  Smart meter devices enable a better understanding of the demand at the
potential risk of private information leakage. One promising solution to
mitigating such risk is to inject noises into the meter data to achieve a
certain level of differential privacy. In this paper, we cast one-shot
non-intrusive load monitoring (NILM) in the compressive sensing framework, and
bridge the gap between theoretical accuracy of NILM inference and differential
privacy's parameters. We then derive the valid theoretical bounds to offer
insights on how the differential privacy parameters affect the NILM
performance. Moreover, we generalize our conclusions by proposing the
hierarchical framework to solve the multi-shot NILM problem. Numerical
experiments verify our analytical results and offer better physical insights of
differential privacy in various practical scenarios. This also demonstrates the
significance of our work for the general privacy preserving mechanism design.
