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Consider statistical learning (e.g. discrete distribution estimation) with local -differential privacy, which preserves each data provider's privacy locally, we aim to optimize statistical data utility under the privacy constraints. Specifically, we study maximizing mutual information between a provider's data and its private view, and give the exact mutual information bound along with an attainable mechanism: -subset mechanism as results. The mutual information optimal mechanism randomly outputs a size subset of the original data domain with delicate probability assignment, where varies with the privacy level and the data domain size . After analysing the limitations of existing local private mechanisms from mutual information perspective, we propose an efficient implementation of the -subset mechanism for discrete distribution estimation, and show its optimality guarantees over existing approaches.