Optimized Sparse Vector Aggregation Under Local Differential Privacy

In crowdsourcing applications, gathering and analyzing users’ strong positive (1) or negative (-1) reactions to a large number of items is crucial for improving service quality, particularly in recommendation systems. However, protecting users’ privacy while handling diverse sparse patterns in contexts with a large dimension size <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</i> poses significant challenges for efficient and privacy-preserving data aggregation. To address these challenges, in this paper, we propose an optimized <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i>-sparse vector mean estimation scheme under Local Differential Privacy (LDP), ensuring that each user’s entire set of up to <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> private values from {−1, 1} satisfies ε-LDP. Specifically, our proposed scheme employs a seed mining technique in conjunction with PRNG Randomizer, which allows users to send their data only once while enabling the server to accurately estimate any value’s mean in the domain. Our scheme achieves an asymptotically optimal error of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">O</i>( 1/ε√<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> ), equivalent to that of a 1-sparse case, while also ensuring efficient communication costs. The communication cost remains at a minimal level of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">O</i>(1) (only 2 bytes per user’s report) for smaller <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> values and scales to <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">O</i>(<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i>) for larger <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i>, due to efficient binning strategies. Extensive experimental results confirm that our results align with theoretical expectations, demonstrating that our scheme not only preserves user privacy but also ensures higher accuracy compared to other schemes.