Related papers: On Regression in Extreme Regions

Under general multivariate regular variation conditions, the extreme Value-at-Risk of a portfolio can be expressed as an integral of a known kernel with respect to a generally unknown spectral measure supported on the unit simplex. The…

This paper concerns estimation and inference for treatment effects in deep tails of the counterfactual distribution of unobservable potential outcomes corresponding to a continuously valued treatment. We consider two measures for the deep…

Expected risk minimization (ERM) is at the core of many machine learning systems. This means that the risk inherent in a loss distribution is summarized using a single number - its average. In this paper, we propose a general approach to…

Nonparametric regression quantiles obtained by inverting a kernel estimator of the conditional distribution of the response are long established in statistics. Attention has been, however, restricted to ordinary quantiles staying away from…

Data in the real-world classification problems are always imbalanced or long-tailed, wherein the majority classes have the most of the samples that dominate the model training. In such setting, the naive model tends to have poor performance…

The classical multivariate extreme-value theory concerns the modeling of extremes in a multivariate random sample, suggesting the use of max-stable distributions. In this work, the classical theory is extended to the case where aggregated…

Concentration inequalities form an essential toolkit in the study of high dimensional (HD) statistical methods. Most of the relevant statistics literature in this regard is based on sub-Gaussian or sub-exponential tail assumptions. In this…

A key building block in the design of ultra-reliable communication systems is a wireless channel model that captures the statistics of rare events occurring due to significant fading. In this paper, we propose a novel methodology based on…

We propose and analyse a reduced-rank method for solving least-squares regression problems with infinite dimensional output. We derive learning bounds for our method, and study under which setting statistical performance is improved in…

The goal in extreme multi-label classification is to learn a classifier which can assign a small subset of relevant labels to an instance from an extremely large set of target labels. Datasets in extreme classification exhibit a long tail…

A theoretical expression is derived for the mean squared error of a nonparametric estimator of the tail dependence coefficient, depending on a threshold that defines which rank delimits the tails of a distribution. We propose a new method…

Heavy-tailed distributions are frequently used to enhance the robustness of regression and classification methods to outliers in output space. Often, however, we are confronted with "outliers" in input space, which are isolated observations…

Tensor regression is an important tool for tensor data analysis, but existing works have not considered the impact of outliers, making them potentially sensitive to such data points. This paper proposes a low tubal rank robust regression…

We address the overlooked unbiasedness in existing long-tailed classification methods: we find that their overall improvement is mostly attributed to the biased preference of tail over head, as the test distribution is assumed to be…

We study the problem of selecting features associated with extreme values in high dimensional linear regression. Normally, in linear modeling problems, the presence of abnormal extreme values or outliers is considered an anomaly which…

Extreme value applications commonly employ regression techniques to capture cross-sectional heterogeneity or time-variation in the data. Estimation of the parameters of an extreme value regression model is notoriously challenging due to the…

Extreme value theory offers a statistical framework for quantifying the risk of rare events, with the generalized Pareto (GP) distribution providing the canonical limit model for univariate threshold exceedances. In many applications,…

We offer a survey of recent results on covariance estimation for heavy-tailed distributions. By unifying ideas scattered in the literature, we propose user-friendly methods that facilitate practical implementation. Specifically, we…

We develop a new extreme value theory for repeated cross-sectional and panel data to construct asymptotically valid confidence intervals (CIs) for conditional extremal quantiles from a fixed number $k$ of nearest-neighbor tail observations.…

Distributional regression aims to estimate the full conditional distribution of a target variable, given covariates. Popular methods include linear and tree-ensemble based quantile regression. We propose a neural network-based…