Designing Privacy Filters for Hidden Markov Processes

We address the problem of releasing a utility process correlated with a hidden sensitive source (both modeled through a hidden Markov model) by designing a privacy filter hiding the sensitive data while maintaining a fidelity criterion on the utility process. The problem is formulated as a constrained minimization of a variant of relative entropy between the sensitive hidden process and the output of the privacy filter. We first explain that in its initial form, the problem is suffering from the curse of dimensionality. Then, we propose a relaxation of it taking into account the information structure of the decoder policies. Such relaxation leads to tractable privacy filtering policies that are illustrated via a simulation study.