In this study,we propose and compare stochastic variants of the extra-gradient alteating direction method,named the stochastic extra-gradient alteating direction method with Lagrangian function (SEGL) and the stochastic extra-gradient alteating direction method with augmented Lagrangian function (SEGAL),to minimize the graph-guided optimization problems,which are composited with two convex objective functions in large scale.A number of important applications in machine leaing follow the graph-guided optimization formulation,such as linear regression,logistic regression,Lasso,structured extensions of Lasso,and structured regularized logistic regression.We conduct experiments on fused logistic regression and graph-guided regularized regression.Experimental results on several genres of datasets demonstrate that the proposed algorithm outperforms other competing algorithms,and SEGAL has better performance than SEGL in practical use.