Improving Computational Complexity in Statistical Models with Local Curvature Information
Authors: Pedram Akbarian, Tongzheng Ren, Jiacheng Zhuo, Sujay Sanghavi, Nhat Ho
ICML 2024 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | In this section, we perform numerical experiments on the generalized linear model to empirically verify our theoretical results regarding the convergence rates and the statistical rates of the sample iterates. |
| Researcher Affiliation | Academia | 1Department of Electrical and Computer Engineering, University of Texas at Austin, Texas, USA 2Computer Science, University of Texas at Austin, Texas, USA 3Department of Statistics and Data Sciences, University of Texas at Austin, Texas, USA. |
| Pseudocode | No | The paper describes algorithms such as Normalized Gradient Descent using mathematical formulas and textual descriptions, but it does not include explicitly labeled pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not provide any explicit statements or links indicating the availability of open-source code for the described methodology. |
| Open Datasets | No | The paper describes the generation of synthetic data for its experiments (e.g., "we created a dataset of samples...", "we generate n i.i.d. Rademacher random variables..."), but it does not provide access information (link, DOI, citation) for a publicly available or open dataset. |
| Dataset Splits | No | The paper mentions "sample size n" and evaluates statistical error for various n, but it does not specify explicit training, validation, and test dataset splits or a cross-validation setup. |
| Hardware Specification | No | The paper describes parameters for synthetic data generation and experiment settings, but it does not provide specific details about the hardware (e.g., CPU, GPU models, memory) used for running the experiments. |
| Software Dependencies | No | The paper mentions using "standard mathematical and statistical libraries" for simulations but does not provide specific software names with version numbers (e.g., Python 3.x, PyTorch 1.x, or specific solver versions). |
| Experiment Setup | Yes | Throughout the simulations for the generalized linear model, we maintained a sample size of n = 1000, a data dimension of d = 2, a noise variance of σ2 = 0.01, and a learning rate of η = 0.1. In the experiments for GLM described in Section 4, we created a dataset of samples {(Xi, Yi)}n i=1 Rd R under the following criteria: Xi follows a normal distribution with zero mean and covariance matrix Id, and Yi = g(X i θ ) + εi. Here, the function g(r) is defined as g(r) := r2, and the noise terms {εi}n i=1 are independent and identically distributed following a zero mean normal distribution with variance σ2. |