Nonlinear association criterion, nonlinear Granger causality and related issues with applications to neuroimage studies

作者：Tao, Chenyang; Feng, Jianfeng^*

来源：Journal of Neuroscience Methods, 2016, 262: 110-132.

DOI：10.1016/j.jneumeth.2016.01.003

• Nonlinear association
• Canonical correlation analysis
• Reproducing kernel Hilbert space
• Granger causality
• Regularization
• Variable selection
• Permutation
• Parametric approximation of p-value

Background: Quantifying associations in neuroscience (and many other scientific disciplines) is often challenged by high-dimensionality, nonlinearity and noisy observations. Many classic methods have either poor power or poor scalability on data sets of the same or different scales such as genetical, physiological and image data. @@@ New method: Based on the framework of reproducing kernel Hilbert spaces we proposed a new nonlinear association criteria (NAC) with an efficient numerical algorithm and p-value approximation scheme. We also presented mathematical justification that links the proposed method to related methods such as kernel generalized variance, kernel canonical correlation analysis and Hilbert-Schmidt independence criteria. NAC allows the detection of association between arbitrary input domain as long as a characteristic kernel is defined. A MATLAB package was provided to facilitate applications. @@@ Results: Extensive simulation examples and four real world neuroscience examples including functional MRI causality, Calcium imaging and imaging genetic studies on autism [Brain, 138(5):13821393 (2015)] and alcohol addiction [PNAS, 112(30):E4085-E4093 (2015)] are used to benchmark NAC. It demonstrates the superior performance over the existing procedures we tested and also yields biologically significant results for the real world examples. @@@ Comparison with existing method(s): NAC beats its linear counterparts when nonlinearity is presented in the data. It also shows more robustness against different experimental setups compared with its nonlinear counterparts. @@@ Conclusions: In this work we presented a new and robust statistical approach NAC for measuring associations. It could serve as an interesting alternative to the existing methods for datasets where nonlinearity and other confounding factors are present.

• 出版日期2016-3-15
• 单位复旦大学