Mean estimation and regression under heavy-tailed distributions--a survey

2019-06-10 · Gabor Lugosi, Shahar Mendelson

We survey some of the recent advances in mean estimation and regression function estimation. In particular, we describe sub-Gaussian mean estimators for possibly heavy-tailed data both in the univariate and multivariate settings. We focus on estimators based on median-of-means techniques but other methods such as the trimmed mean and Catoni's estimator are also reviewed. We give detailed proofs for the cornerstone results. We dedicate a section on statistical learning problems--in particular, regression function estimation--in the presence of possibly heavy-tailed data.

📄 PDF Abstract BibTeX arXiv:1906.04280

Code (0)

등록된 구현이 없습니다.

Tasks

regressionSurvey

Heavy-tailed Streaming Statistical Estimation

2021-08-25 · Che-Ping Tsai, Adarsh Prasad, Sivaraman Balakrishnan, Pradeep Ravikumar

We consider the task of heavy-tailed statistical estimation given streaming $p$-dimensional samples. This could also be viewed as stochastic optimization under heavy-tailed distributions, with an additional $O(p)$ space …

regression Stochastic Optimization

Regularization, sparse recovery, and median-of-means tournaments

2017-01-15 · Gábor Lugosi, Shahar Mendelson

A regularized risk minimization procedure for regression function estimation is introduced that achieves near optimal accuracy and confidence under general conditions, including heavy-tailed predictor and response variab…

regression

Model Selection regression Variable Selection

Mean estimation and regression under heavy-tailed distributions--a survey

Code (0)

Tasks

Similar Papers 제목 키워드 기반

Heavy-tailed Streaming Statistical Estimation

Regularization, sparse recovery, and median-of-means tournaments

Heavy-tailed Contamination is Easier than Adversarial Contamination

Uniform Mean Estimation for Heavy-Tailed Distributions via Median-of-Means

Regularized Modal Regression with Applications in Cognitive Impairment Prediction