Reviews: Learning Additive Exponential Family Graphical Models via \ell_{2,1} -norm Regularized M-Estimation

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.