We present the first efficient and provably consistent estimator for the robust regression problem. The area of robust learning and optimization has generated a significant amount of interest in the learning and statistics communities in recent years owing to its applicability in scenarios with corrupted data, as well as in handling model mis-specifications. In particular, special interest has ...

In this research, a robust optimization approach applied to support vector regression (SVR) is investigated. A novel kernel based-method is developed to address the problem of data uncertainty where each data point is inside a sphere. The model is called robust SVR. Computational results show that the resulting robust SVR model is better than traditional SVR in terms of robustness and generaliz...

Partial Least Squares (PLS) is a standard statistical method in chemometrics. It can be considered as an incomplete, or “partial”, version of the Least Squares estimator of regression, applicable when high or perfect multicollinearity is present in the predictor variables. The Least Squares estimator is well-known to be an optimal estimator for regression, but only when the error terms are norm...

Making any type of decision, from buying a car to siting a nuclear plant, from choosing the best student deserving a scholarship to ranking the cities of the world according to their liveability, involves the evaluation of several alternatives with respect to different aspects, technically called evaluation criteria. Multiple Criteria Decision Aiding (MCDA) (see [13, 14]) provides methodologies...

M-estim::ztes The bootstrap principle is justified for robust M-estimates in regression. (A short proof justifying bootstrapping the empirical process is also given.) l.a.

We propose a robust elastic net (REN) model for high-dimensional sparse regression and give its performance guarantees (both the statistical error bound and the optimization bound). A simple idea of trimming the inner product is applied to the elastic net model. Specifically, we robustify the covariance matrix by trimming the inner product based on the intuition that the trimmed inner product c...

Quantile regression for right- or left-censored outcomes has attracted attention due to its ability accommodate heterogeneity in analysis of survival times. Rank-based inferential methods have desirable properties quantile analysis, but censored data poses challenges the general concept ranking. In this article, we propose a notion rank scores, which enables us construct rank-based tests coeffi...

The behaviour of algorithms for very robust regression depends on the distance between the regression data and the outliers. We introduce a parameter λ that defines a parametric path in the space of models and enables us to study, in a systematic way, the properties of estimators as the groups of data move from being far apart to close together. We examine, as a function of λ, the variance and ...

This paper proposes a distributionally robust approach to logistic regression. We use the Wasserstein distance to construct a ball in the space of probability distributions centered at the uniform distribution on the training samples. If the radius of this ball is chosen judiciously, we can guarantee that it contains the unknown datagenerating distribution with high confidence. We then formulat...