arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2002.04232cs.LGcs.AIcs.DSstat.ML
收藏

从观测中学习和采样原子干涉

Learning and Sampling of Atomic Interventions from Observations

National University of Singapore(新加坡国立大学);Cornell University(康奈尔大学);University of Wisconsin-Madison(威斯康星大学麦迪逊分校);University of Nebraska-Lincoln(内布拉斯加大学林肯分校)

Arnab Bhattacharyya, Sutanu Gayen, Saravanan Kandasamy, Ashwin Maran, N. V. Vinodchandran

摘要:

我们研究的问题,有效地估计一个单一的变量(原子干预)的干预措施的影响,使用观察样本的因果贝叶斯网络。我们的目标是在非参数设置中给出在时间和样本复杂度上都有效的算法。Tian和Pearl(AAAI '02)已经准确地描述了一类因果图,对于这些因果图,原子干预的因果效应可以从观测数据中识别出来。我们将其结果量化。假设P是n个可观测变量的集合$\vec{V}$上的因果模型,关于给定的具有可观测分布$P$的因果图G。令$P_x$表示关于指定变量X与x的干预的可观测量上的干预分布。假设$G$具有有界的度,有界的c-分量($k$),并且观测分布是可识别的,并且满足一定的强正性条件,我们给出了一个算法,该算法从$P$和$O(mn)$时间中提取$m=\tilde{O}(nε^{-2})$样本,并以高概率输出分布$\hat{P}$的描述,使得$d_{\mathrm{TV}}(P_x, \hat{P}) \leq ε$,并且:1. [评估]该描述可以在$O(n)$时间内返回任何将$\vec{v}$分配给$\vec{V}$ 2的概率$\hat{P}(\vec{v})$。[生成]说明可以在$O(n)$时间内从$\hat{P}$返回iid样本。我们还表明,我们的样本复杂性的下限表明,我们的样本复杂性有一个最佳的依赖参数$n$和$ε$,以及如果$k=1$的强阳性参数。

英文摘要:

We study the problem of efficiently estimating the effect of an intervention on a single variable (atomic interventions) using observational samples in a causal Bayesian network. Our goal is to give algorithms that are efficient in both time and sample complexity in a non-parametric setting. Tian and Pearl (AAAI `02) have exactly characterized the class of causal graphs for which causal effects of atomic interventions can be identified from observational data. We make their result quantitative. Suppose P is a causal model on a set $\vec{V}$ of n observable variables with respect to a given causal graph G with observable distribution $P$. Let $P_x$ denote the interventional distribution over the observables with respect to an intervention of a designated variable X with x. Assuming that $G$ has bounded in-degree, bounded c-components ($k$), and that the observational distribution is identifiable and satisfies certain strong positivity condition, we give an algorithm that takes $m=\tilde{O}(nε^{-2})$ samples from $P$ and $O(mn)$ time, and outputs with high probability a description of a distribution $\hat{P}$ such that $d_{\mathrm{TV}}(P_x, \hat{P}) \leq ε$, and: 1. [Evaluation] the description can return in $O(n)$ time the probability $\hat{P}(\vec{v})$ for any assignment $\vec{v}$ to $\vec{V}$ 2. [Generation] the description can return an iid sample from $\hat{P}$ in $O(n)$ time. We also show lower bounds for the sample complexity showing that our sample complexity has an optimal dependence on the parameters $n$ and $ε$, as well as if $k=1$ on the strong positivity parameter.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

↑