Related papers: The Basic Discrete Hilbert Transform with an Infor…
A succinct histogram captures frequent items and their frequencies across clients and has become increasingly important for large-scale, privacy-sensitive machine learning applications. To develop a rigorous framework to guarantee privacy…
In this paper, we propose a new method to estimate instantaneous frequency using a combined approach based on the discrete linear chirp transform (DLCT) and the Wigner distribution (WD). The DLCT locally represents a signal as a…
Whispered speech as an acceptable form of human-computer interaction is gaining traction. Systems that address multiple modes of speech require a robust front-end speech classifier. Performance of whispered vs normal speech classification…
The discrete curvelet transform decomposes an image into a set of fundamental components that are distinguished by direction and size as well as a low-frequency representation. The curvelet representation is approximately sparse; thus, it…
Distributed data analysis is a large and growing field driven by a massive proliferation of user devices, and by privacy concerns surrounding the centralised storage of data. We consider two \emph{adaptive} algorithms for estimating one…
We consider the problem of estimating sparse discrete distributions under local differential privacy (LDP) and communication constraints. We characterize the sample complexity for sparse estimation under LDP constraints up to a constant…
The present chapter [submitted for publication in "Fourier Transforms, Theory and Applications", G. Nikolic (Ed.), InTech (Open Access Publisher), Vienna, 2011] is concerned with the introduction and study of a quadratic discrete Fourier…
Noisy gradient descent and its variants are the predominant algorithms for differentially private machine learning. It is a fundamental question to quantify their privacy leakage, yet tight characterizations remain open even in the…
Federated learning promises to make machine learning feasible on distributed, private datasets by implementing gradient descent using secure aggregation methods. The idea is to compute a global weight update without revealing the…
In this note, we consider the problem of differentially privately (DP) computing an anonymized histogram, which is defined as the multiset of counts of the input dataset (without bucket labels). In the low-privacy regime $\epsilon \geq 1$,…
Via chirp functions from fractional Fourier transforms, the authors introduce fractional Riesz potentials related to chirp functions, establish their relations with fractional Fourier transforms, fractional Laplace operators related to…
In the past decade analysis of big data has proven to be extremely valuable in many contexts. Local Differential Privacy (LDP) is a state-of-the-art approach which allows statistical computations while protecting each individual user's…
This paper presents a new approach in application of the Fourier transform to the complex error function resulting in an efficient rational approximation. Specifically, the computational test shows that with only $17$ summation terms the…
In this short note, we present few results on the use of the discrete Laplace transform in solving first and second order initial value problems of discrete differential equations.
We present a brief review of discrete structures in a finite Hilbert space, relevant for the theory of quantum information. Unitary operator bases, mutually unbiased bases, Clifford group and stabilizer states, discrete Wigner function,…
Data hiding is the art of embedding data into digital media in a way such that the existence of data remains concealed from everyone except the intended recipient. In this paper, we discuss the various Least Significant Bit (LSB) data…
Differential Privacy (DP) mechanisms, especially in high-dimensional settings, often face the challenge of maintaining privacy without compromising the data utility. This work introduces an innovative shuffling mechanism in…
Differentially private multiple testing procedures can protect the information of individuals used in hypothesis tests while guaranteeing a small fraction of false discoveries. In this paper, we propose a differentially private adaptive FDR…
Digital Transforms have important applications on subjects such as channel coding, cryptography and digital signal processing. In this paper, two Fourier Transforms are considered, the discrete time Fourier transform (DTFT) and the finite…
Sensitive statistics are often collected across sets of users, with repeated collection of reports done over time. For example, trends in users' private preferences or software usage may be monitored via such reports. We study the…