A construction of a graphical model
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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≠ 0}, where R_i,j is the conditional dependence coefficient for X_i and X_j given (X_1,…,X_p) \{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 R_i,j; next, for some prespecificated threshold λ>0 we choose an edge {i,j} if |R_i,j| ≥λ. 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.
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