相关论文: Fast Private Kernel Density Estimation via Localit…

We propose a differentially private data generation paradigm using random feature representations of kernel mean embeddings when comparing the distribution of true data with that of synthetic data. We exploit the random feature…

Deep Gaussian process models typically employ discrete hierarchies, but recent advancements in differential Gaussian processes (DiffGPs) have extended these models to infinite depths. However, existing DiffGP approaches often overlook the…

We introduce a novel framework for differentially private (DP) statistical estimation via data truncation, addressing a key challenge in DP estimation when the data support is unbounded. Traditional approaches rely on problem-specific…

We investigate unbiased high-dimensional mean estimators in differential privacy. We consider differentially private mechanisms whose expected output equals the mean of the input dataset, for every dataset drawn from a fixed bounded…

We construct deterministic particle solutions for linear and fast diffusion equations using a nonlocal approximation. We exploit the $2$-Wasserstein gradient flow structure of the equations in order to obtain the nonlocal approximating PDEs…

A fundamental drawback of kernel-based statistical models is their limited scalability to large data sets, which requires resorting to approximations. In this work, we focus on the popular Gaussian kernel and on techniques to linearize…

Gaussian process (GP) regression provides a flexible, nonparametric framework for probabilistic modeling, yet remains computationally demanding in large-scale applications. For one-dimensional data, state space (SS) models achieve…

In this paper we present the theoretical framework needed to justify the use of a kernel-based collocation method (meshfree approximation method) to estimate the solution of high-dimensional stochastic partial differential equations…

In this work, we introduce a new approach for statistical quantification of differential privacy in a black box setting. We present estimators and confidence intervals for the optimal privacy parameter of a randomized algorithm $A$, as well…

A kernel method is proposed to estimate the condensed density of the generalized eigenvalues of pencils of Hankel matrices whose elements have a joint noncentral Gaussian distribution with nonidentical covariance. These pencils arise when…

Differentially private (DP) machine learning has recently become popular. The privacy loss of DP algorithms is commonly reported using $(\varepsilon,\delta)$-DP. In this paper, we propose a numerical accountant for evaluating the privacy…

Local polynomial density (LPD) estimators are widely used for inference on boundary features of the density function. Contrary to conventional wisdom, we show that kernel choice substantially affects efficiency. Theory, simulations, and…

Non-interactive Local Differential Privacy (LDP) requires data analysts to collect data from users through noisy channel at once. In this paper, we extend the frontiers of Non-interactive LDP learning and estimation from several aspects.…

We introduce an alternative method for the calculation of sky maps from data taken with gamma-ray telescopes. In contrast to the established method of smoothing the 2D histogram of reconstructed event directions with a static kernel, we…

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 design new differentially private algorithms for the Euclidean k-means problem, both in the centralized model and in the local model of differential privacy. In both models, our algorithms achieve significantly improved error guarantees…

A major challenge for machine learning is increasing the availability of data while respecting the privacy of individuals. Here we combine the provable privacy guarantees of the differential privacy framework with the flexibility of…

Developing efficient numerical algorithms for the solution of high dimensional random Partial Differential Equations (PDEs) has been a challenging task due to the well-known curse of dimensionality. We present a new solution framework for…

Recent years, local differential privacy (LDP) has been adopted by many web service providers like Google \cite{erlingsson2014rappor}, Apple \cite{apple2017privacy} and Microsoft \cite{bolin2017telemetry} to collect and analyse users' data…

As the third paper in a series regarding the estimation of luminosity functions (LFs) via kernel density estimation (KDE), we present a further generalization of our framework by extending its applicability to multiple flux-limited samples.…