Related papers: Differentially Private Bayesian Inference for Gaus…
In differential privacy, random noise is introduced to privatize summary statistics of a sensitive dataset before releasing them. The noise level determines the privacy loss, which quantifies how easily an adversary can detect a target…
We propose a new highly flexible and tractable Bayesian approach to undertake variable selection in non-Gaussian regression models. It uses a copula decomposition for the joint distribution of observations on the dependent variable. This…
Learning the parameters of Gaussian mixture models is a fundamental and widely studied problem with numerous applications. In this work, we give new algorithms for learning the parameters of a high-dimensional, well separated, Gaussian…
Kaplan-Meier estimators are essential tools in survival analysis, capturing the survival behavior of a cohort. Their accuracy improves with large, diverse datasets, encouraging data holders to collaborate for more precise estimations.…
Differential privacy (DP) is obtained by randomizing a data analysis algorithm, which necessarily introduces a tradeoff between its utility and privacy. Many DP mechanisms are built upon one of two underlying tools: Laplace and Gaussian…
We develop adaptive estimation and inference methods for high-dimensional Gaussian copula regression that achieve the same performance without the knowledge of the marginal transformations as that for high-dimensional linear regression.…
Differential privacy has gained popularity in machine learning as a strong privacy guarantee, in contrast to privacy mitigation techniques such as k-anonymity. However, applying differential privacy to n-gram counts significantly degrades…
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.…
The Gaussian mechanism (GM) represents a universally employed tool for achieving differential privacy (DP), and a large body of work has been devoted to its analysis. We argue that the three prevailing interpretations of the GM, namely…
We present novel, computationally efficient, and differentially private algorithms for two fundamental high-dimensional learning problems: learning a multivariate Gaussian and learning a product distribution over the Boolean hypercube in…
Differential privacy is becoming a gold standard for privacy research; it offers a guaranteed bound on loss of privacy due to release of query results, even under worst-case assumptions. The theory of differential privacy is an active…
We introduce the multi-dimensional Skellam mechanism, a discrete differential privacy mechanism based on the difference of two independent Poisson random variables. To quantify its privacy guarantees, we analyze the privacy loss…
We introduce derivative sensitivity, an analogue to local sensitivity for continuous functions. We use this notion in an analysis that determines the amount of noise to be added to the result of a database query in order to obtain a certain…
Differential privacy is a widely adopted framework designed to safeguard the sensitive information of data providers within a data set. It is based on the application of controlled noise at the interface between the server that stores and…
We study the problem of estimating mixtures of Gaussians under the constraint of differential privacy (DP). Our main result is that $\text{poly}(k,d,1/\alpha,1/\varepsilon,\log(1/\delta))$ samples are sufficient to estimate a mixture of $k$…
In this work, we propose differentially private methods for hypothesis testing, model averaging, and model selection for normal linear models. We consider Bayesian methods based on mixtures of $g$-priors and non-Bayesian methods based on…
The Gaussian distribution is widely used in mechanism design for differential privacy (DP). Thanks to its sub-Gaussian tail, it significantly reduces the chance of outliers when responding to queries. However, it can only provide…
We propose PACE-GGM, a data-adaptive differentially private method for covariance estimation that concentrates its privacy budget on the most informative entries of the empirical covariance matrix, rather than perturbing all entries. This…
Gaussian copulas are widely used in the industry to correlate two random variables when there is no prior knowledge about the co-dependence between them. The perturbed Gaussian copula approach allows introducing the skew information of both…
We develop a novel Bayesian method to select important predictors in regression models with multiple responses of diverse types. A sparse Gaussian copula regression model is used to account for the multivariate dependencies between any…