  This paper adopts Arimoto's $\alpha$-Mutual Information as a tunable privacy
measure, in a privacy-preserving data release setting that aims to prevent
disclosing private data to adversaries. By fine-tuning the privacy metric, we
demonstrate that our approach yields superior models that effectively thwart
attackers across various performance dimensions. We formulate a general
distortion-based mechanism that manipulates the original data to offer privacy
protection. The distortion metrics are determined according to the data
structure of a specific experiment. We confront the problem expressed in the
formulation by employing a general adversarial deep learning framework that
consists of a releaser and an adversary, trained with opposite goals. This
study conducts empirical experiments on images and time-series data to verify
the functionality of $\alpha$-Mutual Information. We evaluate the
privacy-utility trade-off of customized models and compare them to mutual
information as the baseline measure. Finally, we analyze the consequence of an
attacker's access to side information about private data and witness that
adapting the privacy measure results in a more refined model than the
state-of-the-art in terms of resiliency against side information.
