Related papers: Robust Estimation via Robust Gradient Estimation

We provide the first global model recovery results for the IRLS (iteratively reweighted least squares) heuristic for robust regression problems. IRLS is known to offer excellent performance, despite bad initializations and data corruption,…

We consider a high-dimensional linear regression problem. Unlike many papers on the topic, we do not require sparsity of the regression coefficients; instead, our main structural assumption is a decay of eigenvalues of the covariance matrix…

We propose an extended generalization of the pseudo Huber loss formulation. We show that using the log-exp transform together with the logistic function, we can create a loss which combines the desirable properties of the strictly convex…

A wide array of machine learning problems are formulated as the minimization of the expectation of a convex loss function on some parameter space. Since the probability distribution of the data of interest is usually unknown, it is is often…

Penalized smoothing is a standard tool in regression analysis. Classical approaches often rely on basis or kernel expansions, which constrain the estimator to a fixed span and impose smoothness assumptions that may be restrictive for…

Good robust estimators can be tuned to combine a high breakdown point and a specified asymptotic efficiency at a central model. This happens in regression with MM- and tau-estimators among others. However, the finite-sample efficiency of…

We develop a new robust geographically weighted regression method in the presence of outliers. We embed the standard geographically weighted regression in robust objective function based on $\gamma$-divergence. A novel feature of the…

The parameters of the log-logistic distribution are generally estimated based on classical methods such as maximum likelihood estimation, whereas these methods usually result in severe biased estimates when the data contain outliers. In…

We develop a family of accelerated stochastic algorithms that minimize sums of convex functions. Our algorithms improve upon the fastest running time for empirical risk minimization (ERM), and in particular linear least-squares regression,…

We propose a robust inferential procedure for assessing uncertainties of parameter estimation in high-dimensional linear models, where the dimension $p$ can grow exponentially fast with the sample size $n$. Our method combines the…

Analyzing polytomous response from a complex survey scheme, like stratified or cluster sampling is very crucial in several socio-economics applications. We present a class of minimum quasi weighted density power divergence estimators for…

By introducing a weight function into the density power divergence, we develop a new class of robust and smooth estimators for the tail index of Pareto-type distributions, offering improved efficiency in the presence of outliers. These…

In this paper, we consider the situation in which the observations follow an isotonic generalized partly linear model. Under this model, the mean of the responses is modelled, through a link function, linearly on some covariates and…

We consider a composite convex minimization problem associated with regularized empirical risk minimization, which often arises in machine learning. We propose two new stochastic gradient methods that are based on stochastic dual averaging…

Empirical risk minimization is the main tool for prediction problems, but its extension to relational data remains unsolved. We solve this problem using recent ideas from graph sampling theory to (i) define an empirical risk for relational…

Network experiments are powerful tools for studying spillover effects, which avoid endogeneity by randomly assigning treatments to units over networks. However, it is non-trivial to analyze network experiments properly without imposing…

Low-rank matrix estimation under heavy-tailed noise is challenging, both computationally and statistically. Convex approaches have been proven statistically optimal but suffer from high computational costs, especially since robust loss…

Several recent works have developed methods for training classifiers that are certifiably robust against norm-bounded adversarial perturbations. These methods assume that all the adversarial transformations are equally important, which is…

Neural estimators are simulation-based estimators for the parameters of a family of statistical models, which build a direct mapping from the sample to the parameter vector. They benefit from the versatility of available network…

Covariance matrices play a major role in statistics, signal processing and machine learning applications. This paper focuses on the \textit{semiparametric} covariance/scatter matrix estimation problem in elliptical distributions. The class…