Statistical and Geometrical properties of the Kernel Kullback-Leibler divergence
Authors: Anna Korba, Francis Bach, Clémentine CHAZAL
NeurIPS 2024 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | In this section, we illustrate the validity of our theoretical results and the performance of gradient descent for the regularized KKL. In all our experiments, we consider Gaussian kernels k(x, y) = [...] Our code is available on the github repository https://github.com/clementinechazal/KKL-divergence-gradient-flows.git. |
| Researcher Affiliation | Academia | Clémentine Chazal CREST, ENSAE, IP Paris clementine.chazal@ensae.fr Anna Korba CREST, ENSAE, IP Paris anna.korba@ensae.fr Francis Bach INRIA Ecole Normale Supérieure PSL Research university francis.bach@inria.fr |
| Pseudocode | No | The paper does not contain structured pseudocode or algorithm blocks. |
| Open Source Code | Yes | Our code is available on the github repository https://github.com/clementinechazal/KKL-divergence-gradient-flows.git. |
| Open Datasets | No | The paper uses samples generated from known distributions (e.g., Gaussian, Exponential, uniform on specific shapes) rather than explicitly referring to or providing access information for established publicly available datasets. |
| Dataset Splits | No | The paper does not explicitly provide training/test/validation dataset splits, nor does it mention a validation set. |
| Hardware Specification | No | The paper states 'Our experiments run on a standard laptop' in the NeurIPS checklist, but does not provide specific hardware details such as exact GPU/CPU models, processor types, or memory amounts. |
| Software Dependencies | No | The paper mentions 'Python code' in relation to its GitHub repository but does not list specific software dependencies with version numbers (e.g., Python version, library versions like PyTorch or NumPy). |
| Experiment Setup | Yes | For each method, we choose a bandwith σ = 0.1, and we optimize the step-size for each method, and sample n = 100 points from the source and target distribution. In Figure 7 and Figure 8, the stepsize h = C d/(d+4) with C = 0.5 and σ is proportional to the mean of distances between particles σ = mean(d(xi, yj) 2 ) 1/2 n 1/(d+4). The bandwidth of k is fixed at σ = 0.1 for Kale and MMD and at σ = 0.3 for KKL. In Figure 13 this time we repeat the experiment but for a simple gradient descent for KKL with constant step h = 0.01. |