An increasing number of sensors on mobile, Internet of things (IoT), and wearable devices generate time-series measurements of physical activities. Though access to the sensory data is critical to the success of many beneficial applications such as health monitoring or activity recognition, a wide range of potentially sensitive information about the individuals can also be discovered through access to sensory data and this cannot easily be protected using traditional privacy approaches. In this paper, we propose a privacy-preserving sensing framework for managing access to time-series data in order to provide utility while protecting individuals privacy. We introduce Replacement AutoEncoder, a novel algorithm which learns how to transform discriminative features of data that correspond to sensitive inferences, into some features that have been more observed in non-sensitive inferences, to protect users privacy. This efficiency is achieved by defining a user-customized objective function for deep autoencoders. Our replacement method will not only eliminate the possibility of recognizing sensitive inferences, it also eliminates the possibility of detecting the occurrence of them. That is the main weakness of other approaches such as filtering or randomization. We evaluate the efficacy of the algorithm with an activity recognition task in a multi-sensing environment using extensive experiments on three benchmark datasets. We show that it can retain the recognition accuracy of state-of-the-art techniques while simultaneously preserving the privacy of sensitive information. Finally, we utilize the GANs for detecting the occurrence of replacement, after releasing data, and show that this can be done only if the adversarial network is trained on the users original data.