Annealed Importance Sampling for Neural Mass Models.
Annealed Importance Sampling for Neural Mass Models.
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DOI：
10.1371/journal.pcbi.1004797
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发表时间：
2016-03
影响因子：
4.3
通讯作者：
Sengupta B
中科院分区：
文献类型：
--
作者：
Penny W;Sengupta B
神经质量模型提供了一个紧凑的描述动态活动的细胞群在新皮层区域。此外，区域活动模型可以连接在一起形成网络，并使用M/EEG数据和贝叶斯推理对连接强度进行推断。然而，迄今为止，贝叶斯方法在很大程度上局限于变分拉普拉斯（VL）算法，该算法假设后验分布是高斯分布，并找到仅局部最优的模型参数。本文探讨了使用退火重要性抽样（AIS）来解决这些限制。我们使用来自Langevin Monte Carlo （LMC）的建议来实现AIS， LMC使用局部梯度和曲率信息来有效地探索参数空间。在贝叶斯因子的估计方面，VL和AIS对哪个模型是最好的意见一致，但报告的置信程度不同。此外，AIS找到了更好的模型参数，我们在它们的后验分布中发现了非高斯性的证据。人脑中神经元群的活动可以用一组称为神经质量模型的微分方程来描述。然后，这些模型可以连接起来描述多个大脑区域的活动，并通过将它们与人脑成像数据相匹配，可以对大脑区域之间宏观连接的变化做出统计推断。例如，从一个区域到另一个区域的连接强度可能在特定的患者群体中或在特定的认知任务中更强烈地参与。目前的统计推断方法使用基于局部优化原理的贝叶斯算法，并假设模型参数（例如连通性）的不确定性，已经看到数据，遵循高斯分布。本文针对全局贝叶斯优化算法评估了当前的方法，并发现两种方法（局部/全局）一致认为哪种模型是最好的，但发现全局方法产生更好的参数估计。
Neural Mass Models provide a compact description of the dynamical activity of cell populations in neocortical regions. Moreover, models of regional activity can be connected together into networks, and inferences made about the strength of connections, using M/EEG data and Bayesian inference. To date, however, Bayesian methods have been largely restricted to the Variational Laplace (VL) algorithm which assumes that the posterior distribution is Gaussian and finds model parameters that are only locally optimal. This paper explores the use of Annealed Importance Sampling (AIS) to address these restrictions. We implement AIS using proposals derived from Langevin Monte Carlo (LMC) which uses local gradient and curvature information for efficient exploration of parameter space. In terms of the estimation of Bayes factors, VL and AIS agree about which model is best but report different degrees of belief. Additionally, AIS finds better model parameters and we find evidence of non-Gaussianity in their posterior distribution. The activity of populations of neurons in the human brain can be described using a set of differential equations known as a neural mass model. These models can then be connected to describe activity in multiple brain regions and, by fitting them to human brain imaging data, statistical inferences can be made about changes in macroscopic connectivity among brain regions. For example, the strength of a connection from one region to another may be more strongly engaged in a particular patient population or during a specific cognitive task. Current statistical inference approaches use a Bayesian algorithm based on principles of local optimization and the assumption that uncertainty about model parameters (e.g. connectivity), having seen the data, follows a Gaussian distribution. This paper evaluates current methods against a global Bayesian optimization algorithm and finds that the two approaches (local/global) agree about which model is best, but finds that the global approach produces better parameter estimates.