Efficiently estimates sparse linear regression with heavy-tailed and outlier-contaminated data.
problem Estimating sparse linear regression coefficients with heavy-tailed and outlier-contaminated data.
method Efficient computation of estimators with sharp error bounds.
result Sharp error bounds for efficient estimators.
Efficiently estimates sparse linear regression with heavy-tailed data and outliers.
problem Sparse estimation of linear regression coefficients with heavy-tailed covariates and noises, including outliers.
method Efficient computation of robust estimator with nearly optimal error bound.
result Nearly optimal error bound for robust sparse estimation.
Improved robust regression for heavy-tailed and contaminated data.
problem Linear regression with heavy-tailed and adversarially contaminated covariates and responses.
method Applying a filtering algorithm to covariates and then using Huber regression, least trimmed squares, or least absolute deviation estimators on the remaining data.
result Near-optimal error rates achieved for the Huber regression estimator.
Study improves robustness and sparsity in linear regression with adversarial outliers and heavy-tailed noise.
problem Outliers and heavy-tailed noise in linear regression coefficients.
method Sharp concentration inequalities and generic chaining.
result Sharper error bounds under weaker assumptions.
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 t…
Study improves ERM for heavy-tailed data with dependent inputs.
problem Empirical Risk Minimization with dependent and heavy-tailed data.
method Extending risk bounds for ERM with heavy-tailed, dependent data.
result Established risk bounds for ERM with dependent and heavy-tailed data.
In this paper, we consider the problem of linear regression with heavy-tailed distributions. Different from previous studies that use the squared loss to measure the performance, we choose the absolute loss, which is capable of estimating the conditional median. To address the challenge that both the input and output c…
Study examines robust regression in high dimensions with heavy-tailed data.
problem Analyzing robust regression in high-dimensional settings with heavy-tailed data.
method Sharp asymptotic characterisation of M-estimators and ridge regression in elliptical distributions.
result Ridge regression is optimal and universal for finite second moments but can decay faster without them.
The paper improves machine learning for heavy-tailed panel data.
problem Improving estimates for financial and economic data with fat tails.
method Sparse-group LASSO regularization and Fuk-Nagaev concentration inequality.
result Oracle inequalities for panel data estimators.
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 in sparsely populated regions. We show that heavy-tailed stochastic processes (…
Study robust linear regression without distributional assumptions for heavy-tailed responses.
problem Linear regression with heavy-tailed responses and no distributional assumptions.
method Combining truncated least squares, median-of-means, and aggregation theory to construct a non-linear estimator.
result Achieves excess risk of order d/n with optimal sub-exponential tail. Ridge regression performs optimally in noisy environments with heavy-tailed distributions.
problem Performance of ridge regression in noisy environments with heavy-tailed noise.
method Established excess risk bounds using integral operator framework and Fuk-Nagaev inequality.
result Ridge regression achieves optimal convergence rates under heavy-tailed noise, demonstrating robustness.
Heavy Lasso improves robustness in high-dimensional linear regression with heavy-tailed errors.
problem Challenges of classical Lasso in handling heavy-tailed noise and outliers.
method Data-augmented soft-thresholding with Student's t-distribution loss.
result Heavy Lasso achieves comparable rates to Huber loss under theoretical bounds.
Study improves error bounds for sparse regression with heavy-tailed covariates.
problem Estimating sparse coefficients in linear regression with heavy-tailed covariates.
method Employed an ℓ1-penalized Huber regression method. result Error bound identical to Gaussian case for L-subexponential covariates. New algorithm improves heavy-tailed statistical estimation in streaming data.
problem Heavy-tailed statistical estimation in streaming data.
method Clipped stochastic gradient descent algorithm with improved analysis.
result Guarantees exponential concentration with O(1) batch size for mean estimation and linear regression. Study improves robust nonparametric regression in heavy-tailed noise.
problem Robust nonparametric regression with heavy-tailed noise and unbounded functions.
method Huber regression in reproducing kernel Hilbert spaces (RKHS), probabilistic effective hypothesis space, new comparison theorems.
result Explicit finite-sample error bounds and convergence rates for Huber regression in RKHS under heavy-tailed noise.
New robust estimator improves variable selection and coefficient estimation in linear regression with heavy-tailed errors and outliers.
problem Heavy-tailed errors and anomalous predictors in high-dimensional regression.
method Adaptive PENSE estimator for robust variable selection and estimation.
result Adaptive PENSE estimator provides reliable results even under very heavy-tailed errors and aberrant predictors.
New algorithm reduces heavy-tailed linear bandits' computational cost.
problem Stochastic linear bandits with heavy-tailed noise.
method One-pass online mirror descent with adaptive Huber regression.
result Near-optimal regret bound with reduced computational cost.
Paper proposes robust estimators for heavy-tailed data with infinite variance.
problem Developing robust estimators for heavy-tailed data with infinite variance.
method Proposes two robust estimators: ridge log-truncated M-estimator and elastic net log-truncated M-estimator.
result Demonstrates robustness of log-truncated estimations over standard estimations through simulations and real data analysis.
CAIRO separates ranking from scaling to improve robustness.
problem Conflating ranking and scaling in regression leads to model vulnerability.
method Two-stage approach: first learns a scoring function, then recovers scale.
result CAIRO recovers true regression function with auto-calibration guarantees.
Bayesian method selects important covariates in modal regression.
problem Bayesian modal regression with heavy-tailed responses.
method Expectation-maximization algorithm for parameter estimation; test statistic for variable selection.
result Efficacy of the proposed method in identifying important covariates.
Novel SVM approach for extreme quantile regression with heavy tailed inputs.
problem Learning from extreme values in quantile regression.
method Support Vector Machine framework for handling high-dimensional and nonlinear settings.
result Established finite-sample learning guarantees under mild regularity assumptions.
Study differentially private linear regression with heavy-tailed data.
problem Differentially private ℓ1-norm linear regression with heavy-tailed data. method Exponential mechanism for ℓ2-norm bounded second moment; relaxation to ℓ2-norm bounded θ-th moment; coordinate-wise bounded moments. result Achieved upper bounds for privacy-preserving linear regression under various moment conditions.
Bayesian deep learning with heavy-tailed weights achieves near-optimal performance.
problem Deep neural networks with heavy-tailed weights achieve near-optimal performance in various contexts.
method Introduced a Bayesian deep learning prior based on heavy-tailed weights and ReLU activation, showing near-optimal minimax contraction rates.
result Posterior distribution achieves near-optimal minimax contraction rates, adaptive to smoothness and intrinsic dimension.
Two algorithms tackle heavy-tailed rewards in reinforcement learning with linear function approximation.
problem Online sequential decision-making with heavy-tailed rewards.
method AdaOFUL and VARA algorithms for linear stochastic bandits and MDPs, using modified adaptive Huber regression.
result Achieved state-of-the-art and variance-aware regret bounds for heavy-tailed rewards.
New method improves mean estimation for heavy-tailed data.
problem Estimating mean of heavy-tailed distributions.
method Median-of-Means (MoM) with symmetrization technique.
result Improved sample complexity bound for mean estimation.
Study shows heavy-tailed distributions affect reliability of machine learning calibration statistics.
problem Reliability of calibration statistics for machine learning regression tasks is affected by heavy-tailed uncertainty and error distributions.
method Examined two calibration error estimation methods (CE and ZMS) and found ZMS to be less sensitive to heavy-tailed distributions.
result Heavy-tailed distributions make MSE and MV unreliable, but ZMS remains a reliable approach.
Proposes a transfer learning method for high-dimensional quantile regression.
problem Inadequate handling of heterogeneity and heavy tails in transfer learning.
method High-dimensional quantile regression framework with double transfer learning estimator.
result Established error bounds and valid confidence intervals for high-dimensional quantile regression coefficients.
A new method estimates parameters in heavy-tailed corrupted regression with unknown covariance and heterogeneous noise.
problem Estimating parameters in regression with heavy-tailed errors and unknown covariance.
method Near-optimal computationally tractable estimator based on power method and Multiplicative Weight Update algorithm.
result The estimator achieves the optimal statistical rate and breakdown-point under near-optimal sample size.
This paper studies distributed estimation and support recovery for high-dimensional linear regression model with heavy-tailed noise. To deal with heavy-tailed noise whose variance can be infinite, we adopt the quantile regression loss function instead of the commonly used squared loss. However, the non-smooth quantile …
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 variables. The procedure is based on median-of-means tournaments, introduced by the authors in [8]. It is …
This paper improves kernel quantile regression with random features for handling heavy-tailed noises.
problem Handling heavy-tailed noises in kernel quantile regression.
method Introduces a refined error decomposition and establishes a novel connection between KQR-RF and KRR-RF.
result Establishes capacity-dependent learning rates for KQR-RF under mild conditions on the number of random features, which are minimax optimal up to some logarithmic factors.
Paper proposes robust tensor regression method for tensor data analysis.
problem Outliers in tensor data analysis can make existing methods sensitive.
method Nonconvex relaxation of tensor tubal rank in optimization framework.
result Global convergence of proposed estimation algorithm under mild assumptions.
The paper develops a robust algorithm for contextual bandits with heavy-tailed rewards.
problem Contextual bandits with heavy-tailed rewards.
method Develops an algorithm based on Catoni's estimator for robust statistics, applying it to contextual bandits with general function approximation.
result Establishes regret bounds that depend on cumulative reward variance and logarithmically on the reward range and number of rounds.
New algorithms achieve high-probability parameter-free regret in online convex optimization with heavy-tailed data.
problem Achieving high-probability parameter-free regret in online convex optimization with heavy-tailed data.
method Developed new regularization techniques to handle exponentially large iterates and heavy-tailed subgradients.
result Achieved regret bound of O(∥u∥T1/plog(1/δ)) with high probability for subgradients with bounded pth moments. Researchers study heavy-tail properties of SGD using stochastic recurrence equations.
problem Analyzing heavy-tail properties of Stochastic Gradient Descent (SGD).
method Modeling SGD iterations as multivariate affine stochastic recursions and applying the theory of irreducible-proximal (i-p) matrices.
result Extended results of Gürbüzbalaban et al. (2020) by using the theory of i-p matrices.
Paper supports robust estimation in regression with heavy-tailed errors.
problem Support estimation in high-dimensional heteroscedastic mean regression.
method Use of Huber loss function and adaptive LASSO penalty for robust estimation.
result Sign-consistency and optimal rates of convergence in ℓ∞ norm. AIS algorithm improves heavy-tailed distribution estimation.
problem Inconsistent estimators and slow convergence in AIS for heavy-tailed distributions.
method Adapts Student-t proposal distributions by matching escort moments and minimizing α-divergence.
result Improves estimation accuracy for heavy-tailed distributions.
We consider the problem of sparsity-constrained M-estimation when both explanatory and response variables have heavy tails (bounded 4-th moments), or a fraction of arbitrary corruptions. We focus on the k-sparse, high-dimensional regime where the number of variables d and the sample size n are related through $…
This work studies applications and generalizations of a simple estimation technique that provides exponential concentration under heavy-tailed distributions, assuming only bounded low-order moments. We show that the technique can be used for approximate minimization of smooth and strongly convex losses, and specificall…
Heavy-tailed outliers are more resilient to robust estimation than adversarial ones.
problem Developing robust estimators for data with outliers.
method Analyzing the relationship between adversarial and heavy-tailed outlier models.
result Optimal estimators for heavy-tailed outliers are also optimal for adversarial settings, but not vice versa.
The paper develops a minimax optimal method for high-dimensional regression using auxiliary data.
problem High-dimensional additive regression with heavy-tailed errors and transfer learning.
method Smooth backfitting estimator with local linear smoothing, followed by a two-stage estimation method.
result The method achieves the minimax optimal rate under certain conditions.
The paper proposes a method for predicting equity premium using penalized quantile regression.
problem Heteroscedasticity and heavy-tails in equity premium prediction.
method Penalized quantile regression with consistent variable selection across multiple quantiles.
result The proposed method outperforms benchmark methods and reveals interesting predictor relationships.
Interpolating models can have heavy-tailed risk, leading to rare but severe errors.
problem Interpolating models' tail risk is poorly understood, affecting rare but impactful errors.
method Large-deviation methods to study the fragility of high-dimensional linear interpolators.
result Ridgeless regression exhibits heavy-tailed risk, while ridge-regularized estimators have better tail behavior.
We consider least squares estimation in a general nonparametric regression model. The rate of convergence of the least squares estimator (LSE) for the unknown regression function is well studied when the errors are sub-Gaussian. We find upper bounds on the rates of convergence of the LSE when the errors have uniformly …
Stochastic optimization's success linked to heavy-tailed noise.
problem Understanding stochastic optimization's success mechanisms.
method Modeling stochastic optimization as random recurrence relations, analyzing multiplicative noise and heavy-tailed behavior.
result Multiplicative noise leads to heavy-tailed stationary behavior in optimization parameters.
New convergence rates for SGD under heavy-tailed noise with infinite variance.
problem Convergence analysis of SGD under heavy-tailed noise with infinite variance.
method Identifying a condition on the Hessian and providing a convergence rate for the distance to the global optimum.
result SGD can converge to the global optimum under heavy-tailed noise with infinite variance.
Improved linear regression for diverse data batches.
problem Learning from multiple heterogeneous data sources.
method Gradient-based algorithm for different input distributions.
result Significant reduction in the number of required batches and sample size.