Paper ID: | 82 |
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Title: | Private Hypothesis Selection |

This work studies the differentially private hypothesis selection problem. Hypothesis selection problem is a workhorse of statistics/ML and these tasks are often performed on data that is privacy-sensitive, e.g. health data. This work studies the differentially private version of this question. A bit more precisely, given a set of hypotheses Q_1,...Q_k, and given samples from a distribution P, the goal is to find an (approximate) minimizer of the statistical distance between P and Q_i's. This is a well studied problem. The authors show sample complexity bounds to solve this problem privately, and show applications of this algorithm. Comments: The factor of 7 is worse than the classical non-private bound of 3. Can this be improved? Also, the factor of 3 has been improved to 2 for the improper case. Can your work be extended to improve the bound for the improper case.?