In this paper, we study the problem of estimating smooth Generalized Linear Models (GLM)
in the Non-interactive Local Differential Privacy (NLDP) model. Different from its classical
setting, our model allows the server to access some additional public but unlabeled data. By
using Stein's lemma and its variants, we first show that there is an $(\epsilon,\delta) $-NLDP
algorithm for GLM (under some mild assumptions), if each data record is iid sampled from
some sub-Gaussian distribution with bounded $\ell_1 $-norm. Then with high probability, the …

In this paper, we study the problem of estimating smooth Generalized Linear Models (GLMs)
in the Non-interactive Local Differential Privacy (NLDP) model. Different from its classical
setting, our model allows the server to access some additional public but unlabeled data. In
the first part of the paper we focus on GLMs. Specifically, we first consider the case where
each data record is iid sampled from a zero-mean multivariate Gaussian distribution.
Motivated by the Stein's lemma, we present an $(\epsilon,\delta) $-NLDP algorithm for …