Demystifying Orthogonal Monte Carlo and Beyond

Authors: Han Lin, Haoxian Chen, Krzysztof M. Choromanski, Tianyi Zhang, Clement Laroche

NeurIPS 2020 | Conference PDF | Archive PDF | Plain Text | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Experimental 5 Experiments We empirically tested NOMCs in two settings: (1) kernel approximation via random feature maps and (2) estimating sliced Wasserstein distances, routinely used in generative modeling [42]. For (1), we tested the effectiveness of NOMCs for RBF kernels, non-RBF shift-invariant kernels as well as several PNG kernels. For (2), we considered different classes of multivariate distributions. ... The results are presented in Fig. 2 and Fig. 3. Empirical MSEs were computed by averaging over k = 450 independent experiments.
Researcher Affiliation Collaboration Han Lin Columbia University hl3199@columbia.edu Haoxian Chen Columbia University hc3136@columbia.edu Tianyi Zhang Columbia University tz2376@columbia.edu Clement Laroche Columbia University cl3778@columbia.edu Krzysztof Choromanski Google Brain Robotics & Columbia University kchoro@google.com
Pseudocode Yes Algorithm 1: Near Orthogonal Monte Carlo: opt-NOMC variant
Open Source Code Yes Detailed code implementation is available at https://github.com/HL-hanlin/OMC.
Open Datasets No The paper discusses empirical testing for 'kernel approximation' and 'estimating sliced Wasserstein distances' using 'RBF kernels, non-RBF shift-invariant kernels as well as several PNG kernels' and 'different classes of multivariate distributions'. However, it does not provide specific names of public datasets (e.g., CIFAR-10, MNIST), nor does it give links, DOIs, or formal citations for any datasets used in the experiments.
Dataset Splits No The paper mentions 'Empirical MSEs were computed by averaging over k = 450 independent experiments' and discusses varying the 'number of blocks (i.e. the ratio of the number of samples D used and data dimensionality d),' but it does not provide specific training, validation, or test dataset splits (e.g., percentages, sample counts, or references to predefined splits).
Hardware Specification No The paper does not provide any specific hardware details such as GPU or CPU models, processor types, or memory amounts used for running its experiments.
Software Dependencies No The paper provides a link to a GitHub repository, implying software usage, but it does not specify any software dependencies with version numbers (e.g., 'Python 3.x', 'PyTorch 1.x').
Experiment Setup No The paper mentions some experimental details such as 'Empirical MSEs were computed by averaging over k = 450 independent experiments' and tunable parameters for NOMC like 'Parameter δ, ε, T' and 'δ > 0'. However, it does not provide concrete values for these or other typical experimental setup details like learning rates, batch sizes, or specific number of iterations (T) used in the reported experiments.