Related papers: Private Adaptive Covariance Estimation via Gaussia…
We provide optimal lower bounds for two well-known parameter estimation (also known as statistical estimation) tasks in high dimensions with approximate differential privacy. First, we prove that for any $\alpha \le O(1)$, estimating the…
Gaussian processes (GP) provide a prior over functions and allow finding complex regularities in data. Gaussian processes are successfully used for classification/regression problems and dimensionality reduction. In this work we consider…
Differential privacy guarantees allow the results of a statistical analysis involving sensitive data to be released without compromising the privacy of any individual taking part. Achieving such guarantees generally requires the injection…
Due to massive amounts of data distributed across multiple locations, distributed machine learning has attracted a lot of research interests. Alternating Direction Method of Multipliers (ADMM) is a powerful method of designing distributed…
Given a group size m and a sensitive dataset D, group privacy (GP) releases information about D with the guarantee that the adversary cannot infer with high confidence whether the underlying data is D or a neighboring dataset D' that…
We propose an adaptive (stochastic) gradient perturbation method for differentially private empirical risk minimization. At each iteration, the random noise added to the gradient is optimally adapted to the stepsize; we name this process…
The Gaussian process (GP) regression model is a widely employed surrogate modeling technique for computer experiments, offering precise predictions and statistical inference for the computer simulators that generate experimental data.…
This work introduces the concept of parametric Gaussian processes (PGPs), which is built upon the seemingly self-contradictory idea of making Gaussian processes parametric. Parametric Gaussian processes, by construction, are designed to…
We design a class of additive noise mechanisms that satisfy \((\varepsilon, \delta)\)-differential privacy (DP) for scalar, real-valued query functions with known sensitivities, with a particular focus on moderate and low-privacy regimes.…
Continuous-time trajectory representations are a powerful tool that can be used to address several issues in many practical simultaneous localization and mapping (SLAM) scenarios, like continuously collected measurements distorted by robot…
Gaussian Processes (\textbf{GPs}) are flexible non-parametric models with strong probabilistic interpretation. While being a standard choice for performing inference on time series, GPs have few techniques to work in a streaming setting.…
In this paper, we investigate a class of approximate Gaussian processes (GP) obtained by taking a linear combination of compactly supported basis functions with the basis coefficients endowed with a dependent Gaussian prior distribution.…
This paper presents a Gaussian process (GP) model for estimating piecewise continuous regression functions. In scientific and engineering applications of regression analysis, the underlying regression functions are piecewise continuous in…
Estimating a covariance matrix and its associated principal components is a fundamental problem in contemporary statistics. While optimal estimation procedures have been developed with well-understood properties, the increasing demand for…
In this paper we study the problem of estimating the unknown mean $\theta$ of a unit variance Gaussian distribution in a locally differentially private (LDP) way. In the high-privacy regime ($\epsilon\le 1$), we identify an optimal privacy…
The Gaussian process (GP) is a popular way to specify dependencies between random variables in a probabilistic model. In the Bayesian framework the covariance structure can be specified using unknown hyperparameters. Integrating over these…
Although distributed Gaussian process regression (GPR) enables multiple agents with separate datasets to jointly learn a model of the target function, its collaborative nature poses risks of private data leakage. To address this, we propose…
Despite a large corpus of recent work on scaling up Gaussian processes, a stubborn trade-off between computational speed, prediction and uncertainty quantification accuracy, and customizability persists. This is because the vast majority of…
In the low-dimensional case, the generalized additive coefficient model (GACM) proposed by Xue and Yang [Statist. Sinica 16 (2006) 1423-1446] has been demonstrated to be a powerful tool for studying nonlinear interaction effects of…
Differential privacy has seen remarkable success as a rigorous and practical formalization of data privacy in the past decade. This privacy definition and its divergence based relaxations, however, have several acknowledged weaknesses,…