no code implementations • 21 Mar 2022 • Emanuele Dolera, Stefano Favaro, Edoardo Mainini
In Bayesian statistics, posterior contraction rates (PCRs) quantify the speed at which the posterior distribution concentrates on arbitrarily small neighborhoods of a true model, in a suitable way, as the sample size goes to infinity.
no code implementations • 20 Sep 2021 • Emanuele Dolera, Stefano Favaro
This is obtained through a Bahadur-Rao large deviation expansion for the power of the private LR test, bringing out a critical quantity, as a function of the sample size, the dimension of the table and $(\varepsilon,\delta)$, that determines a loss in the power of the test.
no code implementations • 8 Feb 2021 • Emanuele Dolera, Stefano Favaro, Stefano Peluchetti
Under this more general framework, we apply the arguments of the ``Bayesian" proof of the CMS-DP, suitably adapted to the PYP prior, in order to compute the posterior distribution of a point query, given the hashed data.
no code implementations • 7 Feb 2021 • Emanuele Dolera, Stefano Favaro, Stefano Peluchetti
The count-min sketch (CMS) is a randomized data structure that provides estimates of tokens' frequencies in a large data stream using a compressed representation of the data by random hashing.