Séminaire MODAL'X : Hernando Ombao (KAUST)

Résumé : Modeling dependence between nodes in a brain network is central to understanding underlying neural mechanisms such as perception, action, and memory. In this talk, we present a broad range of statistical methods for characterizing dependence in a brain network. We first review a general framework which decomposes each signal into various frequency components and then characterize the dependence properties through these oscillatory activities. The unifying theme across the talk is to explore the strength of dependence and possible lead-lag dynamics through filtering. The proposed framework is capable of representing both linear and non-linear dependencies that could occur instantaneously or after some delay (lagged dependence).
In the first part of the talk, some of the most prominent frequency domain measures, such as coherence, partial coherence, and dual-frequency coherence can be derived as special cases under this general framework. Coherence can be viewed in the proposed framework as the maximal squared correlation between oscillations from a pair of nodes. It gives a more specific information that correlation because it identifies the frequency bands that drive the dependence between nodes.In these second part of the talk, we will discuss methods for characterizing dependence between a pair of communities (of nodes) under the high dimensional setting. Here, we will introduce our proposed Kendall’s Canonical Coherence (KenCoh). The classical method of Canonical Correlation Analysis (CCA) is limited to capturing linear associations, cross-sectional studies, and is sensitive to heavy-tailed observations. The proposed KenCoh method mitigates the limitations by using a rank-based approach under elliptic symmetry. It captures non-linear associations and is robust against outliers. The work presented here is limited to multiple independent trials of multivariate time-series, although this is the usual set-up of experimental studies. Future direction of this work will look into potential Markovian dependence of trials which is applicable when trials has sequencing.
In the third and final part of the talk, we will briefly describe current work on information-theoretic measures of connectivity. This class of measures are based on joint (and conditional) distributions rather than just the first two moments. The proposed spectral transfer entropy (STE) quantifies the magnitude and direction of information flow from a certain frequency-band oscillation of a channel to an oscillation of another channel. The main advantage of our proposed approach is that it allows adjustments for multiple comparisons to control family-wise error rate. Another novel contribution is a simple yet efficient estimation method based on vine copula theory that enables estimates to capture zero (boundary point) without the need for bias adjustments. With the vine copula representation, a null copula model, which exhibits zero STE, is defined, making significance testing for STE straightforward through a standard resampling approach. Lastly, we illustrate the advantage of our proposed measure through some numerical experiments and provide interesting and novel findings on the analysis of EEG recordings linked to a visual task.
This is joint work with the Mara Talento, Sarbojit Roy and Paolo Redondo of the Biostatistics Group at KAUST.