A Statistical Learning Approach to Modal Regression
Authors: Yunlong Feng, Jun Fan, Johan A.K. Suykens
JMLR 2020 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Numerical validations on modal regression are also conducted to verify our findings. |
| Researcher Affiliation | Academia | Yunlong Feng EMAIL Department of Mathematics and Statistics State University of New York The University at Albany Albany, New York 12222, USA, Jun Fan EMAIL Department of Mathematics Hong Kong Baptist University Kowloon, Hong Kong, China, Johan A.K. Suykens EMAIL Department of Electrical Engineering ESAT-STADIUS, KU Leuven Kasteelpark Arenberg 10, Leuven B-3001, Belgium |
| Pseudocode | Yes | Algorithm 1: Iteratively Re-weighted Least Squares Algorithm for Solving (5.1) |
| Open Source Code | No | No explicit statement or link to the open-source code for the methodology described in this paper is provided. |
| Open Datasets | Yes | This speed-flow data contains 1318 observations and are publicly available in the R-package hdrcde. |
| Dataset Splits | Yes | In our experiment, 600 observations are drawn from the above data-generating model and the size of the test set is also set to 600. [...] We implement a first five-fold cross validation under the following criterion |
| Hardware Specification | No | No specific hardware details (like GPU/CPU models, processor types, or memory amounts) are provided in the paper. |
| Software Dependencies | No | The paper mentions the 'R-package hdrcde' but does not provide specific version numbers for it or any other software dependencies. |
| Experiment Setup | Yes | In our empirical studies, the hypothesis space H is chosen as a bounded subset of a reproducing kernel Hilbert space HK that is induced by a Mercer kernel K. Specifically, we employ the following Tikhonov regularization to determine the radius of the working hypothesis space automatically: fz,σ := arg min f HK L R 1 n i=1 ℓσ(yi f(xi)) + λ f 2 K, (5.1) where ℓσ is the loss function ℓσ(t) = σ2(1 exp( t2/σ2)), and λ > 0 is a regularization parameter. [...] For the Mercer kernel K, we use the Gaussian kernel K(x, x ) = exp x x 2/h2 with the bandwidth parameter h > 0. [...] Input: data {(xi, yi)}n i=1, regularization parameter λ > 0, Gaussian kernel bandwidth h > 0, scale parameter σ > 0 and the initial guess α0 Rn, b0 R. [...] the initial value σ0 is set as m 1/5, which is the optimal σ value according to our theoretical analysis. |