The rapid rise of IoT and Big Data can facilitate the use of data to enhance our quality of life. However, the omnipresent and sensitive nature of data can simultaneously generate privacy concerns. Hence, there is a strong need to develop techniques that ensure the data serve the intended purposes, but not for prying into one's sensitive information. We address this challenge via utility maximizing lossy compression of data. Our techniques combine the mathematical rigor of Kernel Learning models with the structural richness of Deep Neural Networks, and lead to the novel Multi-Kernel Learning and Hybrid Learning models. We systematically construct the proposed models in progressive stages, as motivated by the cumulative improvement in the experimental results from the two previously non-intersecting regimes, namely, Kernel Learning and Deep Neural Networks. The final experimental results of the three proposed models on three mobile sensing datasets show that, not only are our methods able to improve the utility prediction accuracies, but they can also cause sensitive predictions to perform nearly as bad as random guessing, resulting in a win-win situation in terms of utility and privacy.