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We introduce an efficient and exact algorithm, together with a faster but approximate version, which implements with a sub-quadratic complexity the hold-out derived from T-estimation. We study empirically the performance of this hold-out in…

In statistics and machine learning, logistic regression is a widely-used supervised learning technique primarily employed for binary classification tasks. When the number of observations greatly exceeds the number of predictor variables, we…

Complex phenomena in engineering and the sciences are often modeled with computationally intensive feed-forward simulations for which a tractable analytic likelihood does not exist. In these cases, it is sometimes necessary to estimate an…

We describe the shrinking neighborhood approach of Robust Statistics, which applies to general smoothly parametrized models, especially, exponential families. Equal generality is achieved by object oriented implementation of the optimally…

Gaussian process regression in its most simplified form assumes normal homoscedastic noise and utilizes analytically tractable mean and covariance functions of predictive posterior distribution using Gaussian conditioning. Its…

We propose reinterpreting copula density estimation as a discriminative task. Under this novel estimation scheme, we train a classifier to distinguish samples from the joint density from those of the product of independent marginals,…

Nonlinear regression problem is one of the most popular and important statistical tasks. The first methods like least squares estimation go back to Gauss and Legendre. Recent models and developments in statistics and machine learning like…

We develop new stochastic gradient methods for efficiently solving sparse linear regression in a partial attribute observation setting, where learners are only allowed to observe a fixed number of actively chosen attributes per example at…

We provide a novel -- and to the best of our knowledge, the first -- algorithm for high dimensional sparse regression with constant fraction of corruptions in explanatory and/or response variables. Our algorithm recovers the true sparse…

We suggest a robust nearest-neighbor approach to classifying high-dimensional data. The method enhances sensitivity by employing a threshold and truncates to a sequence of zeros and ones in order to reduce the deleterious impact of…

Missing data is frequently encountered in many areas of statistics. Propensity score weighting is a popular method for handling missing data. The propensity score method employs a response propensity model, but correct specification of the…

We introduce an optimization model for maximum likelihood-type estimation (M-estimation) that generalizes a large class of existing statistical models, including Huber's concomitant M-estimator, Owen's Huber/Berhu concomitant estimator, the…

This paper studies high-dimensional regression models with lasso when data is sampled under multi-way clustering. First, we establish convergence rates for the lasso and post-lasso estimators. Second, we propose a novel inference method…

Ordinary least square (OLS), maximum likelihood (ML) and robust methods are the widely used methods to estimate the parameters of a linear regression model. It is well known that these methods perform well under some distributional…

Several new estimation methods have been recently proposed for the linear regression model with observation error in the design. Different assumptions on the data generating process have motivated different estimators and analysis. In…

In partially linear additive models the response variable is modelled with a linear component on a subset of covariates and an additive component in which the rest of the covariates enter to the model as a sum of univariate unknown…

We consider the problem of identifying significant predictors in large data bases, where the response variable depends on the linear combination of explanatory variables through an unknown link function, corrupted with the noise from the…

The linear regression models are widely used statistical techniques in numerous practical applications. The standard regression model requires several assumptions about the regres- sors and the error term. The regression parameters are…

Functional data analysis is a fast evolving branch of statistics. Estimation procedures for the popular functional linear model either suffer from lack of robustness or are computationally burdensome. To address these shortcomings, a…

We study the high-dimensional linear regression problem with categorical predictors that have many levels. We propose a new estimation approach, which performs model compression via two mechanisms by simultaneously encouraging (a)…