On the Asymptotic Distribution of the Minimum Empirical Risk
Authors: Jacob Westerhout, Trungtin Nguyen, Xin Guo, Hien Duy Nguyen
ICML 2024 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We illustrate the utility of our approach by applying our results to neural network problems. We firstly provide empirical evidence towards the guarantees of Proposition 5.5. Here we seek to numerically verify the ability of the bootstrap procedures to generate asymptotically correct quantiles. |
| Researcher Affiliation | Academia | 1School of Mathematics and Physics, The University of Queensland, St Lucia, QLD 4072, Australia 2School of Computing, Engineering, and Mathematical Sciences, La Trobe University, Bundoora, VIC 3086, Australia 3Institute of Mathematics for Industry, Kyushu University, Nishi Ward, Fukuoka 819-0395, Japan. |
| Pseudocode | No | The paper provides mathematical derivations and theoretical concepts but does not include any pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not provide any statement or link indicating that its source code is open or publicly available. |
| Open Datasets | No | The paper generates its own data for numerical experiments: 'We generate an 8-dependent stationary sequence (Zi)i [n+8], Zi = (Xi, Yi) for each i [n + 8], from a Gaussian mixture of experts (GMo E; Jacobs et al., 1991) model...'. While the generation process is described, the generated dataset itself is not publicly available or linked. |
| Dataset Splits | No | The paper describes its data generation process and numerical experiments but does not specify explicit training, validation, or test dataset splits. It refers to 'replicates' and 'sample size' but not partitioned datasets for model evaluation. |
| Hardware Specification | No | The paper does not specify any hardware details (e.g., GPU/CPU models, memory, cloud resources) used for running the experiments. |
| Software Dependencies | No | The paper mentions 'minimising the classification loss using the particleswarm global optimizer in MATLAB' but does not provide specific version numbers for MATLAB or the optimizer, which are necessary for reproducibility. |
| Experiment Setup | Yes | To generate the model we consider a binary classification feedforward neural network (NN) with 1 input node and 1 hidden layer, consisting of 3 nodes with Re LU activation. We fit a NN with the same configuration to the data. These networks were fit by minimising the classification loss using the particleswarm global optimizer in MATLAB. We seek to compute 90% CIs for the classification loss, using the standard nonparametric bootstrap and the two consistent procedures of Theorem 5.1. Throughout our experiment, the number of bootstrap resamples was taken to be m = max{5, n/5 }, where m = 5 is only relevant for small sample sizes n. |