Distribution Regression with Sliced Wasserstein Kernels
Authors: Dimitri Meunier, Massimiliano Pontil, Carlo Ciliberto
ICML 2022 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | In this section we compare the numerical performance of SW kernels versus MMD kernels on two tasks. First, we look at the synthetic task that consists of counting the number of components of Gaussian mixture distributions. Then, we present results for distribution regression on the MNIST and Fashion MNIST datasets. Table 1. Test RMSE and standard deviation for the mode classification task... Table 2. Mean accuracy and standard deviation on rotated MNIST and Fashion MNIST... |
| Researcher Affiliation | Academia | 1Gatsby Computational Neuroscience Unit, University College London, London, United Kingdom 2Italian Institute of Technology, Genoa, Italy 3Department of Computer Science, University College London, London, United Kingdom. Correspondence to: Dimitri Meunier <dimitri.meunier.21@ucl.ac.uk>. |
| Pseudocode | Yes | Algorithm 1 Evaluation of ˆΦM,N(ˆPn) |
| Open Source Code | Yes | Code is available at https://github.com/ Dim Sum2k/DRSWK. |
| Open Datasets | Yes | MNIST (Le Cun et al., 2010) and Fashion MNIST (Xiao et al., 2017) |
| Dataset Splits | Yes | A validation set of size 50 is used to select the bandwidth of the Gaussian kernels and the regularisation parameter λ (see Appendix F for details) and a test set of size 100 is used for the results. We use a train set of 1000 images, a validation set of 300 images and a test set of 500 images to evaluate the estimators. |
| Hardware Specification | No | The paper does not provide specific hardware details (e.g., GPU/CPU models, memory) used for running the experiments. |
| Software Dependencies | No | The paper does not provide specific software dependencies with version numbers. |
| Experiment Setup | Yes | A validation set of size 50 is used to select the bandwidth of the Gaussian kernels and the regularisation parameter λ (see Appendix F for details). Appendix F details the hyperparameters tested: Regularization for the Kernel Ridge regression (λ): 25 points between 10-8 and 100 in logarithmic scale; γ for the Euclidean Gaussian kernel: 14 points between 10-3 and 1 in logarithmic scale; γ for the inner Gaussian MMD kernel: 14 points between 10-6 and 100 in logarithmic scale; γ for the outer Gaussian MMD kernel: 7 points between 10-3 and 100 in logarithmic scale; γ for the Gaussian Sliced Wasserstein kernels: 14 points between 10-5 and 100 in logarithmic scale. |