We provide an end-to-end differentially private spectral algorithm for learning LDA, based on matrix/tensor decompositions, and establish theoretical guarantees on utility/consistency of the estimated model parameters. The spectral algorithm consists of multiple algorithmic steps, named as {edges}, to which noise could be injected to obtain differential privacy. We identify emph{subsets of edges}, named as {configurations}, such that adding noise to all edges in such a subset guarantees differential privacy of the end-to-end spectral algorithm. We characterize the sensitivity of the edges with respect to the input and thus estimate the amount of noise to be added to each edge for any required privacy level. We then characterize the utility loss for each configuration as a function of injected noise. Overall, by combining the sensitivity and utility characterization, we obtain an end-to-end differentially private spectral algorithm for LDA and identify the corresponding configuration that outperforms others in any specific regime. We are the first to achieve utility guarantees under the required level of differential privacy for learning in LDA. Overall our method systematically outperforms differentially private variational inference.
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