Quasi-Monte Carlo Features for Kernel Approximation
Authors: Zhen Huang, Jiajin Sun, Yian Huang
ICML 2024 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | In practice, the QMC kernel approximation approach is easily implementable and shows superior performance, as supported by the empirical evidence provided in the paper. |
| Researcher Affiliation | Academia | Zhen Huang 1 Jiajin Sun 1 Yian Huang 1 1Department of Statistics, Columbia University, New York, NY 10027, USA. |
| Pseudocode | No | The paper describes methods and theoretical derivations but does not include any explicitly labeled pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not contain any statements about releasing source code or provide links to a code repository for the described methodology. |
| Open Datasets | Yes | We consider two choices of kernels: (i) the min kernel K(x, x ) = Qd i=1 min(xi, x i), and (ii) the Gaussian kernel K(x, x ) = exp( 1 2σ2 x x 2 2)... Cadata (Pace & Barry, 1997): In this data set (n = 20640, d = 6)... Cod-rna (Uzilov et al., 2006): This benchmark dataset (n = 59535 (train) + 271617 (test), d = 8)... |
| Dataset Splits | No | The paper mentions 'training samples' and 'test data points' with specific sizes for synthetic data, and 'random train-test split, allocating 25% of the data to the test set' for Cadata, and explicit train/test sizes for Cod-rna, but does not explicitly describe a separate validation split. |
| Hardware Specification | No | The paper does not provide specific details about the hardware used for experiments, such as CPU/GPU models, memory, or specific cloud instance types. It only mentions general terms like 'training samples' and 'data points'. |
| Software Dependencies | Yes | Halton sequence implemented in the Sci Py package in Python (Virtanen et al., 2020) is used. |
| Experiment Setup | Yes | The training and test data are generated from Y = f(X) + ε, where f is the regression function, X Unif[0, 1]d, and ε N(0, 1). We consider two choices of kernels: (i) the min kernel K(x, x ) = Qd i=1 min(xi, x i), and (ii) the Gaussian kernel K(x, x ) = exp( 1 2σ2 x x 2 2), with the bandwidth σ set as the median of X X (computed numerically)... The kernel ridge regularization parameter is set as λ = 0.25n 1 2r+1 . |