Related papers: A Tutorial on Computing $t$-Closeness
We propose a numerical accountant for evaluating the tight $(\varepsilon,\delta)$-privacy loss for algorithms with discrete one dimensional output. The method is based on the privacy loss distribution formalism and it uses the recently…
Bures distance holds a special place among various distance measures due to its several distinguished features and finds applications in diverse problems in quantum information theory. It is related to fidelity and, among other things, it…
Computability on uncountable sets has no standard formalization, unlike that on countable sets, which is given by Turing machines. Some of the approaches to define computability in these sets rely on order-theoretic structures to translate…
Organizations that collect and analyze data may wish or be mandated by regulation to justify and explain their analysis results. At the same time, the logic that they have followed to analyze the data, i.e., their queries, may be…
Metric magnitude is a measure of the "size" of point clouds with many desirable geometric properties. It has been adapted to various mathematical contexts and recent work suggests that it can enhance machine learning and optimization…
Distributed algorithms for network science applications are of great importance due to today's large real-world networks. In such algorithms, a node is allowed only to have local interactions with its immediate neighbors. This is because…
Personalized PageRank (PPR) is a traditional measure for node proximity on large graphs. For a pair of nodes $s$ and $t$, the PPR value $\pi_s(t)$ equals the probability that an $\alpha$-discounted random walk from $s$ terminates at $t$ and…
The purpose of this paper is to give a survey on the notions of distance between subsets either of a metric space or of a measure space, including definitions, a classification, and a discussion of the best-known distance functions, which…
Differential privacy (DP) has become the de facto standard for protecting sensitive data, providing strong guarantees that published statistics or models reveal limited information about any individual. However, privacy noise and restricted…
Clustering is a popular machine learning technique for data mining that can process and analyze datasets to automatically reveal sample distribution patterns. Since the ubiquitous categorical data naturally lack a well-defined metric space…
The current COVID-19 pandemic highlights the utility of contact tracing, when combined with case isolation and social distancing, as an important tool for mitigating the spread of a disease [1]. Contact tracing provides a mechanism of…
The Turing machine is one of the simple abstract computational devices that can be used to investigate the limits of computability. In this paper, they are considered from several points of view that emphasize the importance and the…
Let $X$ be a set and $2^X$ be a set of all subsets of $X$. The necessary and sufficient conditions under which a mapping $X \to 2^X$ is a closure of one-point sets in some $T_0$-space $(X, \tau)$ are described. It is proved that every…
The goal of clustering is to group similar objects into meaningful partitions. This process is well understood when an explicit similarity measure between the objects is given. However, far less is known when this information is not readily…
This paper introduces a new clustering technique, called {\em dimensional clustering}, which clusters each data point by its latent {\em pointwise dimension}, which is a measure of the dimensionality of the data set local to that point.…
Symbolic data structures for model checking timed systems have been subject to a significant research, with Difference Bound Matrices (DBMs) still being the preferred data structure in several mature verification tools. In comparison,…
Programmatically generating tight differential privacy (DP) bounds is a hard problem. Two core challenges are (1) finding expressive, compact, and efficient encodings of the distributions of DP algorithms, and (2) state space explosion…
For localization and mapping of indoor environments through WiFi signals, locations are often represented as likelihoods of the received signal strength indicator. In this work we compare various measures of distance between such…
A growing framework of legal and ethical requirements limit scientific and commercial evalua-tion of personal data. Typically, pseudonymization, encryption, or methods of distributed com-puting try to protect individual privacy. However,…
Thermodynamics (in concert with its sister discipline, statistical physics) can be regarded as a data reduction scheme based on partitioning a total system into a subsystem and a bath that weakly interact with each other. The ubiquity and…