Efficient independent component analysis

By Aiyou Chen, Peter J. Bickel. 2006

100 citations recorded by the source corpus.

Independent component analysis (ICA) has been widely used for blind source separation in many fields, such as brain imaging analysis, signal processing and telecommunication. Many statistical techniques based on M-estimates have been proposed for estimating the mixing matrix. Recently, several nonparametric methods have been developed, but in-depth analysis of asymptotic efficiency has not been available. We analyze ICA using semiparametric theories and propose a straightforward estimate based on the efficient score function by using B-spline approximations. The estimate is asymptotically efficient under moderate conditions and exhibits better performance than standard ICA methods in a variety of simulations.

Subfields: Cognitive Neuroscience, Computational Mechanics, Signal Processing

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Cognitive Neuroscience

1. Aapo Hyvärinen
2. Bernhard Schölkopf
3. Kun Zhang
4. Jan Peters
5. Patrik O. Hoyer
6. Peter Buhlmann
7. Shohei Shimizu
8. Jari Miettinen

In Computational Mechanics

1. Jan Peters
2. Alexandre B. Tsybakov
3. Peter Buhlmann
4. Jari Miettinen
5. Bernhard Schölkopf
6. Aapo Hyvärinen
7. Hannu Oja
8. Shohei Shimizu

In Signal Processing

1. Bernhard Schölkopf
2. Jan Peters
3. Kun Zhang
4. Dominik Janzing
5. Aapo Hyvärinen
6. Shohei Shimizu
7. Patrik O. Hoyer
8. Peter Buhlmann

Citations in the corpus

• Kernel‐based tests for joint independence (2016, background): “…stepwise approach to construct the collection of independent features, a more direct option is to minimize a measure of mutual dependence explicitly (such as our d-variable Hilbert–Schmidt independence criterion (HSIC) dHSIC); for more details see Chen and Bickel (2006) or Matteson and Tsay (2016).”
• Independent Component Analysis via Distance Covariance (2013, methodology): “KDICA is conjectured (Chen 2006) to have the same semi-parametric efficiency as the EFFICA estimator (Chen and Bickel 2006) while remaining computationally tractable.”
• Independent component analysis: recent advances (2013, methodology): “The problem was analyzed on a theoretical level by Chen and Bickel (2006), who also proposed a practical method for adapting the G i .”
• Estimation of a Structural Vector Autoregression Model Using Non-Gaussianity (2010, methodology): “Different methods have been developed for approximating log pi, for example, Pham and Garrat (1997), Karvanen and Koivunen (2002) and Chen and Bickel (2006). Here, we have to take into account the fact that those methods usually assume that the independent components have been normalized to unit var”
• Nonparametric independent component analysis (2004, methodology): “The referee also indicated the preprint by Chen and Bickel (2003) which appeared after our paper was submitted and which proves the root-n consistency of the method proposed in Eriksson et al.”
• Fourth Moments and Independent Component Analysis (2014, methodology): “For alternative ways to identify the unmixing matrix, see then Chen and Bickel (2006), Ilmonen and Paindaveine (2011), and Hallin and Mehta (2015), for example. For a general discussion on this identification problem, see also Eriksson and Koivunen (2004).”