Skarf: A library for regularized autoregressive functional connectivity
Poster No:
1452
Submission Type:
Abstract Submission
Authors:
Connor Lane1, Jason Kai2, Michael Milham2, Gregory Kiar3
Institutions:
1Child Mind Institute, New York City, NY, 2Child Mind Institute, New York, NY, 3Center for Data Analytics, Innovation, and Rigor, Child Mind Institute, NYC, NY
First Author:
Co-Author(s):
Introduction:
Methods for brain behavior prediction often rely on functional connectivity features derived from resting-state fMRI [1]. Typically, functional connectivity is computed as a matrix of pairwise similarity measurements between ROI time courses. Alternatively, functional connectivity can be measured by fitting a linear vector autoregressive (VAR) model to the full multivariate parcellated time series [2]. This approach, also known as Granger causality or effective connectivity [3, 4], estimates the linear dependencies between regions jointly, rather than for each pair of ROIs independently. In principle, this can improve the precision of connectivity estimates. Indeed, there is evidence that functional connectivity features derived from autoregressive models are more predictive of behavior than similarity based functional connectivity [5]. However, the approach has not been widely adopted. One challenge is that fitting VAR models is more computationally involved than simple time series similarity comparison. To lower the barrier of entry for experimenting with VAR connectivity, we developed skarf (scikit autoregressive models of functional connectivity).
Methods:
A linear VAR model represents the activity in ROI r at time t as a linear combination of the activities in all other ROIs at one or more past ("lagged") time points (Figure 1b). Importantly, a VAR model is just a special case of multivariate linear regression, where the design matrix consists of flattened sliding windows of the original time series, and the target matrix is the original time series shifted by the prediction offset. We leverage this equivalence by implementing skarf on top of the robust linear modeling tools available in the widely used scikit-learn machine learning library. A key challenge with classic similarity based functional connectivity is intra-subject variability due to spurious functional connections. By contrast, VAR models of functional connectivity provide an explicit mechanism to penalize spurious connections (regularization), and an explicit criterion by which to identify them (cross-validated autoregressive prediction). By building on top of the scikit-learn linear modeling infrastructure, we get free access to a wide variety of regularization (e.g. Ridge, Lasso, Elastic-Net, PLS) and cross-validation schemes (e.g. leave one run out) (Figure 1c). To facilitate comparison between VAR functional connectivity and classic similarity based functional connectivity, we developed a similarity-constrained VAR model, which is parameterized by a fixed functional connectivity matrix. Specifically, the edges of the similarity VAR matrix are estimated as a polynomial transform of the underlying connectivity matrix.
Results:
As a proof of concept, we applied skarf to 100 unrelated subjects from the HCP dataset [6]. We estimated VAR connectivity with elastic-net regularization. The resulting connectomes are highly sparse, with 35+/-17 edges per region. The principal gradient and spectral clustering maps replicate the classic functional network structure (Figure 2). Unlike classic functional connectivity, estimating gradients and clusters for these intrinsically sparse VAR connectomes does not require additional sparse thresholding post-processing (which itself can be viewed as an approximation of matching pursuit, an algorithm for Lasso).
Conclusions:
Linear vector autoregressive (VAR) models are a promising and under-explored approach to estimating resting-state functional connectivity. To lower the barrier of entry, we developed skarf, a library for estimating VAR functional connectivity. The key features of skarf include (1) a minimal linear VAR model designed around reuse of scikit-learn's linear modeling functionality, (2) support for a range of regularization penalties and cross-validation schemes, (3) a novel similarity-constrained VAR model to facilitate comparison with classic similarity based functional connectivity.
Modeling and Analysis Methods:
Classification and Predictive Modeling
Connectivity (eg. functional, effective, structural) 2
fMRI Connectivity and Network Modeling 1
Multivariate Approaches
Task-Independent and Resting-State Analysis
Keywords:
Computing
Data analysis
FUNCTIONAL MRI
Machine Learning
Modeling
Multivariate
Open-Source Software
1|2Indicates the priority used for review
Abstract Information
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2. Valdés-Sosa, P. A., Sánchez-Bornot, J. M., Lage-Castellanos, A., Vega-Hernández, M., Bosch-Bayard, J., Melie-García, L., & Canales-Rodríguez, E. (2005). Estimating brain functional connectivity with sparse multivariate autoregression. Philosophical Transactions of the Royal Society B: Biological Sciences, 360(1457), 969-981.
3. Granger, C. W. (1969). Investigating causal relations by econometric models and cross-spectral methods. Econometrica: journal of the Econometric Society, 424-438.
4. Friston, K. J. (2011). Functional and effective connectivity: a review. Brain connectivity, 1(1), 13-36.
5. Liégeois, R., Li, J., Kong, R., Orban, C., Van De Ville, D., Ge, T., ... & Yeo, B. T. (2019). Resting brain dynamics at different timescales capture distinct aspects of human behavior. Nature communications, 10(1), 2317.
6. Van Essen, D. C., Smith, S. M., Barch, D. M., Behrens, T. E., Yacoub, E., Ugurbil, K., & Wu-Minn HCP Consortium. (2013). The WU-Minn human connectome project: an overview. Neuroimage, 80, 62-79.