论文标题
用于学习非参数因果图的多项式时间算法
A polynomial-time algorithm for learning nonparametric causal graphs
论文作者
论文摘要
我们为多项式时间算法建立有限样本保证，用于从数据中学习非线性，非参数定向的无环图（DAG）模型。该分析是无模型的，不假定线性，添加性，独立的噪音或忠诚。取而代之的是，我们对剩余方差施加条件，该方差与以前具有相等方差的线性模型上的工作密切相关。与具有变量订购的Oracle知识的最佳算法相比，该算法的额外成本在尺寸$ d $和样品数量$ n $中是线性的。最后，我们将所提出的算法与模拟研究中的现有方法进行了比较。
We establish finite-sample guarantees for a polynomial-time algorithm for learning a nonlinear, nonparametric directed acyclic graphical (DAG) model from data. The analysis is model-free and does not assume linearity, additivity, independent noise, or faithfulness. Instead, we impose a condition on the residual variances that is closely related to previous work on linear models with equal variances. Compared to an optimal algorithm with oracle knowledge of the variable ordering, the additional cost of the algorithm is linear in the dimension $d$ and the number of samples $n$. Finally, we compare the proposed algorithm to existing approaches in a simulation study.
