataset. |
| Hardware Specification | No | The paper does not provide any specific details about the hardware (e.g., CPU, GPU models, memory) used to run the experiments. |
| Software Dependencies | No | The paper mentions using "code available from http://www.di.ens.fr/~fbach/quadrature.html" for Bach's algorithm, but it does not specify any version numbers for this or any other software components, libraries, or programming languages. |
| Experiment Setup | Yes | The setting is what we have described with d = 1, and weights are obtained without regularization as in [2]... Averages over 100 runs are shown. |