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∈, where we assume that the coordinates of ∈ 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 (Formula Presented) 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.
| Original language | English |
|---|---|
| Journal | Electronic Journal of Statistics |
| Volume | 8 |
| Pages (from-to) | 1438–1459 |
| Number of pages | 22 |
| ISSN | 1935-7524 |
| DOIs | |
| Publication status | Published - 30 Jan 2014 |