Graphical causal models for random networks

推断因果关系一直是许多研究领域的主要目标之一。当今世界的例子包括，但不限于，推断癌症的潜在原因、基因操纵的影响、移民的原因及其对经济的影响等等。特定的统计模型，通常被称为因果模型，已被用于从观察数据中推断这种因果关系。人们在定义、解释和应用因果模型方面进行了广泛的研究，最近，这些模型已经成为统计学和计算机科学的主流。今天，推断因果关系的一种非常流行的方法是基于我们所说的图形因果模型的使用。它们应用图形(马尔可夫)模型，这是图上的统计模型，其节点是表示感兴趣的数量的随机变量。边表示这些变量之间的概率相关性，条件是图中的其他一些变量，加上一些额外的假设，这可以解释为因果关系。图形模型在统计学、概率论和机器学习中得到了广泛的应用，并被广泛应用于从遗传学到经济学的各个领域。另一方面，在线和其他社交网络以及以网络为代表的其他类型数据的激增，导致了各种统计(随机)网络模型的引入。然而，推断网络边之间的因果关系，或节点属性和网络边之间的因果关系，是一个重要但研究较少的任务。尽管有一些关于使用非图形因果模型的研究，也有一些基于图形模型的方法的尝试，但文献中缺乏用于网络模型的通用因果框架。这个项目的主要目标是利用这种联系在随机网络上应用图形化因果模型的理论。图形化和网络模型都使用图。然而，与图形模型相反，在网络模型中，图的节点是固定的个体，而边是随机的。尽管这两种类型的模型是在完全不同的统计学分支中引入和研究的，但它们之间存在着天然的联系。这种联系允许我们(原则上)通过将图形模型理论专门用于随机网络模型的特定分布以及图形模型中使用的特定类型的图形来发展与网络模型的图形模型有关的每一种理论。这是一种新的方法，它将成为对网络进行图形化因果推理的基础。这在这个时刻尤其重要，因为特别适合于因果建模的不同类型的网络数据激增。

Inferring causal relationships has always been one of the main objectives in many fields of study. Examples in today's world include, but are not limited to, inferring potential causes of cancer, the effect of gene manipulation, the cause of immigration and its effect on the economy, and much more.Specific statistical models, known generically as causal models, have been used to infer such causal relationships from observed data. Extensive research has been conducted on defining, interpreting, and applying causal models, and recently, these models have become a mainstream in statistics and computer science. Today, a very popular method for inferring causal relationships is based on the use of what we call graphical causal models. These apply graphical (Markov) models, which are statistical models over graphs with nodes that are random variables representing the quantities of interest. Edges indicate probabilistic dependence among these variables conditional on some other variables in thegraph, which with some additional assumptions can be interpreted as causal relationships. Graphical models have been extensively used in statistics, probability theory, and machine learning, and are applied in a wide range of areas from genetics to economics.On the other hand, the surge of online and other social networks as well as other types of data represented as networks, has led to the introduction of a wide range of statistical (random) network models. However, inferring causal relationships among the edges of the network, or between the nodal attributes and the edges of the network, is an important yet less studied task. Despite some research on using non-graphical causal models, and also some attempts on approaches based on graphical models, a general causal framework for network models is lacking in the literature. The main objective of this project is to use this connection to apply the theory of graphical causal models on random networks.Both graphical and network models use graphs. However, as opposed to graphical models, in network models, nodes of the graph are fixed individuals, and edges are random. Although these two types of models have been introduced and studied in completely different branches of statistics, there is a natural connection between them. This connection allows us to (in principle) develop every theory pertaining to graphical models for network models by specializing the theory of graphical models to the specific distributions of random network models as well as the specific type of graphs used in graphical models. This is a novel approach, which will be the basis of performing graphical causal inference on networks. This is especially important at this moment in time because of the surge in different types of network data that are particularly well-suited for causal modeling.