We investigate a subclass of exponential family graphical models of which the sufficient statistics are defined by arbitrary additive forms. We propose two ℓ2,1norm regularized maximum likelihood estimators to learn the model parameters from i.i.d.

We investigate a subclass of exponential family graphical models of which the sufficient statistics are defined by arbitrary additive forms. We propose two $\ell_{2,1}$-norm regularized maximum likelihood estimators to learn the model parameters from i.i.d.

In Theorem 1, the error rate is as expected since max{q,r} theta* _{2,0} is approximately the number of parameters in the model. I think the factor of max{q,r} should not be omitted from Section 1.1, last paragraph so as not to be misleading. I am surprised however that the same factor of max{q,r} is not present in the error rate in Theorem 2, being replaced instead by (q r) inside the logarithm. This result should be checked since if I understand correctly, the number of parameters is still something like q or r times theta*_s _{2,0}. If Theorem 2 is correct as currently stated then a more thorough justification in words is needed.

We investigate a subclass of exponential family graphical models of which the sufficient statistics are defined by arbitrary additive forms.

We investigate a subclass of exponential family graphical models of which the sufficient statistics are defined by arbitrary additive forms. We propose two $\ell_{2,1}$-norm regularized maximum likelihood estimators to learn the model parameters from i.i.d. The first one is a joint MLE estimator which estimates all the parameters simultaneously. The second one is a node-wise conditional MLE estimator which estimates the parameters for each node individually. For both estimators, statistical analysis shows that under mild conditions the extra flexibility gained by the additive exponential family models comes at almost no cost of statistical efficiency.

We investigate a subclass of exponential family graphical models of which the sufficient statistics are defined by arbitrary additive forms. We propose two $\ell_{2,1}$-norm regularized maximum likelihood estimators to learn the model parameters from i.i.d. samples. The first one is a joint MLE estimator which estimates all the parameters simultaneously. The second one is a node-wise conditional MLE estimator which estimates the parameters for each node individually. For both estimators, statistical analysis shows that under mild conditions the extra flexibility gained by the additive exponential family models comes at almost no cost of statistical efficiency. A Monte-Carlo approximation method is developed to efficiently optimize the proposed estimators. The advantages of our estimators over Gaussian graphical models and Nonparanormal estimators are demonstrated on synthetic and real data sets.