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.