Related papers: Private measurement of nonlinear correlations betw…

In this paper, the defining properties of a valid measure of the dependence between two random variables are reviewed and complemented with two original ones, shown to be more fundamental than other usual postulates. While other popular…

As the use of differential privacy (DP) becomes widespread, the development of effective tools for reasoning about the privacy guarantee becomes increasingly critical. In pursuit of this goal, we demonstrate novel relationships between DP…

Distance covariance and distance correlation have been widely adopted in measuring dependence of a pair of random variables or random vectors. If the computation of distance covariance and distance correlation is implemented directly…

Linear regression is a fundamental tool for statistical analysis, which has motivated the development of linear regression methods that satisfy provable privacy guarantees so that the learned model reveals little about any one data point…

Distance correlation is a new measure of dependence between random vectors. Distance covariance and distance correlation are analogous to product-moment covariance and correlation, but unlike the classical definition of correlation,…

We investigate the problem of detecting dependencies between the components of a high-dimensional vector. Our approach advances the existing literature in two important respects. First, we consider the problem under privacy constraints.…

In regression analysis, associations between continuous predictors and the outcome are often assumed to be linear. However, modeling the associations as non-linear can improve model fit. Many flexible modeling techniques, like (fractional)…

Data scientists often seek to identify the most important features in high-dimensional datasets. This can be done through $L_1$-regularized regression, but this can become inefficient for very high-dimensional datasets. Additionally,…

Gaussian copulas are widely used to estimate multivariate distributions and relationships. We present algorithms for estimating Gaussian copula correlations that ensure differential privacy. We first convert data values into sets of two-way…

The release of differentially private streaming data has been extensively studied, yet striking a good balance between privacy and utility on temporally correlated data in the stream remains an open problem. Existing works focus on…

Differential privacy (DP) has become the de facto standard for protecting sensitive data, providing strong guarantees that published statistics or models reveal limited information about any individual. However, privacy noise and restricted…

Mutual information is a nonlinear measure used in time series analysis in order to measure the linear and non-linear correlations at any lag $\tau$. The aim of this study is to evaluate some of the most commonly used mutual information…

Recently, the first author proposed a measure to calculate Pearson correlations for node values expressed in a network, by taking into account distances or metrics defined on the network. In this technical note, we show that using an…

We propose a method for detecting differential gene expression that exploits the correlation between genes. Our proposal averages the univariate scores of each feature with the scores in correlation neighborhoods. In a number of real and…

We introduce the coverage correlation coefficient, a novel nonparametric measure of statistical association designed to quantifies the extent to which two random variables have a joint distribution concentrated on a singular subset with…

Hypothesis tests are a crucial statistical tool for data mining and are the workhorse of scientific research in many fields. Here we study differentially private tests of independence between a categorical and a continuous variable. We take…

Principal components analysis (PCA) is a standard tool for identifying good low-dimensional approximations to data in high dimension. Many data sets of interest contain private or sensitive information about individuals. Algorithms which…

In this paper, we consider differentially private classification when some features are sensitive, while the rest of the features and the label are not. We adapt the definition of differential privacy naturally to this setting. Our main…

Learning a classifier from private data collected by multiple parties is an important problem that has many potential applications. How can we build an accurate and differentially private global classifier by combining locally-trained…

In certain privacy-sensitive scenarios within fields such as clinical trial simulations, federated learning, and distributed learning, researchers often face the challenge of estimating correlations between variables without access to…