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.