Second-order instantaneous causal analysis of spontaneous MEG

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Abstract Submission 

Yongjie Zhu¹, Lauri Parkkonen², Aapo Hyvärinen¹

¹Department of Computer Science, University of Helsinki, Helsinki, Finland, ²Department of Neuroscience and Biomedical Engineering, Aalto University, Espoo, Finland

Yongjie Zhu  
Department of Computer Science, University of Helsinki
Helsinki, Finland

Lauri Parkkonen  
Department of Neuroscience and Biomedical Engineering, Aalto University
Espoo, Finland

Aapo Hyvärinen  
Department of Computer Science, University of Helsinki
Helsinki, Finland

Despite decades of research, discovering instantaneous causal relationships from observational brain imaging data, such as spontaneous MEG and fMRI, remains a difficult problem. Popular methods, such as Granger Causality (GC) [1] and Non-Gaussian Structural Equation Models (e.g., linear non-gaussian acyclic model, LiNGAM) [2], either fall short in handling complex aspects of neuroimaging data such as contemporaneous effects or the data is not non-Gaussian enough.

Here we propose a model with instantaneous causality and temporally dependent variables, both of which are very empirically plausible in neuroimaging data. Then, we propose a method to estimate such causal models based on a pairwise approach inspired by [3]. The method is based on likelihood ratio with a connection to mutual information computed from second-order statistics between the residual and data variables to construct a simple decision criterion. Since the method is based on second-order statistics, we call it Second-Order Causal (SOC) analysis. To estimate the whole causal connectivity networks of n variables (or nodes), we apply a two-stage approach that is well-known in the literature [3, 4]. The L1-penalized inverse covariance (graphical lasso estimator) was used to estimate which nodes are connected, and then the proposed pairwise method was used to estimate the causal directions for each pair of connected nodes. We first applied the proposed method to simulated data generated according to the generative causal models. Then, we applied it to a resting-state MEG dataset from the CamCAN repository [5] (650 healthy subjects) with a split-half analysis to examine the consistency as well as to a brain age prediction task to show the usefulness. Specifically, the parcelled cortical MEG data was separated and reduced into 15 sources with nonlinear independent component analysis (NICA) [6]. The energies of NICA sources were computed and resampled into a sampling frequency of 1 Hz. Regarding the consistency analysis of the causal whole networks, we reported the consistency of the L1-penalized precision matrix and consistency of the causal methods (e.g., SOC, GC and pairwise LiNGAM (pwLiNGAM) [3]), and the consistency of the two-stage methods combining the two.

The simulations (Fig. 1A-D) confirm that the SOC method is able to estimate the proposed model with instantaneous causality and time-dependent variables when the true regressor does not have the same autocorrelation as the noise. Compared with GC, SOC performs better, especially in cases where the number of time points is typically quite small and limited. Moreover, pwLiNGAM [3] is unable to work when the autocorrelated variables are generated with Gaussian innovations.
When applied on CamCAN data, the method gives consistent results across intra- and inter-subject in a split-half test (correlation between two halves for each subject or group) when estimating causal directionalities (Fig.1 E-J). The SOC method gives significantly better inter- and intra-subject results than GC and pwLiNGAM methods. Fig. 2A shows the resulting causal connectivity networks, with the influences significant at a 5% level. One can see that the connections tend to be strong between sources, which are close to each other. Fig. 2B-C shows better performance in a brain age prediction task as well.

We presented a model and corresponding estimation method for instantaneous causal discovery in time-dependent variables based on second-order blind source separation methods. Since the method exploits only autocorrelations of the variables and not non-Gaussianity, it could be particularly useful for time-dependent brain imaging data such as fMRI, or energies of E/MEG data, which follow practically instantaneous causal relationships as above, due to the slow temporal scale of the measurement system.

Connectivity (eg. functional, effective, structural) ¹

EEG/MEG Modeling and Analysis ²

Methods Development

Task-Independent and Resting-State Analysis

Data analysis

Machine Learning

MEG