Additive Error Guarantees for Weighted Low Rank Approximation
Authors: Aditya Bhaskara, Aravinda Kanchana Ruwanpathirana, Maheshakya Wijewardena
ICML 2021 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | In this section we evaluate our algorithm (wlra-iter) for weighted low rank approximation by comparing its performance with three baselines: (a) applying SVD to the matrix A (svd) (b) applying SVD to weighted matrix W A (wsvd) (c) regularized weighted low rank approximation algorithm with sketching in Ban et al. (2019b) (rwlra-sk). ... We conduct two sets of experiments. In the first set, we vary the output rank k and show how the error changes for each algorithm. In the second set, we demonstrate how the error in each algorithm changes as the signal to noise ratio (SNR) varies: the signal is a low rank matrix and we add Gaussian noise to it. In each experiment, we measure the scaled error... Figure 1 shows the error of each algorithm for different weight matrices. Figure 2 shows the error rates of each algorithm for different weight matrices. |
| Researcher Affiliation | Academia | Aditya Bhaskara * 1 Aravinda Kanchana Ruwanpathirana * 1 Maheshakya Wijewardena * 1 ... 1School of Computing, University of Utah, Salt Lake City, Utah, USA. Correspondence to: Maheshakya <pmaheshakya4@gmail.com>. |
| Pseudocode | Yes | Algorithm 1 Weighted low rank approximation with L2 error |
| Open Source Code | Yes | The full code is also provided. |
| Open Datasets | No | The paper describes generating synthetic data and mentions "two real datasets" in the supplement, but provides no concrete access information (link, DOI, citation) for any publicly available or open dataset in the main text. |
| Dataset Splits | No | The paper does not provide specific dataset split information (exact percentages, sample counts, citations to predefined splits, or detailed splitting methodology) needed to reproduce the data partitioning. |
| Hardware Specification | No | The paper does not provide specific hardware details (exact GPU/CPU models, processor types with speeds, memory amounts, or detailed computer specifications) used for running its experiments. |
| Software Dependencies | No | The paper does not provide specific ancillary software details, such as library or solver names with version numbers, needed to replicate the experiment. |
| Experiment Setup | Yes | Here we fix σ = 0.005 (thus SNR 0.16) and λ = 0.05 for weight matrix setting W2 and λ = 0.01 for weight matrix settings W1, W3 in rwlra-wk. [...] Here we fix k = 50 and λ = 0.005 for weight matrix setting W1 and λ = 0.01 for weight matrix settings W2, W3 in rwlrawk. We set the sketch size parameter in rwlra-sk to 100 in all experiments. |