The Scaling Limit of High-Dimensional Online Independent Component Analysis
Authors: Chuang Wang, Yue Lu
NeurIPS 2017 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Numerical solutions of this PDE... Numerical simulations show that our asymptotic analysis is accurate even for moderate dimensions. Numerical verifications of the ODE results are shown in Figure 1(a). In our experiment, the ambient dimension is set to n = 5000 and we plot the averaged results as well as error bars (corresponding to one standard deviation) over 10 independent trials. To demonstrate the usefulness of the PDE analysis in providing detailed information about the performance of the algorithm, we show in Figure 3 the performance of sparse support recovery using a simple hard-thresholding scheme on the estimates provided by the algorithm. |
| Researcher Affiliation | Academia | Chuang Wang and Yue M. Lu John A. Paulson School of Engineering and Applied Sciences Harvard University 33 Oxford Street, Cambridge, MA 02138, USA {chuangwang,yuelu}@seas.harvard.edu |
| Pseudocode | No | The paper describes algorithms and mathematical formulations but does not include structured pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not provide any explicit statements about open-sourcing code or links to a code repository. |
| Open Datasets | No | The paper describes a generative model for data (yk = 1 nξck + ak) and discusses numerical simulations, but it does not use a named, publicly available dataset with concrete access information such as a URL, DOI, or specific repository name. |
| Dataset Splits | No | The paper describes numerical simulations and compares theoretical predictions to these simulations. However, it does not mention specific training, validation, or test dataset splits in the conventional sense, as it generates synthetic data for its simulations rather than using a pre-existing dataset. |
| Hardware Specification | No | The paper does not specify any hardware details (e.g., CPU, GPU models, memory) used for running the numerical simulations. |
| Software Dependencies | No | The paper does not specify any software names with version numbers that would be necessary to reproduce the numerical simulations or analysis. |
| Experiment Setup | Yes | In our experiment, the ambient dimension is set to n = 5000 and we plot the averaged results as well as error bars (corresponding to one standard deviation) over 10 independent trials. Two different initial values of q0 = Q2 0 are used. Example 2: In this experiment, we verify the accuracy of the asymptotic predictions given by the PDE (6). The settings are similar to those in Example 1. In addition, we assume that the feature vector ξ is sparse, consisting of ρn nonzero elements, each of which is equal to 1/ ρ. In our experiment, n = 104, and the sparsity level is set to ρ = 0.3. We use f(x) = x3 in (2) to detect the feature vector ξ. |