通过皮尔逊风险不变性进行因果广义线性模型
Causal generalized linear models via Pearson risk invariance
AI总结：
本文提出通过皮尔逊风险不变性来识别因果广义线性模型，无需多环境数据，适用于单数据环境下的因果发现。
摘要：
在异质设置下，因果模型的预测不变性已被一些最近的因果发现方法所利用，通常专注于恢复感兴趣的靶变量的因果父母。现有方法需要从多个足够不同的环境中获取观测数据，这很少可用。在本文中，我们考虑了一个结构方程模型，其中靶变量由其父母的广义线性模型描述。除了具有有限矩外，对系统中其他变量的条件分布不作建模假设，并且目标变量的非线性效应可以通过广义加性结构自然地加以容纳。在此设置下，我们通过两个关键性质来唯一地表征因果模型：因果模型下的皮尔逊风险不变性，以及在因果父母条件下，因果参数最大化期望似然。这两个性质构成了在所有可能模型中搜索因果模型的计算策略的基础。对于变量数量大的系统，提出了一种逐步贪心搜索方法。关键的是，对于具有已知离散参数的广义线性模型，如泊松和逻辑回归，因果模型可以从单一数据环境中识别出来。该方法在R包causalreg中实现。
英文摘要：
Prediction invariance of causal models under heterogeneous settings has been exploited by a number of recent methods for causal discovery, typically focussing on recovering the causal parents of a target variable of interest. Existing methods require observational data from a number of sufficiently different environments, which is rarely available. In this paper, we consider a structural equation model where the target variable is described by a generalized linear model conditional on its parents. Besides having finite moments, no modelling assumptions are made on the conditional distributions of the other variables in the system, and nonlinear effects on the target variable can naturally be accommodated by a generalized additive structure. Under this setting, we characterize the causal model uniquely by means of two key properties: the Pearson risk invariant under the causal model and, conditional on the causal parents, the causal parameters maximize the expected likelihood. These two properties form the basis of a computational strategy for searching the causal model among all possible models. A stepwise greedy search is proposed for systems with a large number of variables. Crucially, for generalized linear models with a known dispersion parameter, such as Poisson and logistic regression, the causal model can be identified from a single data environment. The method is implemented in the R package causalreg.
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