Provided an arbitrary nonintrusive load monitoring (NILM) algorithm, we seek bounds on the probability of distinguishing between scenarios, given an aggregate power consumption signal. We introduce a framework for studying a general NILM algorithm, and analyze the theory in the general case. Then, we specialize to the case where the error is Gaussian. In both cases, we are able to derive upper bounds on the probability of distinguishing scenarios. Finally, we apply the results to real data to derive bounds on the probability of distinguishing between scenarios as a function of the measurement noise, the sampling rate, and the device usage.
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