Principal Component Projection and Regression in Nearly Linear Time through Asymmetric SVRG
Authors: Yujia Jin, Aaron Sidford
NeurIPS 2019 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We corroborate these findings with preliminary empirical experiments. |
| Researcher Affiliation | Academia | Yujia Jin Stanford Universty yujiajin@stanford.edu Aaron Sidford Stanford Universty sidford@stanford.edu |
| Pseudocode | Yes | Algorithm 1: ISPCP(A,v,λ,γ,ϵ,δ) and Algorithm 2: Asy SVRG(M,ˆv,z0,ϵ,δ) |
| Open Source Code | No | The paper does not provide any explicit statements about releasing source code or links to a code repository. |
| Open Datasets | No | Datasets. Similar to that in previous work [7, 8], we set λ = 0.5,n = 2000,d = 50 and form a matrix A=UΛ1/2V R2000 50. Here, U and V are random orthonormal matrices, and Σ contains randomly chosen singular values σi = λi. Referring to [0,λ(1 γ)] [λ(1+γ),1] as the away-fromλ region, and λ(1 γ) [0.9,1] λ(1+γ) [1,1.1] as the close-to-λ region, we generate λi differently to simulate the following three different cases: i. Eigengap-Uniform Case: generate all λi uniformly in the away-from-λ region. ii. Eigengap-Skewed Case: generate half the λi uniformly in the away-from-λ and half uniformly in the close-to-λ regions. iii. No-Eigengap-Skewed Case: uniformly generate half in [0,1], and half in the close-to-λ region. |
| Dataset Splits | No | The paper describes synthetic data generation but does not specify any training, validation, or test splits. It only states the overall dimensions of the generated data (n=2000, d=50). |
| Hardware Specification | No | The paper discusses numerical experiments but does not specify the hardware used (e.g., CPU, GPU models, memory). |
| Software Dependencies | No | The paper mentions implementing algorithms (e.g., polynomial, chebyshev, lanczos, rational) but does not provide specific software dependencies with version numbers (e.g., Python 3.8, PyTorch 1.9). |
| Experiment Setup | Yes | We set λ = 0.5,n = 2000,d = 50 and form a matrix A=UΛ1/2V R2000 50. Here, U and V are random orthonormal matrices, and Σ contains randomly chosen singular values σi = λi. |