  Private and public organizations regularly collect and analyze digitalized
data about their associates, volunteers, clients, etc. However, because most
personal data are sensitive, there is a key challenge in designing
privacy-preserving systems. To tackle privacy concerns, research communities
have proposed different methods to preserve privacy, with Differential privacy
(DP) standing out as a formal definition that allows quantifying the
privacy-utility trade-off. Besides, with the local DP (LDP) model, users can
sanitize their data locally before transmitting it to the server. The objective
of this thesis is thus two-fold: O$_1$) To improve the utility and privacy in
multiple frequency estimates under LDP guarantees, which is fundamental to
statistical learning. And O$_2$) To assess the privacy-utility trade-off of
machine learning (ML) models trained over differentially private data. For
O$_1$, we first tackled the problem from two "multiple" perspectives, i.e.,
multiple attributes and multiple collections throughout time, while focusing on
utility. Secondly, we focused our attention on the multiple attributes aspect
only, in which we proposed a solution focusing on privacy while preserving
utility. In both cases, we demonstrate through analytical and experimental
validations the advantages of our proposed solutions over state-of-the-art LDP
protocols. For O$_2$, we empirically evaluated ML-based solutions designed to
solve real-world problems while ensuring DP guarantees. Indeed, we mainly used
the input data perturbation setting from the privacy-preserving ML literature.
This is the situation in which the whole dataset is sanitized independently
and, thus, we implemented LDP algorithms from the perspective of the
centralized data owner. In all cases, we concluded that differentially private
ML models achieve nearly the same utility metrics as non-private ones.
