A Pseudo-Euclidean Iteration for Optimal Recovery in Noisy ICA
Authors: James R. Voss, Mikhail Belkin, Luis Rademacher
NeurIPS 2015 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | 4 Experimental Results We compare the proposed PEGI algorithm with existing ICA algorithms. In addition to qorth+GI-ICA (i.e., GI-ICA with quasi-orthogonalization for preprocessing), we use the following baselines: JADE [3] is a popular fourth cumulant based ICA algorithm designed for the noise free setting. We use the implementation of Cardoso and Souloumiac [5]. |
| Researcher Affiliation | Academia | James Voss The Ohio State University vossj@cse.ohio-state.edu Mikhail Belkin The Ohio State University mbelkin@cse.ohio-state.edu Luis Rademacher The Ohio State University lrademac@cse.ohio-state.edu |
| Pseudocode | Yes | Algorithm 1 Recovers a column of A up to a scaling factor if u0 is generically chosen. Inputs: Unit vector u0, C, f k 1 repeat uk f(C uk 1)/ f(C uk 1) k k + 1 until Convergence (up to sign) return uk |
| Open Source Code | No | The paper provides links to implementations of baseline algorithms (JADE and Fast ICA) used for comparison, e.g., 'JADE [3] is a popular fourth cumulant based ICA algorithm designed for the noise free setting. We use the implementation of Cardoso and Souloumiac [5]. http://perso.telecom-paristech.fr/cardoso/Algo/Jade/jadeR.m, 2005.' and 'Matlab Fast ICA v 2.5. http://research.ics.aalto.fi/ica/fastica/code/dlcode.shtml, 2005.' However, it does not state that the code for the proposed PEGI algorithm is open-source or provide a link to it. |
| Open Datasets | No | The paper uses simulated data, describing how it was generated ('We constructed mixing matrices A with condition number 3 via a reverse singular value decomposition... We drew data from a noisy ICA model X = AS + η... We generated 100 matrices A for our experiments with 100 corresponding ICA data sets for each sample size and noise power.'). It does not provide access information (link, DOI, citation) for a publicly available dataset. |
| Dataset Splits | No | The paper mentions varying 'sample size' for experiments, but does not specify explicit training, validation, or test dataset splits, nor does it refer to predefined splits or cross-validation. |
| Hardware Specification | No | No specific hardware details (such as GPU/CPU models or memory specifications) used for running the experiments were provided in the paper. |
| Software Dependencies | Yes | The paper states: 'We use the implementation of Cardoso and Souloumiac [5]. Matlab JADE for real-valued data v 1.8. http://perso.telecom-paristech.fr/ cardoso/Algo/Jade/jadeR.m, 2005.' and 'We use the implementation of G avert et al. [10]. Matlab Fast ICA v 2.5. http://research.ics. aalto.fi/ica/fastica/code/dlcode.shtml, 2005.' These provide specific version numbers for the software used for baseline comparisons. |
| Experiment Setup | Yes | We constructed mixing matrices A with condition number 3 via a reverse singular value decomposition (A = UΛV T ). The matrices U and V were random orthogonal matrices, and Λ was chosen to have 1 as its minimum and 3 as its maximum singular values, with the intermediate singular values chosen uniformly at random. We drew data from a noisy ICA model X = AS + η where cov(η) = Σ was chosen to be malaligned with cov(AS) = AAT . We set Σ = p(10I AAT ) where p is a constant defining the noise power. ... The source distributions used in our ICA experiments were the Laplace and Bernoulli distribution with parameters 0.05 and 0.5 respectively, the t-distribution with 3 and 5 degrees of freedom respectively, the exponential distribution, and the uniform distribution. Each distribution was normalized to have unit variance, and the distributions were each used twice to create 14-dimensional data. |