Related papers: Differentially Private Ordinary Least Squares
We consider the task of privately obtaining prediction error guarantees in ordinary least-squares regression problems with Gaussian covariates (with unknown covariance structure). We provide the first sample-optimal polynomial time…
In this paper we combine two important extensions of ordinary least squares regression: regularization and optimal scaling. Optimal scaling (sometimes also called optimal scoring) has originally been developed for categorical data, and the…
This paper fortifies the recently introduced hierarchical-optimization recursive least squares (HO-RLS) against outliers which contaminate infrequently linear-regression models. Outliers are modeled as nuisance variables and are estimated…
Linear Vector AutoRegressive (VAR) models where the innovations could be unconditionally heteroscedastic and serially dependent are considered. The volatility structure is deterministic and quite general, including breaks or trending…
Given a linear regression setting, Iterative Least Trimmed Squares (ILTS) involves alternating between (a) selecting the subset of samples with lowest current loss, and (b) re-fitting the linear model only on that subset. Both steps are…
We consider least squares estimation in a general nonparametric regression model. The rate of convergence of the least squares estimator (LSE) for the unknown regression function is well studied when the errors are sub-Gaussian. We find…
Functional partial least squares (FPLS) is commonly used for fitting scalar-on-function regression models. For the sake of accuracy, FPLS demands that each realization of the functional predictor is recorded as densely as possible over the…
We study the total least squares (TLS) problem that generalizes least squares regression by allowing measurement errors in both dependent and independent variables. TLS is widely used in applied fields including computer vision, system…
Least squares (LS)-based subset selection methods are popular in linear regression modeling. Best subset selection (BS) is known to be NP-hard and has a computational cost that grows exponentially with the number of predictors. Recently,…
A new statistical technique for constructing linear latent structure (LLS) models from available data, supported by well established theoretical results and an efficient algorithm, is presented. The method reduces the problem of estimating…
In order to sample marginalized and/or hard-to-reach populations, respondent-driven sampling (RDS) and similar techniques reach their participants via peer referral. Under a Markov model for RDS, previous research has shown that if the…
We investigate a problem of finding the minimum, in which each user has a real value and we want to estimate the minimum of these values under the local differential privacy constraint. We reveal that this problem is fundamentally…
Testing whether a sample survey is a credible representation of the population is an important question to ensure the validity of any downstream research. While this problem, in general, does not have an efficient solution, one might take a…
The analysis of survey data is a frequently arising issue in clinical trials, particularly when capturing quantities which are difficult to measure. Typical examples are questionnaires about patient's well-being, pain, or consent to an…
Linear $L_1$-regularized models have remained one of the simplest and most effective tools in data science. Over the past decade, screening rules have risen in popularity as a way to eliminate features when producing the sparse regression…
In real data analysis with structural equation modeling, data are unlikely to be exactly normally distributed. If we ignore the non-normality reality, the parameter estimates, standard error estimates, and model fit statistics from normal…
We study the problem of Differentially Private Stochastic Convex Optimization (DP-SCO) with heavy-tailed data. Specifically, we focus on the $\ell_1$-norm linear regression in the $\epsilon$-DP model. While most of the previous work focuses…
We give the first polynomial-time algorithm for performing linear or polynomial regression resilient to adversarial corruptions in both examples and labels. Given a sufficiently large (polynomial-size) training set drawn i.i.d. from…
Linear regression in $\ell_p$-norm is a canonical optimization problem that arises in several applications, including sparse recovery, semi-supervised learning, and signal processing. Generic convex optimization algorithms for solving…
With a rapid increase in volume and complexity of data sets, there is a need for methods that can extract useful information, for example the relationship between two data sets measured for the same persons. The Partial Least Squares (PLS)…