One-Step Estimator for Permuted Sparse Recovery
Authors: Hang Zhang, Ping Li
ICML 2023 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Numerical experiments are presented to corroborate our theoretical claims. This section presents the numerical experiments to verify our main theorem, to put it more specifically, Theorem 3: we would like to prove the correct permutation can be obtained, i.e., { opt = \}, with n p and SNR c. |
| Researcher Affiliation | Industry | Hang Zhang Ping Li Amazon Linked In Ads 410 Terry Ave N, Seattle, WA 98109, USA 700 Bellevue Way NE, Bellevue, WA 98004, USA hagzhang@amazon.com pinli@linkedin.com |
| Pseudocode | Yes | Algorithm 1 One-step estimator. Input: observation Y and sensing matrix X. Output: pair ( opt, Bopt), which is written as opt = argmax 2Pn , Y thres(X>Y)> X> Bopt = argmin B(2n) 1$$$ $$$ opt>Y XB F + \nk Bk1, where thres( ) applies to each column and thresholds all entries to zero except the one with the largest magnitude, Pn denotes the set of all possible permutation matrices, k k1 , P i,j |( )i,j| denotes the absolute sum of all entries, and \n > 0 is some regularizer coefficient. |
| Open Source Code | No | The paper does not provide any explicit statements about releasing source code or links to a code repository for the methodology described. |
| Open Datasets | Yes | This subsection evaluates our algorithm on the real-world dataset, namely, MNIST dataset (Le Cun et al., 1998). |
| Dataset Splits | No | The paper mentions using 'training' and 'test' sets from the MNIST dataset but does not provide specific details on the dataset splits (e.g., percentages, sample counts, or explicit standard split references) beyond referring to pre-existing MNIST sets. |
| Hardware Specification | No | The paper does not provide any specific hardware details such as GPU or CPU models, memory, or computational resources used for running the experiments. |
| Software Dependencies | No | The paper does not specify any software dependencies with version numbers, such as programming languages, libraries, or frameworks used for implementation. |
| Experiment Setup | Yes | We let Xij i.i.d N(0, 1) and pick the sample number n to be {100, 150} and set h = n/4. We vary the signal length p to be {500, 600}. Then we set the sparsity number k within the region {10, 15, 20}. And the stable rank srank(B\) is within the range {150, 200, 250}. Setting \n in (3) as c2σ log p/n |