Independent Component Analysis via Distance Covariance
By David S. Matteson, Ruey S. Tsay. 2013
127 citations recorded by the source corpus.
ABSTRACT This article introduces a novel statistical framework for independent component analysis (ICA) of multivariate data. We propose methodology for estimating mutually independent components, and a versatile resampling-based procedure for inference, including misspecification testing. Independent components are estimated by combining a nonparametric probability integral transformation with a generalized nonparametric whitening method based on distance covariance that simultaneously minimizes all forms of dependence among the components. We prove the consistency of our estimator under minimal regularity conditions and detail conditions for consistency under model misspecification, all while placing assumptions on the observations directly, not on the latent components. U statistics of certain Euclidean distances between sample elements are combined to construct a test statistic for mutually independent components. The proposed measures and tests are based on both necessary and sufficient conditions for mutual independence. We demonstrate the improvements of the proposed method over several competing methods in simulation studies, and we apply the proposed ICA approach to two real examples and contrast it with principal component analysis.
Subfields: Analytical Chemistry, Electrochemistry, 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 Analytical Chemistry
- Jan Peters
- Peter Buhlmann
- Bernhard Schölkopf
- Bodhisattva Sen
- Xin Jin
- John M. Maheu
- Niklas Pfister
- Nabarun Deb
In Electrochemistry
In Signal Processing
- Jan Peters
- Bernhard Schölkopf
- Bodhisattva Sen
- Niklas Pfister
- Peter Buhlmann
- Xin Jin
- John M. Maheu
- Nabarun Deb
Citations in the corpus
- Kernel‐based tests for joint independence (2016, background): “ to construct the collection of independent features, a more direct option is to explicitly minimize a measure of mutual dependence (such as our dHSIC), for more details see Chen and Bickel (2006) or Matteson and Tsay (2016).1 For testing joint independence, consider the distribution P(X1,...,Xd) of”
- Modeling Realized Covariances and Returns (2013, methodology): “2 Dynamic Conditional Correlation Model The second model is a dynamic conditional correlation (DCC-t) model of Engle (2002) with Student-t innovations, rt|r1:t−1 ∼ t(0, Ht, ζ) (34) Ht = DtRtDt (35) Dt = diag(σi,t) (36) σ(2) i,t = ωi + κir 2 i,t−1 + λiσ 2 i,t−1, i = 1, .”
- Multivariate Rank-Based Distribution-Free Nonparametric Testing Using Measure Transportation (2019, background): “[96] Matteson, D.”