[论文精读]Effective connectivity: Influence, causality and biophysical modeling_dynamic effective connectivity learning based on n-优快云博客

论文网址：Effective connectivity: Influence, causality and biophysical modeling - ScienceDirect

英文是纯手打的！论文原文的summarizing and paraphrasing。可能会出现难以避免的拼写错误和语法错误，若有发现欢迎评论指正！文章偏向于笔记，谨慎食用

2.3. Model specification

2.3.1. State-space models of effective connectivity

2.3.2. Nodes and random variables

2.3.3. The observation equation

2.3.4. The state equation

2.3.5. Specification of priors

2.3.6. Model comparison and Identifiability

2.3.7. Summary

2.4. Model inversions and inference

2.4.1. Discrete or continuous time?

2.4.2. Time, frequency or generalized coordinates?

2.4.3. Model inversion and inference

2.4.4. Summary

2.5. Statistical causal modeling

2.5.1. Philosophical background

2.5.2. Structural causal modeling: graphical models and Bayes–Nets

2.5.3. Summary

2.5.4. WAGS influence

2.5.5. More general models

2.5.6. Direct influence

2.5.7. Testing and measuring WAGS influence

2.5.8. Dynamic structural causal modeling

2.6. Challenges for causal modeling in Neuroimaging

2.6.1. Conclusion and suggestions for further work

3. 知识补充

3.1. Non-parametric model

3.2. Observation equation

4. Reference

1. 省流版

1.1. 心得

（1）文章是偏综述，定位是“Comments and Controversies”，含有非常多的专业名称，新手极度不推荐

（2）有一点早了，可能和现在的研究有点不太能直接对接

1.2. 论文总结图

2. 论文逐段精读

2.1. Abstract

①They record Causal Modeling, Granger Causal Modeling and other modeling methods

2.2. Introduction

①Causal modeling in Neuroimaging:

②Data driven and model driven methods:

③Causal relations: temporal (Granger-like influence, also WAGS influence) or physical influence (intervention and control)

eschew vt.避免；(有意地)避开；回避 distal adj.远端的；末梢的

dispel vt.消除(尤指感觉或信仰)；驱散

recapitulate v.概括；重述；概述 epistemological adj. 认识论的；认识论；知识论；论意义上的；知识论上的

precedence n.优先；优先权

2.3. Model specification

2.3.1. State-space models of effective connectivity

①They reckon generative models help to analyze causality

2.3.2. Nodes and random variables

①Activity of neurons: $x_{r}(t)$ or $x(r,t)\colon r\in R$ , where $R$ denotes the ROI

②Joint distribution of generative model: $X=\{X_{\setminus i},X_{i}\}$ , where $X_{\setminus i}$ denotes nodes without node $i$

membrane n.(身体内的)膜；(植物的)细胞膜；(可起防水、防风等作用的)膜状物

depolarization n.去极化；去极（化）（作用）；退极（性）；消（退）磁；消偏振（作用）；去偏光

hemodynamic adj.血液动力学的

2.3.3. The observation equation

①Sensor data at time $t_{k}\mathrm{=}k\Delta$ and $q \in Q$ predicted by $x_{r}(t)$ :

$y_q(t_k)=g(x_r,t)+e(t_k)\colon r\in R_r,t\in[t_k,t_{k-1}]$

②Observation equation in neuroimaging:

retarded adj.弱智的；迟钝的；智力发育迟缓的 v.阻碍；减缓；使放慢速度

retard vt.延缓；阻碍；减缓；使放慢速度 n.弱智；迟钝的人

smearing v.诽谤；弄脏；诋毁；(用油性或稀软物质)胡乱涂抹；弄上油污 n.污点，拖尾效应；弄脏的；蹭脏（smear 进行时形式）

smear v.弄脏；诽谤，诋毁；<美俚>贿赂；<美俚>打垮，击败；被擦模糊；把…制成涂片；把（字迹、图画等）蹭得模糊不清；（用油性或稀软物质）胡乱涂抹；弄上油污 n.（显微镜的）涂片；(尤指政治上的)抹黑，丑化；污迹；污点；污渍；黏稠物，涂抹物；（登山）不平衡的脚点 adj.
诽谤的，诋毁的

2.3.4. The state equation

①The evolution/updating of the neuronal states:

$x_r(t)=f\bigl(x_{r'\in R_r}(\tau),u(\tau),\xi_{r'\in R_{r'}}(\tau)\bigr)\colon\tau\in\bigl(t,t-t_0\bigr]$

where $x_{r^{\prime}}(\tau)\colon r^{\prime}\in R_{r^{\prime}}\subseteq R$ denotes the feature of nodes, $u(\tau)$ denotes the exogenous inputs, $\xi_{r^{\prime}(\tau)}$ is the stochastic process

②State equations:

③GCM is used for modeling continuous space and discrete time (mainly based on stocastic linear iteration model), DCM models on discrete (ROI) space on continuous time (mainly used deterministic ordinary differential equations (ODE))

2.3.5. Specification of priors

①Formal priors and modeling:

②Sparse multivariate autoregression of concurrent EEG/fMRI recordings:

euphemism n.委婉语；委婉说法

2.3.6. Model comparison and Identifiability

①Identify the identifiability of models

2.3.7. Summary

①Universal equation:

②文章分为数据驱动和模型驱动，而模型驱动是包含生物物理先验知识的，也可以算知识驱动

2.4. Model inversions and inference

2.4.1. Discrete or continuous time?

①Estimating continuous models by sampling discrete data when there are 3 time serieses:

$\begin{pmatrix}\operatorname dX_1(t)\\\operatorname dX_2(t)\\\operatorname dX_3(t)\end{pmatrix}=A\begin{bmatrix}X_1(t)\\X_2(t)\\X_3(t)\end{bmatrix}\operatorname dt+\sum^{1/2}\operatorname dB(t)$

and over the interval $[t+\Delta t,t]$ :

$\begin{gathered} \left.\left(\begin{array}{c}X_1(t+\Delta t)\\X_2(t+\Delta t)\\X_3(t+\Delta t)\end{array}\right.\right)=\exp(A\Delta t)\left(\begin{array}{c}X_1(t)\\X_2(t)\\X_3(t)\end{array}\right)+e(t+\Delta t) \\ e(t+\Delta t)=\int_{0}^{\Delta t}\exp(sA)\sum^{1/2}\operatorname{d}B(t-s) \\ \Sigma_{discrete}=\int_{0}^{\Delta t}\exp(sA)\sum\exp\left(sA^{T}\right)\operatorname{d}s \\ e(t+\Delta t)-\mathcal{N}(0,\Sigma_{discrete}) \end{gathered}$

the noise is reflected in $\Sigma_{discrete}$ .

②Models in non-linear systems:

$\begin{aligned}\operatorname{d}X(t)&=f(X(t))\operatorname{d}t+\sum^{1/2}\operatorname{d}B(t)\\X(t)&=\begin{bmatrix}X_1(t)\\X_2(t)\\X_3(t)\end{bmatrix}\end{aligned}$

$X(t+\Delta t)=X(t)+A^{-1}\left(\exp(A\Delta t)-I\right)f(X(t))+e(t+\Delta t)$

2.4.2. Time, frequency or generalized coordinates?

①They recommand the data domain conversion

2.4.3. Model inversion and inference

①To optimize model parameters, inversion strategy can be used to estimate

2.4.4. Summary

①They review the distinction between autoregression (AR) models and models formulated in continuous time (DCM)

2.5. Statistical causal modeling

2.5.1. Philosophical background

①Causal modeling is a legitimate statistical approach

2.5.2. Structural causal modeling: graphical models and Bayes–Nets

①Different dependence methods:

2.5.3. Summary

①There is a slight conflict between the directed causality of the brain and the undirected connections involving loops and feedback loops

2.5.4. WAGS influence

①Wiener–Akaike–Granger–Schweder (WAGS) Influences:

where the top figure denotes the weak influence and the bottom denotes strong influence

②Conditional Independence relations:

③Lack of independent definition of impact types:

2.5.5. More general models

①The Martingale component is an unpredictable part of a stochastic process

2.5.6. Direct influence

①False causal relationship:

2.5.7. Testing and measuring WAGS influence

①Inference for model means whether there is influence or not, and for parameter means the strength of the influence

②Interested parameters:

	Inference for model	Inference for parameter
DCM	Bayes factor	the conditional expectation of the parameter (effective connectivity)
GCM	equivalent likelihood ratio (Granger causal F-statistics)	conditional estimate of the corresponding autoregression coefficient

2.5.8. Dynamic structural causal modeling

①Listing some DCMs

②Direct and indirect influence of DCM:

2.6. Challenges for causal modeling in Neuroimaging

①There is virtually no lagged (or instantaneous) interaction observed among the Regions of Interest (ROIs), indicating a high degree of simultaneity in their activities.

②In fMRI analysis, the sole coefficients that withstand the rigorous False Discovery Rate (FDR) threshold are those that associate each ROI exclusively with its own past states, suggesting an intrinsic temporal continuity within individual regions.

③Functional Magnetic Resonance Imaging (fMRI) does not exert any discernible influence on the Electroencephalogram (EEG) recordings, indicating a lack of direct interference between these two neuroimaging modalities.

④Numerous intriguing interactions emerge among EEG sources, revealing complex dynamics and interdependencies within the underlying neural networks.

⑤While EEG sources provide valuable insights, they do not significantly impact the functional Magnetic Resonance Imaging (fMRI) process. Instead, fMRI and EEG offer complementary perspectives on brain activity, each with its unique strengths and limitations.