Exponential Spectral Pursuit: An Effective Initialization Method for Sparse Phase Retrieval
Authors: Mengchu Xu, Yuxuan Zhang, Jian Wang
ICML 2024 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | In this section, we conduct numerical experiments to evaluate the performance of ESP. To compare the performance of different methods, we introduce two metrics: i) relative error and ii) fraction of recovered support. |
| Researcher Affiliation | Academia | 1School of Data Science, Fudan University, Shanghai, China. Correspondence to: Jian Wang <jian wang@fudan.edu.cn>. |
| Pseudocode | Yes | Algorithm 1 Exponential Spectral Pursuit Input: sparsity k, samples y, and sampling matrix A. Step 1: Search an index imax corresponding to the largest diagonal element of L. Step 2: Select an index set S corresponding to the most significant k entries in the imax-th column of L. Step 3: Use the principle eigenvector of LS as the estimate of z Cn and re-scale it to z = λ. Output: z. |
| Open Source Code | No | The paper does not provide any statements about releasing source code or links to a code repository. |
| Open Datasets | No | In our experiments, the sampling vectors {ai}m i=1 are n-dimensional standard complex Gaussian random vectors. The input k-sparse signal x Cn has supp(x) generated at random and nonzero elements i) drawn from standard complex Gaussian or ii) being 1 s, which are called sparse Gaussian and sparse 0-1 signal, respectively. |
| Dataset Splits | No | The paper describes generating synthetic data for experiments and conducting a specified number of independent trials (e.g., '1,000 independent trials', '200 independent trials'), but does not specify dataset splits (e.g., train/validation/test) in the conventional sense for pre-existing datasets. |
| Hardware Specification | No | The paper does not provide specific details about the hardware used to run the experiments, such as GPU or CPU models. |
| Software Dependencies | No | The paper does not list specific software dependencies with version numbers used for the experiments. |
| Experiment Setup | Yes | Recall that the original TP involves two hyper-parameters η1, η2. We optimized them and set η1 = 0.2, η2 = 5. To show the importance of optimization, we use TP-UD to represent TP with un-designed hyper-parameters η1 = 0.9, η2 = 1.1 and test its performance. |