Related papers: A universal robustification procedure
This PhD thesis contains several contributions to the field of statistical causal modeling. Statistical causal models are statistical models embedded with causal assumptions that allow for the inference and reasoning about the behavior of…
A general method to combine several estimators of the same quantity is investigated. In the spirit of model and forecast averaging, the final estimator is computed as a weighted average of the initial ones, where the weights are constrained…
We propose a scalable robust learning algorithm combining kernel smoothing and robust optimization. Our method is motivated by the convex analysis perspective of distributionally robust optimization based on probability metrics, such as the…
Under a partially linear models we study a family of robust estimates for the regression parameter and the regression function when some of the predictor variables take values on a Riemannian manifold. We obtain the consistency and the…
We develop an asymptotic theory of adversarial estimators ('A-estimators'). They generalize maximum-likelihood-type estimators ('M-estimators') as their average objective is maximized by some parameters and minimized by others. This class…
Wasserstein distributionally robust estimators have emerged as powerful models for prediction and decision-making under uncertainty. These estimators provide attractive generalization guarantees: the robust objective obtained from the…
In this paper, we develop a computational approach for estimating the mean value of a quantity in the presence of uncertainty. We demonstrate that, under some mild assumptions, the upper and lower bounds of the mean value are efficiently…
To tackle massive data, subsampling is a practical approach to select the more informative data points. However, when responses are expensive to measure, developing efficient subsampling schemes is challenging, and an optimal sampling…
Robust estimation of a mean vector, a topic regarded as obsolete in the traditional robust statistics community, has recently surged in machine learning literature in the last decade. The latest focus is on the sub-Gaussian performance and…
In this paper we study the aggregation problem that can be formulated as follows. Assume that we have a family of estimators $\mathcal{F}$ built on the basis of available observations. The goal is to construct a new estimator whose risk is…
There has been increasing interest in recent years in the development of approaches to estimate causal effects when the number of potential confounders is prohibitively large. This growth in interest has led to a number of potential…
We propose to smooth the entire objective function, rather than only the check function, in a linear quantile regression context. Not only does the resulting smoothed quantile regression estimator yield a lower mean squared error and a more…
Causal inference with observational studies often relies on the assumptions of unconfoundedness and overlap of covariate distributions in different treatment groups. The overlap assumption is violated when some units have propensity scores…
Randomized smoothing is the current state-of-the-art method for producing provably robust classifiers. While randomized smoothing typically yields robust $\ell_2$-ball certificates, recent research has generalized provable robustness to…
We propose dual regression as an alternative to the quantile regression process for the global estimation of conditional distribution functions under minimal assumptions. Dual regression provides all the interpretational power of the…
Several statistical models are given in the form of unnormalized densities, and calculation of the normalization constant is intractable. We propose estimation methods for such unnormalized models with missing data. The key concept is to…
We introduce and study a family of robust estimators for the functional logistic regression model whose robustness automatically adapts to the data thereby leading to estimators with high efficiency in clean data and a high degree of…
Asymptotic expansions for a wide class of distribution are studied. A simple method for computation of the series coefficients is suggested. The case when regularization parameter of the distribution depends on the asymptotic parameter is…
We study the isotonic regression estimator over a general countable pre-ordered set. We obtain the limiting distribution of the estimator and study its properties. It is proved that, under some general assumptions, the limiting distribution…
We study the problem of robustly estimating the posterior distribution for the setting where observed data can be contaminated with potentially adversarial outliers. We propose Rob-ULA, a robust variant of the Unadjusted Langevin Algorithm…