8 research outputs found
-Divergence Inequalities via Functional Domination
This paper considers derivation of -divergence inequalities via the
approach of functional domination. Bounds on an -divergence based on one or
several other -divergences are introduced, dealing with pairs of probability
measures defined on arbitrary alphabets. In addition, a variety of bounds are
shown to hold under boundedness assumptions on the relative information. The
journal paper, which includes more approaches for the derivation of
f-divergence inequalities and proofs, is available on the arXiv at
https://arxiv.org/abs/1508.00335, and it has been published in the IEEE Trans.
on Information Theory, vol. 62, no. 11, pp. 5973-6006, November 2016.Comment: A conference paper, 5 pages. To be presented in the 2016 ICSEE
International Conference on the Science of Electrical Engineering, Nov.
16--18, Eilat, Israel. See https://arxiv.org/abs/1508.00335 for the full
paper version, published as a journal paper in the IEEE Trans. on Information
Theory, vol. 62, no. 11, pp. 5973-6006, November 201
The Sphere Packing Bound via Augustin's Method
A sphere packing bound (SPB) with a prefactor that is polynomial in the block
length is established for codes on a length product channel
assuming that the maximum order Renyi capacity among the component
channels, i.e. , is . The
reliability function of the discrete stationary product channels with feedback
is bounded from above by the sphere packing exponent. Both results are proved
by first establishing a non-asymptotic SPB. The latter result continues to hold
under a milder stationarity hypothesis.Comment: 30 pages. An error in the statement of Lemma 2 is corrected. The
change is inconsequential for the rest of the pape
On the Privacy of Sublinear-Communication Jaccard Index Estimation via Min-hash Sketching
The min-hash sketch is a well-known technique for low-communication approximation of the Jaccard index between two input sets. Moreover, there is a folklore belief that min-hash sketch based protocols protect the privacy of the inputs. In this paper, we investigate this folklore to quantify the privacy of the min-hash sketch.
We begin our investigation by considering the privacy of min-hash in a centralized setting where the hash functions are chosen by the min-hash functionality and are unknown to the participants. We show that in this case the min-hash output satisfies the standard definition of differential privacy (DP) without any additional noise. This immediately yields a privacy-preserving sublinear-communication semi-honest 2-PC protocol based on FHE where the hash function is evaluated homomorphically.
To improve the efficiency of this protocol, we next consider an implementation in the random oracle model. Here, the protocol participants jointly sample public prefixes for domain separation of the random oracle, and locally evaluate the resulting hash functions on their input sets. Unfortunately, we show that in this public hash function setting, the min-hash output is no longer DP. We therefore consider the notion of distributional differential privacy (DDP) introduced by Bassily et al.~(FOCS 2013). We show that if the honest party\u27s set has sufficiently high min-entropy then the output of the min-hash functionality achieves DDP, again without any added noise. This yields a more efficient semi-honest two-party protocol in the random oracle model, where parties first locally hash their input sets and then perform a 2PC for comparison.
By proving that our protocols satisfy DP and DDP respectively, our results formally confirm and qualify the folklore belief that min-hash based protocols protect the privacy of their inputs