LazyIter：一种计算Markov等价DAG的快速算法及实验设计
LazyIter: A Fast Algorithm for Counting Markov Equivalent DAGs and Designing Experiments
摘要：
一组随机变量之间的因果关系通常由有向无环图（DAG）表示，其中如果$X$是$Y$的直接原因，则存在从变量$X$到变量$Y$的有向边。从纯粹的观测数据，真正的因果图可以识别到马尔可夫等价类（MEC），这是一组DAG与变量之间的相同的条件独立性。MEC的大小是通过执行干预来恢复真实因果图的复杂性的度量。我们提出了一种有效的迭代方法，在可能的MEC干预结果。我们利用所提出的方法计算MEC的大小和实验设计在主动和被动的学习设置。相比以前的工作计算MEC的大小，我们提出的算法减少了时间复杂度的一个因素，$O(n)$稀疏图，其中$n$是系统中的变量的数量。此外，结合动态规划，我们设计了一个被动实验设计的优化算法。实验结果表明，我们提出的算法计算MEC的大小和实验设计优于最先进的。
英文摘要：
The causal relationships among a set of random variables are commonly represented by a Directed Acyclic Graph (DAG), where there is a directed edge from variable $X$ to variable $Y$ if $X$ is a direct cause of $Y$. From the purely observational data, the true causal graph can be identified up to a Markov Equivalence Class (MEC), which is a set of DAGs with the same conditional independencies between the variables. The size of an MEC is a measure of complexity for recovering the true causal graph by performing interventions. We propose a method for efficient iteration over possible MECs given intervention results. We utilize the proposed method for computing MEC sizes and experiment design in active and passive learning settings. Compared to previous work for computing the size of MEC, our proposed algorithm reduces the time complexity by a factor of $O(n)$ for sparse graphs where $n$ is the number of variables in the system. Additionally, integrating our approach with dynamic programming, we design an optimal algorithm for passive experiment design. Experimental results show that our proposed algorithms for both computing the size of MEC and experiment design outperform the state of the art.
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