ABSTRACT

Discrete Dynamic Bayesian Network (dDBN) is used in many challenging causal modelling applications, such as human brain connectivity, due to its multivariate, non-deterministic, and nonlinear capability. Since there is not a ground truth for brain connectivity, the resulting model cannot be evaluated quantitatively. However, we should at least make sure that the best structure results for the used modelling approach and the data. Later, this result can be appreciated by further correlated literature of anatomy and physiology. Nearly all of the previously published studies rest on limited data, which brings doubt to the resulting structures. In theory, an immense number of samples is required, which is impossible to collect in practice. In this study, the appropriate number of data which makes a dDBN modelling trustable is searched by practical experiments and found to be $O\left(K^{p+1}\right)$ for binary and ternary-valued networks, where K is the cardinality of the random variables and p is the maximum number of parents possibly present in the network. If a modelling approach satisfies this amount of data, we can at least say that the resulting structure is trustable.

摘要

离散动态贝叶斯网络 (dDBN) 因其多变量、非确定性和非线性能力而被用于许多具有挑战性的因果建模应用程序，例如人脑连接。由于没有大脑连接的基本事实，因此无法定量评估所得模型。然而，我们至少应该确保所使用的建模方法和数据的最佳结构结果。后来，这一结果可以通过进一步相关的解剖学和生理学文献来理解。几乎所有先前发表的研究都依赖于有限的数据，这给最终的结构带来了疑问。理论上，需要大量的样本，在实践中是不可能收集到的。在这项研究中，$○\left({ķ}^{p+1}\right)$对于二元和三元值网络，其中K是随机变量的基数，p是网络中可能存在的最大父节点数。如果建模方法满足这么多数据，我们至少可以说生成的结构是可信的。