Adaptive Learning of Density Ratios in RKHS
Authors: Werner Zellinger, Stefan Kindermann, Sergei V. Pereverzyev
JMLR 2023 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | A numerical illustration is provided. |
| Researcher Affiliation | Academia | Werner Zellinger EMAIL Johann Radon Institute for Computational and Applied Mathematics Austrian Academy of Sciences Linz, Austria Stefan Kindermann EMAIL Industrial Mathematics Institute Johannes Kepler University Linz Linz, Austria Sergei V. Pereverzyev EMAIL Johann Radon Institute for Computational and Applied Mathematics Austrian Academy of Sciences Linz, Austria |
| Pseudocode | No | The paper describes mathematical methods and theoretical derivations. It does not include any clearly labeled pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not contain any explicit statements about releasing source code or provide links to a code repository for the described methodology. |
| Open Datasets | No | The numerical example uses data from two Gaussian distributions P, Q having means 4, 2 and standard deviations 1/ 5, respectively. While the parameters are specified, no concrete access information (link, DOI, citation for a pre-existing dataset) for a publicly available dataset is provided. |
| Dataset Splits | No | Section 5 mentions sample sizes m = n {3, 10, 100} for the numerical example. However, it does not specify any training, validation, or test dataset splits. |
| Hardware Specification | No | The paper does not provide any specific hardware details such as GPU/CPU models, processor types, or memory used for running the experiments. |
| Software Dependencies | No | The paper mentions using the 'conjugate gradient method' and specific kernel functions, but it does not specify any software names with version numbers that would be required to replicate the experiment. |
| Experiment Setup | Yes | We use two different density ratio estimation methods in Eq. (11), the Exp approach, and, the Ku LSIF approach as described in Example 1. In particular, we approximate a minimizer of Eq. (11) by the conjugate gradient method applied to the parameters α1, . . . , αm+n of Eq. (11) when evaluated at a model ansatz fλ z = Pm+n j=1 αjk(xj, ) with reproducing kernel k(x, x ) := 1 + e (x x )2 /2 of H, as suggested by the representer theorem (Sch olkopf et al., 2001). Following our goal of choosing λ, we fix a geometric sequence (λi)l i=1 R with λi := 10i, i { 3, . . . , 1} and compute ... for some M R and the pessimistic choice α = 1 in Assumption 6. ... We therefore follow (Lu et al., 2020, Remark 6.1) and choose M = Mj := Tr( b Hλj(fλj z )) 2. The results of our experiment can be found in Figure 2. The choice λ in Eq. (32) corresponds to λ = 10 2 for Ku LSIF in all three cases of dataset size m = n {3, 10, 100}. |