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2014 Quantifying identifiability in independent component analysis
Alexander Sokol, Marloes H. Maathuis, Benjamin Falkeborg
Electron. J. Statist. 8(1): 1438-1459 (2014). DOI: 10.1214/14-EJS932

Abstract

We are interested in consistent estimation of the mixing matrix in the ICA model, when the error distribution is close to (but different from) Gaussian. In particular, we consider $n$ independent samples from the ICA model $X=A\epsilon$, where we assume that the coordinates of $\epsilon$ are independent and identically distributed according to a contaminated Gaussian distribution, and the amount of contamination is allowed to depend on $n$. We then investigate how the ability to consistently estimate the mixing matrix depends on the amount of contamination. Our results suggest that in an asymptotic sense, if the amount of contamination decreases at rate $1/\sqrt{n}$ or faster, then the mixing matrix is only identifiable up to transpose products. These results also have implications for causal inference from linear structural equation models with near-Gaussian additive noise.

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Alexander Sokol. Marloes H. Maathuis. Benjamin Falkeborg. "Quantifying identifiability in independent component analysis." Electron. J. Statist. 8 (1) 1438 - 1459, 2014. https://doi.org/10.1214/14-EJS932

Information

Published: 2014
First available in Project Euclid: 20 August 2014

zbMATH: 1298.62045
MathSciNet: MR3263128
Digital Object Identifier: 10.1214/14-EJS932

Subjects:
Primary: 62F12
Secondary: 62F35

Rights: Copyright © 2014 The Institute of Mathematical Statistics and the Bernoulli Society

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