Quantifying identifiability in independent component analysis
Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
Standard
Quantifying identifiability in independent component analysis. / Sokol, Alexander; Maathuis, Marloes H.; Falkeborg, Benjamin.
I: Electronic Journal of Statistics, Bind 8, 30.01.2014, s. 1438–1459.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
Harvard
APA
Vancouver
Author
Bibtex
}
RIS
TY - JOUR
T1 - Quantifying identifiability in independent component analysis
AU - Sokol, Alexander
AU - Maathuis, Marloes H.
AU - Falkeborg, Benjamin
PY - 2014/1/30
Y1 - 2014/1/30
N2 - 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.
AB - 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.
KW - math.ST
KW - stat.TH
KW - 62F12, 62F35
U2 - 10.1214/14-EJS932
DO - 10.1214/14-EJS932
M3 - Journal article
VL - 8
SP - 1438
EP - 1459
JO - Electronic Journal of Statistics
JF - Electronic Journal of Statistics
SN - 1935-7524
ER -
ID: 129924944