Unique sparse decomposition of low rank matrices

Authors: Dian Jin, Xin Bing, Yuqian Zhang

NeurIPS 2021 | Conference PDF | Archive PDF | Plain Text | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Experimental In this section we verify the empirical performance of our proposed procedure for recovering A under model (1.1) in different scenarios. Due to the space limit, we defer more experiments to the Appendix of this paper.
Researcher Affiliation Academia Dian Jin Rutgers University dj370@scarletmail.rutgers.edu Xin Bing Cornell University xb43@cornell.edu Yuqian Zhang Rutgers University yqz.zhang@rutgers.edu
Pseudocode Yes Due to the limitation of space we defer our discussion of deflation procedure in appendix. Algorithm 1 in Section D
Open Source Code No The paper includes a general statement in the checklist that assets are provided (either supplemental material or URL), but does not contain an explicit statement in the main body about releasing the source code for its methodology or provide a direct link to a code repository.
Open Datasets No To generate the data Y = AX, we generate the columns of A by using the normalized left singular vectors of R Rp r where Rij i.i.d. N(0, 1). The sparse coefficient matrix X Rr n are generated as Xij i.i.d. BG(θ).
Dataset Splits No The paper generates synthetic data for its experiments but does not provide specific details on train/validation/test dataset splits, sample counts for splits, or cross-validation setup.
Hardware Specification No The paper does not provide any specific hardware details such as GPU models, CPU types, or memory used for running the experiments.
Software Dependencies No The paper does not list specific software dependencies with their version numbers.
Experiment Setup Yes Experiment setup To generate the data Y = AX, we generate the columns of A by using the normalized left singular vectors of R Rp r where Rij i.i.d. N(0, 1). The sparse coefficient matrix X Rr n are generated as Xij i.i.d. BG(θ). To evaluate the success of recovering one column vector of A for any estimate q Sp 1, we use the following criterion, Err(q) = min 1 i r p1 | q, ai |q If Err(q) ρe, we say the vector q recovers the ground-truth column vector of A. We choose ρe = 1 10 2 in our simulation settings.