Kernel Density Estimation for Dynamical Systems
Authors: Hanyuan Hang, Ingo Steinwart, Yunlong Feng, Johan A.K. Suykens
JMLR 2018 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Our main purpose in this paper is to conduct some theoretical analysis and practical implementations on the kernel density estimator for dynamical systems. ... We discuss the bandwidth selection problem in Section 5 and provide some numerical simulations. |
| Researcher Affiliation | Academia | Hanyuan Hang Institute of Statistics and Big Data Renmin University of China 100872 Beijing, China; Ingo Steinwart Institute for Stochastics and Applications University of Stuttgart 70569 Stuttgart, Germany; Yunlong Feng Department of Mathematics and Statistics State University of New York The University at Albany Albany, New York 12222, USA; Johan A.K. Suykens Department of Electrical Engineering, ESAT-STADIUS, KU Leuven Kasteelpark Arenberg 10, Leuven, B-3001, Belgium |
| Pseudocode | No | The paper does not contain any structured pseudocode or algorithm blocks. Methods are described in prose, and mathematical derivations are presented using equations and theorems. |
| Open Source Code | No | The paper does not provide any concrete access information to source code, such as a repository link, an explicit code release statement, or code in supplementary materials. |
| Open Datasets | No | In our experiments, observations x1, , xn are generated from the following model1 ( xi = T i(x0), xi = xi + εi, i = 1, , n, (17) where εi N(0, σ2), σ is set to 0.01 and the initial state x0 is randomly generated based on the density f. For the map T in (17), we choose Logistic map in Example 2 and Gauss map in Example 3. |
| Dataset Splits | No | The paper mentions varying sample sizes for its generated data (e.g., 'We vary the sample size among {5 102, 103, 5 103, 104}'), but it does not describe specific training, validation, or test dataset splits in the traditional sense for empirical evaluation. |
| Hardware Specification | No | The paper does not provide specific hardware details (e.g., CPU, GPU models, memory) used for running its experiments. |
| Software Dependencies | No | The paper mentions using a 'Gaussian kernel' for kernel density estimators but does not list any specific software or library names with version numbers required for replication. |
| Experiment Setup | Yes | In our experiments, observations x1, , xn are generated from the following model1 ( xi = T i(x0), xi = xi + εi, i = 1, , n, (17) where εi N(0, σ2), σ is set to 0.01 and the initial state x0 is randomly generated based on the density f. For the map T in (17), we choose Logistic map in Example 2 and Gauss map in Example 3. We vary the sample size among {5 102, 103, 5 103, 104}, implement bandwidth selection procedures over 20 replications and select the bandwidth from a grid of values in the interval [h L, h U] with 100 equispaced points. Here, h L is set as the minimum distance between consecutive points xi, i = 1, , n (Devroye and Lugosi, 1997), while h U is chosen according to the maximal smoothing principle proposed in Terrell (1990). ... the criterion of comparing different selected bandwidths is the following absolute mean error (AME): i=1 |f D,h(ui) f(ui)|, where u1, , um are m equispaced points in the interval [0, 1] and m is set to 10000. |