AUTHORS: Yi Li, A. Adam Ding
Download as PDF
Measures of statistical dependence is of great importance for machine learning and statistical models. Recently, a new measure, the robust copula dependence (RCD) is shown to be equitable in treating dependence of linear and nonlinear relationships. The paper propose extensions of RCD to multivariate and conditional cases, which is crucial for many applications. We study the theoretical and empirical properties of the extended RCD. We successfully apply to several example applications including learning delayed time in nonlinear systems, independence testing with mixture alternatives and feature selection
KEYWORDS: Multivariate dependence, robust-equitable, independence testing
REFERENCES:
[
1] B. P. Bezruchko, A. S. Karavaev, V. I. Ponomarenko,
and M. D. Prokhorov. Reconstruction of time-delay
systems from chaotic time series. Phys. Rev. E,
64:056216, Oct 2001.
[2] Thomas Blumentritt and Friedrich Schmid. Mutual
information as a measure of multivariate association: analytical properties and statistical estimation.
Journal of Statistical Computation and Simulation,
82(9):1257–1274, 2012.
[3]Yale Chang, Yi Li, Adam Ding, and Jennifer Dy.
A robust-equitable copula dependence measure for
feature selection. In Artificial Intelligence and
Statistics, pages 84–92, 2016.
[4]Suzana de Siqueira Santos, Daniel Yasumasa Takahashi, Asuka Nakata, and Andre Fujita.
A comparative study of statistical methods used to identify dependencies between gene expression signals.
Briefings in Bioinformatics, 2013.
[5]A Adam Ding, Jennifer G Dy, Yi Li, and Yale Chang.
A robust-equitable measure for feature ranking and
selection. The Journal of Machine Learning Research, 18(1):2394–2439, 2017.
[6]T.S. Ferguson. A Course in Large Sample Theory.
Chapman & Hall Texts in Statistical Science Series.
Taylor & Francis, 1996.
[7]Kenji Fukumizu, Arthur Gretton, Xiaohai Sun, and
Bernhard Scholkopf. Kernel measures of condi- ¨
tional dependence. In NIPS, volume 20, pages 489–
496, 2007.
[8]Arthur Gretton, Ralf Herbrich, Alexander Smola,
Olivier Bousquet, and Bernhard Scholkopf. Ker- ¨
nel methods for measuring independence. J. Mach.
Learn. Res., 6:2075–2129, December 2005.
[9]Sashank J Reddi and Barnabas P ´ oczos. Scale invariant ´
conditional dependence measures. In Proceedings
of The 30th International Conference on Machine
Learning, pages 1355–1363, 2013.
[10]Bo Jiang, Chao Ye, and Jun S. Liu. Nonparametric
ksample tests via dynamic slicing. Journal of the
American Statistical Association, 110(510):642–
653, 2015.
[11]Harry Joe. Relative entropy measures of multivariate dependence.
Journal of the American Statistical
Association, 84(405):157–164, 1989.
[12]Yi Li and A. Adam Ding. An r package for estimating
robust copula dependence. International Journal of
Pure Mathematics, 4:17–21, 2017.
[13]Ben Murrell, Daniel Murrell, and Hugh Murrell.
Discovering general multidimensional associations.
PloS one, 11(3):e0151551, 2016.
[14]R. B. Nelsen. An introduction to copulas (Springer series in statistics).
Springer-Verlag New York, Inc.,
Secaucus, NJ, USA, 2006.
[15]Barnabas P ´ oczos, Zoubin Ghahramani, and Jeff G. ´
Schneider. Copula-based kernel dependency measures.
In International Conference on Machine
Learning, 2012.
[16]M. D. Prokhorov and V. I. Ponomarenko. Estimation
of coupling between time-delay systems from time
series. Phys. Rev. E, 72:016210, Jul 2005.
[17]M.D. Prokhorov, V.I. Ponomarenko, and V.S. Khorev.
Recovery of delay time from time series based on
the nearest neighbor method. Physics Letters A,
377(43):3106 – 3111, 2013.
[18]A. Renyi. On measures of dependence. ´
Acta Mathematica Academiae Scientiarum Hungarica, 10(3-
4):441–451, 1959.
[19]David N Reshef, Yakir A Reshef, Hilary K Finucane, Sharon R Grossman, Gilean McVean, Peter J
Turnbaugh, Eric S Lander, Michael Mitzenmacher,
and Pardis C Sabeti. Detecting novel associations
in large data sets. science, 334(6062):1518–1524,
2011.
[20]Le Song, Alex Smola, Arthur Gretton, Justin Bedo,
and Karsten Borgwardt. Feature selection via dependence maximization. J. Mach. Learn. Res.,
13(1):1393–1434, May 2012.
[21]Gabor J Sz ´ ekely, Maria L Rizzo, et al. Brownian dis- ´
tance covariance. The annals of applied statistics,
3(4):1236–1265, 2009.
[22]Edward F. Wolff. N-dimensional measures of dependence. Stochastica, 4(3):175–188, 1980.
