Agnostic Estimation for Phase Retrieval
Authors: Matey Neykov, Zhaoran Wang, Han Liu
JMLR 2020 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Our theory is backed up by thorough numerical results. In this section we provide numerical experiments based on the three models (8), (9) and (10) where the random variable ε N(0, 1). All models are compared with the Truncated Power Method (TPM), proposed in Yuan and Zhang (2013). |
| Researcher Affiliation | Academia | Matey Neykov EMAIL Carnegie Mellon University Department of Statistics & Data Science Zhaoran Wang EMAIL Northwestern University Department of Industrial Engineering and Management Sciences Han Liu EMAIL Northwestern University |
| Pseudocode | Yes | Algorithm 1 input : (Yi, Xi)n i=1: data, λn, νn: tuning parameters 1. Split the sample into two approximately equal sets S1, S2, with |S1| = n/2 , |S2| = n/2 . 2. Let bΣ := |S1| 1 P i S1 Yi(X 2 i Id). Solve (17). Let bv be the first eigenvector of b A. 3. Let Y = |S2| 1 P i S2 Yi. Solve the following program: bb = argminb(2|S2|) 1P i S2((Yi Y )X i bv X i b)2 + νn b 1. (18) 4. Return bβ := bb/ bb 2. Algorithm 2 Optional Refinement input : (Yi, Xi)n i=1: data, ν n: tuning parameter, output bβ from the Algorithm 1 5. Let Y = n 1 P i [n] Yi. Solve the following program: bb = argminb(2n) 1Pn i=1((Yi Y )X i bβ X i b)2 + ν n b 1. (19) 6. Return bβ := bb/ bb 2. |
| Open Source Code | No | The paper does not provide any explicit statement about making their own implementation code available, nor does it provide a link to a code repository. It mentions external algorithms like 'Truncated Power Method (TPM)' and 'TWF algorithm' but not their own source code. |
| Open Datasets | No | In this section we provide numerical experiments based on the three models (8), (9) and (10) where the random variable ε N(0, 1). Our setup is as follows. In all scenarios the vector β was held fixed at β = ( s 1/2, s 1/2, . . . , s 1/2 | {z } s , 0, . . . 0 | {z } d s ). The paper describes a synthetic data generation process for its experiments rather than using a named, publicly available dataset. |
| Dataset Splits | Yes | 1. Split the sample into two approximately equal sets S1, S2, with |S1| = n/2 , |S2| = n/2 . ... To select the νn parameter for (18) a pre-specified grid of parameters {ν1, . . . , νl} was selected, and the following heuristic procedure based on K-fold cross-validation was used. We divide S2 into K = 5 approximately equally sized non-intersecting sets S2 = j [K] e Sj 2. |
| Hardware Specification | No | The paper does not contain any specific hardware details such as GPU models, CPU types, or cloud computing resources used for running the experiments. |
| Software Dependencies | No | All models are compared with the Truncated Power Method (TPM), proposed in Yuan and Zhang (2013). ... In the case of phase retrieval, the TWF algorithm was also ran at a total number of 2000 iterations, using the tuning parameters originally suggested in Cai et al. (2015). The paper mentions specific algorithms (TPM, TWF) but does not provide details on the software environment (e.g., programming languages, libraries, frameworks) or their version numbers. |
| Experiment Setup | Yes | The SDP parameter was kept at a constant value (0.015) throughout all simulations... To select the νn parameter for (18) a pre-specified grid of parameters {ν1, . . . , νl} was selected, and the following heuristic procedure based on K-fold cross-validation was used. We divide S2 into K = 5 approximately equally sized non-intersecting sets... The TPM is ran for 2000 iterations. In the case of phase retrieval, the TWF algorithm was also ran at a total number of 2000 iterations. |