Universality in Learning from Linear Measurements
Authors: Ehsan Abbasi, Fariborz Salehi, Babak Hassibi
NeurIPS 2019 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Although Theorem 1 holds for n and m growing to infinity, the result of our numerical simulations in Section 3.2, indicates the validity of universality for values of m and n ranging in the order of hundreds. To validate the result of Theorem 1, we performed numerical simulations under various distributions for the measurement vectors. For our simulations in Figure 1, we use the estimator E{x0, A, Rn, ℓ1} to recover a k-sparse signal x0 under three random ensembles for the measurement vectors {ai}m i=1. |
| Researcher Affiliation | Academia | Ehsan Abbasi Department of Electrical Engineering California Institute of Technology Pasadena, CA, 91125 eabbasi@caltech.edu Fariborz Salehi Department of Electrical Engineering California Institute of Technology Pasadena, CA, 91125 fsalehi@caltech.edu Babak Hassibi Department of Electrical Engineering California Institute of Technology Pasadena, CA, 91125 hassibi@caltech.edu |
| Pseudocode | No | The paper does not contain any sections or blocks explicitly labeled as 'Pseudocode' or 'Algorithm'. |
| Open Source Code | No | The paper does not provide any concrete access information (e.g., repository link, explicit statement of code release) for the source code of the methodology described. |
| Open Datasets | No | The paper discusses generating measurement vectors from certain distributions (e.g., Gaussian, Bernoulli, χ1) for numerical simulations but does not refer to or provide access information for any named, publicly available datasets. |
| Dataset Splits | No | The paper does not provide specific dataset split information (e.g., exact percentages, sample counts, or detailed splitting methodology) for training, validation, or testing. |
| Hardware Specification | No | The paper does not provide specific hardware details (e.g., exact GPU/CPU models, processor types, or memory amounts) used for running its experiments. |
| Software Dependencies | No | The paper does not provide specific ancillary software details (e.g., library or solver names with version numbers) needed to replicate the experiment. |
| Experiment Setup | Yes | In the simulations we used vectors of size n = 256. The data is averaged over 10 independent realization of the measurements. In the simulations we used matrices of size n = 40. The data is averaged over 20 independent realization of the measurements. For each trial, we generate a random matrix M Rn n, with i.i.d. standard Gaussian random variables. Σ = MMT will play the role of the covariance matrix of the measurement vectors. For Figure 1a, {ai}m i=1 are drawn independently from the Gaussian distribution N(0, Σ). For the measurement vectors of the Figure 1b, we first generate i.i.d centered bernouli vectors Ber(.8), and multiply each vector by M. For the measurement vectors of the Figure 1c, we first generate i.i.d centered χ1 vectors, and multiply each vector by M. |