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We thank all the reviewers for their valuable comments and suggestions. We will revise accordingly in the final version. Response to Reviewer_1 The conditions on the initial solution can be satisfied in two ways: (i) Do multiple random initializations and use the initial solution leading to largest Q function. This is a heuristic that practitioners often do for EM algorithm; (ii) Use result of tensor methods, e.g., [9], as an initial solution, for which we can obtain rigorous theoretical guarantees. We would like to suggest the use of gradient ascent implementation for two reasons: (i) For complex models, it can be hard to derive the closed form of the exact M-step; (ii) For high dimensional models, the exact M-step is not always well defined.