Lossy Communication Subject to Statistical Parameter Privacy

German Bassi (1) , Pablo Piantanida (2) , Mikael Skoglund (1)

1 KTH - Royal Institute of Technology [Stockholm]
2 L2S - Laboratoire des signaux et systèmes

We investigate the problem of sharing (communi-cating) the outcomes of a memoryless source when some of its statistical parameters must be kept private. Privacy is measured in terms of the Bayesian statistical risk according to a desired loss function while the quality of the reconstruction is measured by the average per-letter distortion. We first bound -uniformly over all possible estimators- the expected risk from below. This information-theoretic bound depends on the mutual information between the parameters and the disclosed (noisy) samples. We then present an achievable scheme that guarantees an upper bound on the average distortion while keeping the risk above a desired threshold, even when the length of the sample increases.

Domains: Information Theory [cs.IT]; Information Theory [math.IT]; Statistics [math.ST]; Machine Learning [cs.LG]

German Bassi, Pablo Piantanida, Mikael Skoglund. Lossy Communication Subject to Statistical Parameter Privacy. IEEE International Symposium on Information Theory (ISIT 2018), Jun 2018, Vail, United States. ⟨10.1109/isit.2018.8437690⟩. ⟨hal-01756020⟩