Learning Theory of Randomized Kaczmarz Algorithm
Authors: Junhong Lin, Ding-Xuan Zhou
JMLR 2015 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | The paper includes theoretical contributions with proofs and mathematical analysis (e.g., Theorems 3, 4, 5, 6, 8 and Lemmas), but also features a "Simulations and Discussions" section where numerical experiments are performed: "In this section we provide some numerical simulations and further discussions on our error analysis. To illustrate our derived convergence rates and compare with the existing literature, we carry out numerical simulations corresponding to Example 2 with the same data distributions as in (Needell, 2010): m = 200, d = 100, A R200 100 is a Gaussian matrix with each entry drawn independently from the standard normal distribution N(0, 1), and y R100 is a Gaussian noise with each component drawn independently from the normal distribution with mean 0 and standard deviation 0.02. The measurement vectors {ψt = 1 ϕt ϕt} are drawn from the normalized rows of A as in Example 2 and {eyt = yt/ ϕt } with mean x = 0. We conduct 100 trials for each choice of the relaxation parameter sequences ηt = 1, ηt = 1/t, ηt = 1/t. In each trial, algorithm (4) is run 100 times with random Gaussian initial vectors of norm x1 = 0.02. Figure 1 depicts the error xt+1 x for t = 1, . . . , 1500 (averaged with 100 trials and 100 initial vectors)." The presence of numerical simulations and result plotting classifies it as experimental. |
| Researcher Affiliation | Academia | Both authors, Junhong Lin and Ding-Xuan Zhou, are affiliated with the "Department of Mathematics City University of Hong Kong". The email address EMAIL also points to an academic institution. Therefore, the affiliation is purely academic. |
| Pseudocode | No | The paper describes algorithms using mathematical equations (e.g., equations 1, 2, 3, 4, 14, 15) and theoretical steps, but it does not contain a clearly labeled 'Pseudocode' or 'Algorithm' block with structured, step-by-step instructions in a code-like format. |
| Open Source Code | No | The paper does not contain any explicit statements about releasing source code, nor does it provide any links to a code repository or mention code in supplementary materials for the methodology described. |
| Open Datasets | No | The paper describes how the data for simulations was generated: "A R200 100 is a Gaussian matrix with each entry drawn independently from the standard normal distribution N(0, 1), and y R100 is a Gaussian noise with each component drawn independently from the normal distribution with mean 0 and standard deviation 0.02." This indicates the use of synthetically generated data rather than a publicly available or open dataset with access information. |
| Dataset Splits | No | The paper describes the generation of synthetic data and the setup for numerical simulations: "m = 200, d = 100, A R200 100 is a Gaussian matrix with each entry drawn independently from the standard normal distribution N(0, 1), and y R100 is a Gaussian noise with each component drawn independently from the normal distribution with mean 0 and standard deviation 0.02. ... We conduct 100 trials for each choice of the relaxation parameter sequences ηt = 1, ηt = 1/t, ηt = 1/t. In each trial, algorithm (4) is run 100 times with random Gaussian initial vectors of norm x1 = 0.02." However, it does not provide specific train/test/validation dataset splits, as the data is generated for each trial rather than split from a larger, fixed dataset. |
| Hardware Specification | No | The paper does not provide any specific details about the hardware used for running the numerical simulations, such as GPU models, CPU specifications, or memory. |
| Software Dependencies | No | The paper does not mention any specific software, libraries, or programming languages with their version numbers that were used for the implementation or simulation of the algorithms. |
| Experiment Setup | Yes | The paper provides specific details regarding the experimental setup in the "Simulations and Discussions" section: "m = 200, d = 100, A R200 100 is a Gaussian matrix with each entry drawn independently from the standard normal distribution N(0, 1), and y R100 is a Gaussian noise with each component drawn independently from the normal distribution with mean 0 and standard deviation 0.02. ... We conduct 100 trials for each choice of the relaxation parameter sequences ηt = 1, ηt = 1/t, ηt = 1/t. In each trial, algorithm (4) is run 100 times with random Gaussian initial vectors of norm x1 = 0.02." |