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Neural Information Processing Systems 

We thank the reviewers for their time and their valuable feedback. For the final version, we will improve the presentation as suggested. We address below some of their additional concerns. R2: [contributions] Indeed, the method of moments is not new and has already been applied to ICA and LDA (see refs in the paper). However, given the popularity of LDA in machine learning, we believe that our combination of several threads in this setting makes valuable contributions.