Improving the utility of locally differentially private protocols for longitudinal and multidimensional frequency estimates

This paper investigates the problem of collecting multidimensional data throughout time (i.e., longitudinal studies) for fundamental task frequency estimation under Local Differential Privacy (LDP) guarantees. Contrary to a single attribute, aspect demands particular attention privacy budget. Besides, when user statistics longitudinally, progressively degrades. Indeed, "multiple" settings in combination many attributes and several collections time) impose challenges, which this proposes first solution estimates LDP. To tackle these issues, we extend analysis three state-of-the-art LDP protocols (Generalized Randomized Response -- GRR, Optimized Unary Encoding OUE, Symmetric SUE) both collections. While known literature uses OUE SUE two rounds sanitization (a.k.a. memoization), i.e., L-OUE L-SUE, respectively, analytically experimentally show that starting with then provides higher utility L-OSUE). Also, small domain sizes, propose Longitudinal GRR (L-GRR), than other based on unary encoding. Last, also new named Adaptive LOngitudinal Multidimensional FREquency Estimates (ALLOMFREE), randomly samples attribute be sent whole budget adaptively selects optimal protocol, either L-GRR or L-OSUE. As shown results, ALLOMFREE consistently considerably outperforms L-SUE quality estimates.