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We are very grateful to the careful and throughout reviews from all reviewers. Reviewer_1 The reviewer comments that our novel results are both practically and theoretically important, and also suggests that we provide more discussion and examples on our technical conditions such as the decomposability condition, subspace compatibility constant etc. We have done so, though due to space limitations we have pushed examples illustrating our conditions to the supplementary material, in the section on proof ingredients for the results in section 5. In detail, for each model, we check and illustrate why those aforementioned technical conditions hold in every subsection of Section B. We will try to illustrate these comments in the main paper. Reviewer_2 The reviewer suggests giving more illustration about why the existing theoretical framework for regularization does not work for inference with latent variables. Briefly, the reason is as follows.