Causal Discovery of Feedback Networks with Functional Magnetic Resonance Imaging

Abstract

We test the adequacies of several proposed and two new statistical methods for recovering the causal structure of systems with feedback that generate noisy time series closely matching real BOLD time series. We compare: an adaptation for time series of the first correct method for recovering the structure of cyclic linear systems; multivariate Granger causal regression; the GIMME algorithm; the Ramsey et al. non-Gaussian methods; two non-Gaussian methods proposed by Hyvärinen and Smith; a method due to Patel, et al.; and the GlobalMIT algorithm. We introduce and also compare two new methods, the Fast Adjacency Skewness (FASK) and Two-Step, which exploit non-Gaussian features of the BOLD signal in different ways. We give theoretical justifications for the latter two algorithms. Our test models include feedback structures with and without direct feedback (2-cycles), excitatory and inhibitory feedback, models using experimentally determined structural connectivities of macaques, and empirical resting state and task data. We find that averaged over all of our simulations, including those with 2-cycles, several of these methods have a better than 80% orientation precision (i.e., the probability a directed edge is in the true generating structure given that a procedure estimates it to be so) and the two new methods also have better than 80% recall (probability of recovering an orientation in the data generating model). Recovering inhibitory direct feedback loops between two regions is especially challenging.

A generative model of whole-brain effective connectivity

“…3C). Again, it was also these p i 0 values that were optimal with regard to the trade-off between sensitivity and specificity of sparse rDCM.Finally, at the request of one reviewer, we compared the performance of sparse rDCM for the original small-world S50 network from Smith et al (2011) to three other methods that infer directed interactions in large-scale brain networks from fMRI data: Multivariate Granger causality (MVGC; Goebel et al, 2003;Roebroeck et al, 2005;Seth, 2010), (ii) Fast Adjacency Skewness (FASK; Sanchez-Romero et al, 2018), and (iii) Fast Greedy Equivalence Search (FGES;Chickering, 2003;Ramsey et al, 2017;Ramsey et al, 2010). In brief, for most settings, sparse rDCM showed comparable or better sensitivity than these approaches.…”

The Resting-State Causal Human Connectome is Characterized by Hub Connectivity of Executive and Attentional Networks

“…The copyright holder for this preprint this version posted October 21, 2021. ; https://doi.org/10.1101/2021.10.20.465211 doi: bioRxiv preprint et al, 2019), these methods have never been used in an applied research context, and often perform worse than the skew-based orientation method we use (Sanchez-Romero et al, 2019). Notably, the GANGO method is capable of discovering 3-cycle or greater feedback loops, so only direct feedback loops remain unmeasured.…”

“…For an intuitive information theoretic perspective on how non-Gaussian information can be used to orient edges between pairs of variables, see (Hyvärinen & Smith, 2013). We used a MATLAB implementation of an outlier-robust skew-based measure of the pairwise likelihood ratio (Hyvärinen & Smith, 2013), which has shown to generate optimal estimates of causal direction in simulated fMRI data (Ramsey et al, 2014;Sanchez-Romero et al, 2019). These steps resulted in n = 442 sparse effective connective graphs, which we characterized using various graph theoretic analyses.…”

“…However, fMRI connectivity methods have typically been limited to undirected connectivity, providing information about connected brain regions (hereafter adjacencies), but not the direction of these connections (hereafter orientations). The need to extend studies of human brain connectivity to directed (effective) connectivity measures is recognized (Ramsey et al, 2010;Reid et al, 2019;Smith, 2012;Valdes-Sosa et al, 2011), but methods for fMRI effective connectivity are limited (Ramsey et al, 2010(Ramsey et al, , 2014Sanchez-Romero et al, 2019;Smith et al, 2011). Granger prediction (Granger, 1969) attempts to recover causal influences using time-lagged regressions but has negligible accuracy in detecting adjacencies or orientations in simulated fMRI data (Smith et al, 2011).…”

“…Dynamic causal modeling (DCM) builds a generative model of the neural basis of the fMRI signal (Friston et al, 2003), but is designed for use in a task-based context and is generally not scalable enough to support whole-cortex analyses (but see recent advances in regression-DCM [Frässle et al, 2021]). However, methods grounded in causal discovery show high promise for uncovering causal connectivity from fMRI (Mumford & Ramsey, 2014;Ramsey et al, 2014;Sanchez-Romero et al, 2019), and for dealing with the high dimensionality of whole-cortex data (Ramsey et al, 2017). Suitable combinations of causal discovery-based methods can achieve near-perfect (>90%) accuracy in simulated fMRI data (Hyvärinen & Smith, 2013;Ramsey et al, 2014), and can even achieve high accuracy in uncovering feedback cycles (Sanchez-Romero et al, 2019).…”