Matrix Denoising with Doubly Heteroscedastic Noise: Fundamental Limits and Optimal Spectral Methods
Authors: Yihan Zhang, Marco Mondelli
NeurIPS 2024 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Numerical experiments demonstrate the significant advantage of our theoretically principled method with the state of the art. |
| Researcher Affiliation | Academia | Yihan Zhang Institute of Science and Technology Austria zephyr.z798@gmail.com Marco Mondelli Institute of Science and Technology Austria marco.mondelli@ist.ac.at |
| Pseudocode | No | The paper describes the AMP algorithm in (5.11) using mathematical equations, but it is not presented as a formal pseudocode block or labeled as an algorithm. |
| Open Source Code | No | All experiments use synthetic data and can be reproduced given the instructions in Section 5. Data and code are not released. |
| Open Datasets | No | The paper uses synthetic data generated with specified parameters (n=4000, d=2000, P=Q=N(0,1)) and does not refer to a publicly available dataset. |
| Dataset Splits | No | The paper uses synthetic data and discusses running '20 i.i.d. trials' for data points, but does not specify training, validation, or test splits in the traditional sense for a dataset. |
| Hardware Specification | No | All experiments are synthetic and can be run efficiently on standard personal computers. No specific hardware details (e.g., CPU/GPU models, memory) are provided. |
| Software Dependencies | No | The paper mentions 'standard SVD algorithms or power iteration' but does not specify any software names with version numbers. |
| Experiment Setup | Yes | In both figures, n = 4000, d = 2000 (so = 2), and P = Q = N(0, 1). Each data point is computed from 20 i.i.d. trials and error bars are reported at 1 standard deviation. We let be either the identity or a Toeplitz matrix [77, 41, 19], i.e., i,j = |i j| with = 0.9. We let be a circulant matrix [40, 39]: the first row has 1 in the first position, c = 0.0078 in the second through (+ 1)-st position and in the last positions (= 300), with the remaining entries being 0; for 2 i d, the i-th row is a cyclic shift of the (i 1)-st row to the right by 1 position. |