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Discovering Dynamic Effective Connectome of Brain with Bayesian Dynamic DAG Learning

Abdolmahdi Bagheri, Mohammad Pasande, Kevin Bello, Babak Nadjar Araabi, Alireza Akhondi-Asl

TL;DR

Bayesian Dynamic DAG learning with M-matrices Acyclicity characterization (BDyMA) method is introduced to address the challenges in discovering DEC and investigates the trustworthiness of DTI data as prior knowledge for DEC discovery and shows improvements in DEC discovery when the DTI data is incorporated into the process.

Abstract

Understanding the complex mechanisms of the brain can be unraveled by extracting the Dynamic Effective Connectome (DEC). Recently, score-based Directed Acyclic Graph (DAG) discovery methods have shown significant improvements in extracting the causal structure and inferring effective connectivity. However, learning DEC through these methods still faces two main challenges: one with the fundamental impotence of high-dimensional dynamic DAG discovery methods and the other with the low quality of fMRI data. In this paper, we introduce Bayesian Dynamic DAG learning with M-matrices Acyclicity characterization (BDyMA) method to address the challenges in discovering DEC. The presented dynamic causal model enables us to discover direct feedback loop edges as well. Leveraging an unconstrained framework in the BDyMA method leads to more accurate results in detecting high-dimensional networks, achieving sparser outcomes, making it particularly suitable for extracting DEC. Additionally, the score function of the BDyMA method allows the incorporation of prior knowledge into the process of dynamic causal discovery which further enhances the accuracy of results. Comprehensive simulations on synthetic data and experiments on Human Connectome Project (HCP) data demonstrate that our method can handle both of the two main challenges, yielding more accurate and reliable DEC compared to state-of-the-art and traditional methods. Additionally, we investigate the trustworthiness of DTI data as prior knowledge for DEC discovery and show the improvements in DEC discovery when the DTI data is incorporated into the process.

Discovering Dynamic Effective Connectome of Brain with Bayesian Dynamic DAG Learning

TL;DR

Bayesian Dynamic DAG learning with M-matrices Acyclicity characterization (BDyMA) method is introduced to address the challenges in discovering DEC and investigates the trustworthiness of DTI data as prior knowledge for DEC discovery and shows improvements in DEC discovery when the DTI data is incorporated into the process.

Abstract

Understanding the complex mechanisms of the brain can be unraveled by extracting the Dynamic Effective Connectome (DEC). Recently, score-based Directed Acyclic Graph (DAG) discovery methods have shown significant improvements in extracting the causal structure and inferring effective connectivity. However, learning DEC through these methods still faces two main challenges: one with the fundamental impotence of high-dimensional dynamic DAG discovery methods and the other with the low quality of fMRI data. In this paper, we introduce Bayesian Dynamic DAG learning with M-matrices Acyclicity characterization (BDyMA) method to address the challenges in discovering DEC. The presented dynamic causal model enables us to discover direct feedback loop edges as well. Leveraging an unconstrained framework in the BDyMA method leads to more accurate results in detecting high-dimensional networks, achieving sparser outcomes, making it particularly suitable for extracting DEC. Additionally, the score function of the BDyMA method allows the incorporation of prior knowledge into the process of dynamic causal discovery which further enhances the accuracy of results. Comprehensive simulations on synthetic data and experiments on Human Connectome Project (HCP) data demonstrate that our method can handle both of the two main challenges, yielding more accurate and reliable DEC compared to state-of-the-art and traditional methods. Additionally, we investigate the trustworthiness of DTI data as prior knowledge for DEC discovery and show the improvements in DEC discovery when the DTI data is incorporated into the process.
Paper Structure (22 sections, 20 equations, 7 figures, 1 table, 1 algorithm)

This paper contains 22 sections, 20 equations, 7 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Method
  3. Dynamic DAG structure learning
  4. Optimization problem
  5. Deriving objective likelihood functions
  6. Algorithm
  7. Data
  8. Synthetic data
  9. Causal sufficiency and selected Parcellation
  10. Data acquisition
  11. DTI data preprocessing
  12. Empirical data
  13. Result
  14. Results for the synthetic data
  15. Results for the empirical data
  16. ...and 7 more sections

Figures (7)

  • Figure 1: An example of a cyclic dynamic structure with $m=1$
  • Figure 2: Structural connectivities between two hemispheres, corpus callosum and subcortical regionscox2016ageing.
  • Figure 3: SHD values of $\boldsymbol{A}$ and $\boldsymbol{B}$ matrices for data 1, data 2, and data 3 extracted with the BDyMA without prior, with binary prior knowledge and probabilistic prior knowledge, LiNGAM, DYNOTEARS, Number of Nodes $\in \{50,75, 100,125,150\}$
  • Figure 4: The Rogers-Tanimoto and KR-20 values for all the edges with the BDyMA and DYNOTEARS method. a. The Rogers-Tanimoto index for DECs of the $\boldsymbol{B}$ matrices. b. The Rogers-Tanimoto index for DECs of the $\boldsymbol{A}$ matrices. C. The KR-20 index for DECs of the $\boldsymbol{B}$ matrices. D. The KR-20 index for DECs of the $\boldsymbol{A}$ matrices.
  • Figure 5: Weight density distributions of edges in functional connectivities and $\boldsymbol{B}$ matrices extracted with and without prior knowledge
  • ...and 2 more figures