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COPICA—independent component analysis via copula techniques

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Abstract

Independent component analysis (ICA) is a modern computational method developed in the last two decades. The main goal of ICA is to recover the original independent variables by linear transformations of the observations. In this study, a copula-based method, called COPICA, is proposed to solve the ICA problem. The proposed COPICA method is a semiparametric approach, the marginals are estimated by nonparametric empirical distributions and the joint distributions are modeled by parametric copula functions. The COPICA method utilizes the estimated copula parameter as a dependence measure to search the optimal rotation matrix that achieves the ICA goal. Both simulation and empirical studies are performed to compare the COPICA method with the state-of-art methods of ICA. The results indicate that the COPICA attains higher signal-to-noise ratio (SNR) than several other ICA methods in recovering signals. In particular, the COPICA usually leads to higher SNRs than FastICA for near-Gaussian-tailed sources and is competitive with a nonparametric ICA method for two dimensional sources. For higher dimensional ICA problem, the advantage of using the COPICA is its less storage and less computational effort.

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Acknowledgements

The authors gratefully acknowledge the National Science Council in Taiwan, National Center for Theoretical Sciences (South), Tainan, Taiwan and the Deutsche Forschungsgemeinschaft through the SFB 649 “Economic Risk”, Humboldt-Universitat zu Berlin. This work was supported in part by National Science Council under grants NSC 96-2118-M-390-002- (Chen), NSC 100-2118-M-110-001-003- (Guo) and NSC 101-2118-M-390-002- (Huang).

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Authors and Affiliations

  1. Dept. of Statistics, National Cheng Kung University, Tainan, 701, Taiwan

    Ray-Bing Chen

  2. Dept. of Applied Math., National Sun Yat-sen University, Kaohsiung, 804, Taiwan

    Meihui Guo

  3. Center for Applied Statistics and Economics, Humboldt-Universität zu Berlin, Berlin, Germany

    Wolfgang K. Härdle

  4. Lee Kong Chian School of Business, Singapore Management University, Singapore, Singapore

    Wolfgang K. Härdle

  5. Dept. of Applied Math., National University of Kaohsiung, Kaohsiung, 811, Taiwan

    Shih-Feng Huang

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  1. Ray-Bing Chen
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  2. Meihui Guo
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  3. Wolfgang K. Härdle
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  4. Shih-Feng Huang
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Correspondence to Meihui Guo.

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Chen, RB., Guo, M., Härdle, W.K. et al. COPICA—independent component analysis via copula techniques. Stat Comput 25, 273–288 (2015). https://doi.org/10.1007/s11222-013-9431-3

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