Convergence guarantees for kernel-based quadrature rules in misspecified settings
Authors: Motonobu Kanagawa, Bharath K. Sriperumbudur, Kenji Fukumizu
NeurIPS 2016 | Conference PDF | Archive PDF | Plain Text | 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. |