We present a nonparametric graphical model. Our model uses an undirected graph that represents conditional independence for general random variables defined by the conditional dependence coefficient (Azadkia and Chatterjee (2021)). The set of edges of the graph are defined as $E=\{(i,j):R_{i,j}\neq 0\}$, where $R_{i,j}$ is the conditional dependence coefficient for $X_i$ and $X_j$ given $(X_1,\ldots,X_p) \backslash \{X_{i},X_{j}\}$. We propose a graph structure learning by two steps selection procedure: first, we compute the matrix of sample version of the conditional dependence coefficient $\widehat{R_{i,j}}$; next, for some prespecificated threshold $\lambda>0$ we choose an edge $\{i,j\}$ if $ \left|\widehat{R_{i,j}} \right| \geq \lambda.$ The graph recovery structure has been evaluated on artificial and real datasets. We also applied a slight modification of our graph recovery procedure for learning partial correlation graphs for the elliptical distribution.

翻译：我们提出了一种非参数图模型。该模型利用无向图来表示由条件依赖系数（Azadkia and Chatterjee (2021)）定义的广义随机变量的条件独立性。图的边集定义为 $E=\{(i,j):R_{i,j}\neq 0\}$，其中 $R_{i,j}$ 表示在给定 $(X_1,\ldots,X_p) \backslash \{X_{i},X_{j}\}$ 条件下 $X_i$ 与 $X_j$ 的条件依赖系数。我们提出了一种两步筛选的图结构学习方法：首先计算条件依赖系数的样本版本矩阵 $\widehat{R_{i,j}}$；接着，对于预设阈值 $\lambda>0$，若 $\left|\widehat{R_{i,j}} \right| \geq \lambda$，则选择边 $\{i,j\}$。该图恢复结构已在人工数据集和真实数据集上进行了评估。此外，我们还将图恢复过程稍作修改，应用于椭圆分布的部分相关图学习。