Related papers: Sample Complexity Bounds for Scalar Parameter Esti…
Differential privacy changes the effective sample size governing CVaR learning. For tail mass $\tau$, the privacy-relevant sample size is not $n$, but $n\tau$; equivalently, the effective private tail sample size is $\epsilon n\tau$.…
With changes in privacy laws, there is often a hard requirement for client data to remain on the device rather than being sent to the server. Therefore, most processing happens on the device, and only an altered element is sent to the…
We consider the problem of hypothesis testing for discrete distributions. In the standard model, where we have sample access to an underlying distribution $p$, extensive research has established optimal bounds for uniformity testing,…
The estimation of high dimensional quantum states is an important statistical problem arising in current quantum technology applications. A key example is the tomography of multiple ions states, employed in the validation of state…
Differential privacy is a cryptographically-motivated definition of privacy which has gained significant attention over the past few years. Differentially private solutions enforce privacy by adding random noise to a function computed over…
We study the statistical complexity of private linear regression under an unknown, potentially ill-conditioned covariate distribution. Somewhat surprisingly, under privacy constraints the intrinsic complexity is \emph{not} captured by the…
A central challenge in machine learning is to understand how noise or measurement errors affect low-rank approximations, particularly in the spectral norm. This question is especially important in differentially private low-rank…
Variational quantum circuits characterise the state of a quantum system through the use of parameters that are optimised using classical optimisation procedures that typically rely on gradient information. The circuit-execution complexity…
We prove lower bounds on the number of samples needed to privately estimate the covariance matrix of a Gaussian distribution. Our bounds match existing upper bounds in the widest known setting of parameters. Our analysis relies on the…
In this paper, we establish sample complexity bounds for learning high-dimensional simplices in $\mathbb{R}^K$ from noisy data. Specifically, we consider $n$ i.i.d. samples uniformly drawn from an unknown simplex in $\mathbb{R}^K$, each…
We study the problem of counting the number of distinct elements in a dataset subject to the constraint of differential privacy. We consider the challenging setting of person-level DP (a.k.a. user-level DP) where each person may contribute…
A quantum generalized divergence by definition satisfies the data-processing inequality; as such, the relative decrease in such a divergence under the action of a quantum channel is at most one. This relative decrease is formally known as…
The eligibility of various advanced quantum algorithms will be questioned if they can not guarantee privacy. To fill this knowledge gap, here we devise an efficient quantum differentially private (QDP) Lasso estimator to solve sparse…
We study the computational cost of differential privacy in terms of memory efficiency. While the trade-off between accuracy and differential privacy is well-understood, the inherent cost of privacy regarding memory use remains largely…
Differential privacy is a mathematical notion of data privacy that has fast become the de facto standard in privacy-preserving data analysis. Recently a lot of work has focused on differential privacy in the quantum setting. Continuing on…
Adding random noise to database query results is an important tool for achieving privacy. A challenge is to minimize this noise while still meeting privacy requirements. Recently, a sufficient and necessary condition for $(\epsilon,…
Local differential privacy~(LDP) is an information-theoretic privacy definition suitable for statistical surveys that involve an untrusted data curator. An LDP version of quasi-maximum likelihood estimator~(QMLE) has been developed, but the…
Training differentially private machine learning models requires constraining an individual's contribution to the optimization process. This is achieved by clipping the $2$-norm of their gradient at a predetermined threshold prior to…
We consider differentially private approximate singular vector computation. Known worst-case lower bounds show that the error of any differentially private algorithm must scale polynomially with the dimension of the singular vector. We are…
We study the setup where each of $n$ users holds an element from a discrete set, and the goal is to count the number of distinct elements across all users, under the constraint of $(\epsilon, \delta)$-differentially privacy: - In the…