Rainbow boxes: a technique for visualizing overlapping sets and an application to the comparison of drugs properties

International audienceOverlapping set visualization is a well-known problem in information visualization. This problem considers elements and sets containing all or part of the elements, a given element possibly belonging to more than one set. A typical example is the properties of the 20 amino-acids. A more complex application is the visual comparison of the contraindications or the adverse effects of several similar drugs. The knowledge involved is voluminous, each drug has many contraindications and adverse effects, some of them are shared with other drugs.In this paper, we present rainbow boxes, a novel technique for visualizing overlapping sets, and its application to the properties of amino-acids and to the comparison of drug properties. We also describe a user study comparing rainbow boxes to tables and showing that the former allowed physicians to find information significantly faster. We finally discuss the limits and the perspectives of rainbow boxes

Sampling Correctors

In many situations, sample data is obtained from a noisy or imperfect source. In order to address such corruptions, this paper introduces the concept of a sampling corrector. Such algorithms use structure that the distribution is purported to have, in order to allow one to make "on-the-fly" corrections to samples drawn from probability distributions. These algorithms then act as filters between the noisy data and the end user. We show connections between sampling correctors, distribution learning algorithms, and distribution property testing algorithms. We show that these connections can be utilized to expand the applicability of known distribution learning and property testing algorithms as well as to achieve improved algorithms for those tasks. As a first step, we show how to design sampling correctors using proper learning algorithms. We then focus on the question of whether algorithms for sampling correctors can be more efficient in terms of sample complexity than learning algorithms for the analogous families of distributions. When correcting monotonicity, we show that this is indeed the case when also granted query access to the cumulative distribution function. We also obtain sampling correctors for monotonicity without this stronger type of access, provided that the distribution be originally very close to monotone (namely, at a distance $O(1/\log^2 n)$). In addition to that, we consider a restricted error model that aims at capturing "missing data" corruptions. In this model, we show that distributions that are close to monotone have sampling correctors that are significantly more efficient than achievable by the learning approach. We also consider the question of whether an additional source of independent random bits is required by sampling correctors to implement the correction process

Multi-Party Threshold Private Set Intersection with Sublinear Communication

In multi-party threshold private set intersection (PSI), $n$ parties each with a private set wish to compute the intersection of their sets if the intersection is sufficiently large. Previously, Ghosh and Simkin (CRYPTO 2019) studied this problem for the two-party case and demonstrated interesting lower and upper bounds on the communication complexity. In this work, we investigate the communication complexity of the multi-party setting $(n\geq 2)$. We consider two functionalities for multi-party threshold PSI. In the first, parties learn the intersection if each of their sets and the intersection differ by at most $T$. In the second functionality, parties learn the intersection if the union of all their sets and the intersection differ by at most $T$. For both functionalities, we show that any protocol must have communication complexity $\Omega(nT)$. We build protocols with a matching upper bound of $O(nT)$ communication complexity for both functionalities assuming threshold FHE. We also construct a computationally more efficient protocol for the second functionality with communication complexity $\widetilde{O}(nT)$ under a weaker assumption of threshold additive homomorphic encryption. As a direct implication, we solve one of the open problems in the work of Ghosh and Simkin (CRYPTO 2019) by designing a two-party protocol with communication cost $\widetilde{O}(T)$ from assumptions weaker than FHE. As a consequence of our results, we achieve the first ``regular\u27\u27 multi-party PSI protocol where the communication complexity only grows with the size of the set difference and does not depend on the size of the input sets