Heavy-Tailed Analogues of the Covariance Matrix for ICA
Authors: Joseph Anderson, Navin Goyal, Anupama Nandi, Luis Rademacher
AAAI 2017 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Our contributions are experimental and theoretical. We provide a new and practical ICA algorithm, HTICA, building upon the previous theoretical work in (Anderson et al. 2015). ... We demonstrate the effectiveness of HTICA on both synthetic and real-world data. ... In this section, we show experimentally that heavy-tailed data poses a significant challenge for current ICA algorithms, and compare them with HTICA in different settings. We observe some clear situations where heavy-tails seriously affect the standard ICA algorithms, and that these problems are frequently avoided by using the heavy-tailed ICA framework. |
| Researcher Affiliation | Collaboration | Joseph Anderson The Ohio State University andejose@cse.ohio-state.edu Navin Goyal Microsoft Research navingo@microsoft.com Anupama Nandi The Ohio State University nandi.10@osu.edu Luis Rademacher University of California, Davis lrademac@ucdavis.edu |
| Pseudocode | Yes | Subroutine 1 Orthogonalization via centroid body scaling |
| Open Source Code | No | The paper does not provide concrete access to source code for the methodology described in this paper. While it references 'ICALAB toolboxes' (Cichocki et al. ), this refers to an existing implementation, not the authors' specific code for HTICA. |
| Open Datasets | Yes | To study the algorithm with real data, we use recordings of human speech provided by (Donohue 2009). ... Donohue, K. D. 2009. http://www.engr.uky.edu/ donohue/audio/Data/audioexpdata.htm. Accessed: 2016-05-01. |
| Dataset Splits | No | The paper describes how synthetic and real-world data are used but does not provide specific training, validation, or test dataset split information. |
| Hardware Specification | No | The paper does not provide specific hardware details (such as CPU, GPU models, or memory) used for running its experiments. |
| Software Dependencies | No | The paper mentions existing ICA algorithms and toolboxes (e.g., Fast ICA, JADE, ICALAB toolboxes) but does not provide specific version numbers for any software dependencies used in its experiments or implementation. |
| Experiment Setup | Yes | To generate the synthetic data, we create a simple heavytailed density function fη(x) proportional to (|x| + 1.5) η, which is symmetric, and for η > 1, fη is the density of a distribution which has finite k < η 1 moment. The signal S is generated with each Si independently distributed from fηi. The mixing matrix A Rn n is generated with each coordinate i.i.d. N(0, 1), columns normalized to unit length. ... When performing the damping, we binary search over R so that about 25% of the samples are rejected. |