Related papers: Differentially Private Ordinary Least Squares
A general method of minimization using correlation coefficients and order statistics is evaluated relative to least squares procedures in the estimation of parameters for normal data in simple linear regression.
There has been increasing demand for establishing privacy-preserving methodologies for modern statistics and machine learning. Differential privacy, a mathematical notion from computer science, is a rising tool offering robust privacy…
The iteratively reweighted least squares method (IRLS) is a popular technique used in practice for solving regression problems. Various versions of this method have been proposed, but their theoretical analyses failed to capture the good…
A significant hurdle for analyzing large sample data is the lack of effective statistical computing and inference methods. An emerging powerful approach for analyzing large sample data is subsampling, by which one takes a random subsample…
In this paper, we revisit the problem of sparse linear regression in the local differential privacy (LDP) model. Existing research in the non-interactive and sequentially local models has focused on obtaining the lower bounds for the case…
Relating a set of variables X to a response y is crucial in chemometrics. A quantitative prediction objective can be enriched by qualitative data interpretation, for instance by locating the most influential features. When high-dimensional…
The performance of Least Squares (LS) estimators is studied in isotonic, unimodal and convex regression. Our results have the form of sharp oracle inequalities that account for the model misspecification error. In isotonic and unimodal…
In this paper, we investigate one of the most fundamental nonconvex learning problems, ReLU regression, in the Differential Privacy (DP) model. Previous studies on private ReLU regression heavily rely on stringent assumptions, such as…
We study differentially private stochastic optimization in convex and non-convex settings. For the convex case, we focus on the family of non-smooth generalized linear losses (GLLs). Our algorithm for the $\ell_2$ setting achieves optimal…
Least absolute deviation regression is applied using a fixed number of points for all values of the index to estimate the index and scale parameter of the stable distribution using regression methods based on the empirical characteristic…
We present a sample- and time-efficient differentially private algorithm for ordinary least squares, with error that depends linearly on the dimension and is independent of the condition number of $X^\top X$, where $X$ is the design matrix.…
Detecting out-of-distribution (OOD) nodes in the graph-based machine-learning field is challenging, particularly when in-distribution (ID) node multi-category labels are unavailable. Thus, we focus on feature space rather than label space…
We revisit the problem of linear regression under a differential privacy constraint. By consolidating existing pieces in the literature, we clarify the correct dependence of the feature, label and coefficient domains in the optimization…
The purpose of model selection algorithms such as All Subsets, Forward Selection and Backward Elimination is to choose a linear model on the basis of the same set of data to which the model will be applied. Typically we have available a…
In the social sciences, small- to medium-scale datasets are common, and linear regression is canonical. In privacy-aware settings, much work has focused on differentially private (DP) linear regression, but mostly on point estimation with…
This paper aims to reevaluate the Taylor Rule, through a linear and a nonlinear method, such that its estimated federal funds rates match those actually previously implemented by the Federal Reserve Bank. In the linear method, this paper…
We propose an algorithm to select parameter subset combinations that can be estimated using an ordinary least-squares (OLS) inverse problem formulation with a given data set. First, the algorithm selects the parameter combinations that…
High-dimensional spectral data -- routinely generated in dairy production -- are used to predict a range of traits in milk products. Partial least squares (PLS) regression is ubiquitously used for these prediction tasks. However, PLS…
To the best of our knowledge, there are no methods today for training differentially private regression models on sparse input data. To remedy this, we adapt the Frank-Wolfe algorithm for $L_1$ penalized linear regression to be aware of…
Partial Least Squares (PLS) is a widely used method for data integration, designed to extract latent components shared across paired high-dimensional datasets. Despite decades of practical success, a precise theoretical understanding of its…