Paper presents robust confidence sequences for means with known moment bounds and arbitrary corruption.
problem Tackles robustness to outliers and adversarial corruptions in mean estimation.
method Designs new robust exponential supermartingales to create confidence sequences.
result Achieves optimal width and shows smaller margin of error compared to fixed-time robust methods.
We analyze the performance of the Tukey median estimator under total variation (TV) distance corruptions. Previous results show that under Huber's additive corruption model, the breakdown point is 1/3 for high-dimensional halfspace-symmetric distributions. We show that under TV corruptions, the breakdown point reduces …
A robust loss for anomaly mitigation and unsupervised contamination classification
problem Detecting and mitigating contamination in supervised and unsupervised settings
method Neural Bayesian Anomaly Mitigation (NBAM)
result Recovering the structure of contamination and identifying label-flip pairs
Robust CG methods avoid data corruption and solve structured statistical estimation problems.
problem Data corruption and heavy-tailed data in structured statistical estimation.
method Robustification of Conditional Gradient (CG) type methods using Huber's corruption model and robust mean gradient estimation.
result Robust CG methods converge linearly with correct sample complexity, even for high-dimensional problems.
Improved robust regression with clean covariates achieves better rates than Huber's model.
problem Robust regression under adaptive contamination of responses with clean covariates.
method Exploiting clean covariates to construct an estimator achieving better rates than Huber's model.
result Improved estimation rate even with constant contamination, achieving consistency.
Robust estimators for Gaussian sparse tasks with optimal error under contamination.
problem Robust mean estimation, PCA, and linear regression in the presence of Huber contamination.
method Novel multidimensional filtering method for sparse regime.
result Optimal error guarantees within constant factors for Gaussian robust k k k -sparse mean estimation. Study robust linear regression with outliers, providing exact asymptotics for ERM performance.
problem Robust linear regression in high-dimension with outliers.
method Analyzes ℓ 2 \ell_2 ℓ 2 , ℓ 1 \ell_1 ℓ 1 , and Huber losses, providing asymptotic performance metrics. result Optimally-regularised ERM is asymptotically consistent with simple calibration, but Huber loss requires norm calibration.
New robust regression method works with fewer data points than previous methods.
problem Adversary can corrupt most of the data, making traditional regression models unreliable.
method Developed a Huber loss estimator for robust linear regression with nearly linear sample size and inverse-polynomial inlier fraction.
result The Huber loss estimator is consistent for nearly linear sample size and inverse-polynomial inlier fraction.
We solve robust regression and matrix completion problems with sparse and low-rank models.
problem Adversarial contamination and noisy matrix completion in high-dimensional settings.
method Subgaussian statistical learning framework, trace-regression with matrix decomposition, novel Huber-type loss.
result Near-optimal estimation rates for robust regression and matrix completion.
Develops a robust GMM estimator for outlier-tolerant inference.
problem Sensitive GMM estimation to outliers in inference problems.
method Robustified GMM estimator with computational efficiency and recovery guarantees.
result First computationally efficient GMM estimator for ε ε ε fraction of adversarial outliers with O ( ε ) O(\sqrtε) O ( ε ) recovery guarantee. Paper proposes an algorithm for robust estimation using Huber's criterion.
problem Non-convexity and non-robustness of joint maximum likelihood estimation.
method Block-wise minimization majorization framework with data-adaptive step sizes.
result Improved convergence and robustness in sparse learning.
Generalized Huber's theorem for specific manifold curvature types.
problem Finite point conformal compactification on manifolds with certain curvature integrability.
method Generalization of Huber's theorem to higher dimensions with $L^ rac{n}{2}$ integrable Ricci curvatures.
result Validated finite point conformal compactification theorem for new class of manifolds.
Huber regression assessed for robustness in statistical learning.
problem Understanding Huber regression in nonparametric statistical learning.
method Assessment from statistical learning perspective, focusing on risk consistency, adaptive tuning, and convergence rates.
result Huber regression can be asymptotically mean regression calibrated under ( 1 + ε ) (1+ε) ( 1 + ε ) -moment conditions, justifying its robustness. Deep Huber QRNs predict Huber quantiles for house prices.
problem Predicting more functionals of predictive probability distributions.
method Training a DL algorithm with the Huber quantile scoring function.
result DHQRNs provide satisfactory absolute performance in house price prediction.
The Huber loss is a robust loss function used for a wide range of regression tasks. To utilize the Huber loss, a parameter that controls the transitions from a quadratic function to an absolute value function needs to be selected. We believe the standard probabilistic interpretation that relates the Huber loss to the H…
The paper proves new inequalities on the unit ball in higher dimensions.
problem Establishing new weighted inequalities on the unit ball.
method Limiting approach to prove Carleman and Huber inequalities.
result Sharp weighted Carleman and Huber inequalities on the unit ball.
Proposes a new Huber loss combining absolute and quadratic properties.
problem Improving robustness in learning models.
method Introduces a generalized Huber loss with a log-exp transform and provides an efficient minimization algorithm.
result Shows that the new loss function can be minimized efficiently.
Paper introduces a new robust loss function for RL.
problem Heuristic selection of threshold parameters in quantile Huber loss.
method Derived from Wasserstein distance, captures noise in quantile values.
result Enhances robustness against outliers and enables parameter adjustment.
A new Markov subsampling strategy based on Huber criterion improves data processing from noisy full data.
problem High noise level in data leads to poor performance of subsampling procedures.
method Design a Markov subsampling strategy based on Huber criterion to construct an informative subset from noisy full data.
result The estimator based on HMS is statistically consistent with a sub-Gaussian deviation bound.
Super learner with Huber loss improves cost prediction and causal effect estimation in healthcare expenditure data.
problem Challenges in modeling healthcare expenditure distributions with standard super learning methods.
method Proposes a super learner using Huber loss, a robust loss function that down-weights outliers.
result Demonstrates appreciable finite-sample gains in cost prediction and causal effect estimation.
Incorporating sparsity priors in learning tasks can give rise to simple, and interpretable models for complex high dimensional data. Sparse models have found widespread use in structure discovery, recovering data from corruptions, and a variety of large scale unsupervised and supervised learning problems. Assuming the …
The paper extends Huber's theorem to higher dimensions with specific geometric constraints.
problem Applying Huber's theorem to higher-dimensional conformal metrics with bounded scalar curvature.
method Analyzing conformal metrics on a punctured ball with L n 2 L^\frac{n}{2} L 2 n bounded scalar curvature. result The volume density at infinity is precisely one, and the blow-down metric is R n \mathbb{R}^n R n . The paper introduces a new FOR framework using Huber and ε-insensitive losses.
problem Handling outliers and sparsity in functional output regression.
method Proposes a flexible FOR framework with infimal convolution losses and computable algorithms.
result Demonstrates efficiency and effectiveness on synthetic and real-world data.
Study minimax robustness in statistical estimation under Wasserstein contamination.
problem Adversarial perturbations in statistical data.
method Developed minimax theory for ℓ q r \ell_q^r ℓ q r losses under Wasserstein- r r r contaminations. result Exact minimax risk identified for joint contaminations in location estimation and prediction in linear regression.
New analysis improves SGD for robust and quantile regression with sub-quadratic convergence.
problem Improving SGD for robust and quantile regression with sub-quadratic convergence.
method Piecewise Lyapunov function for first-order differentiable functions.
result First geometrical convergence result for sub-quadratic SGD.
This paper examines how noise affects deep neural networks and improves their performance.
problem The impact of noise on the stability of deep ReLU neural networks for nonparametric regression.
method Investigates the optimal rate of convergence for deep ReLU neural networks under Huber loss, considering the p-th moment of noise and the smoothness of the function.
result The optimal rate of convergence cannot be achieved by ordinary least squares but can be by Huber loss with a properly chosen parameter.
We show that for compact orientable hyperbolic orbisurfaces, the Laplace spectrum determines the length spectrum as well as the number of singular points of a given order. The converse also holds, giving a full generalization of Huber's theorem to the setting of compact orientable hyperbolic orbisurfaces.
Proposes a new loss function for robust learning.
problem Creating a robust loss function for machine learning.
method Extended pseudo Huber loss with log-exp transform and logistic function.
result Linear convergence algorithm for minimizer finding.
This paper solves hedging in incomplete markets using neural networks.
problem Hedging in incomplete markets with risk factor, illiquidity, and discrete transaction dates.
method Proposes a jump-diffusion model and uses RNN, LSTM, and Mogrifier-LSTM neural networks for hedging strategies.
result Mogrifier-LSTM is the fastest and most effective model for hedging.
New proof shows faster convergence rate for robust estimation with Lasso in adversarially contaminated outputs.
problem Robust estimation of parameters in the presence of adversarial output contamination.
method Extended Lasso with Huber loss function and L 1 L_1 L 1 penalty, focusing on specific properties of the Huber function. result Same convergence rate as Dalalyan and Thompson (2019), but with a different proof.
Paper proposes a robust framework for detecting multiple periodic components in time series.
problem Detecting multiple periodic components in time series with interlaced patterns and external noise.
method Applying maximal overlap discrete wavelet transform to isolate periodic components, ranking them by wavelet variance, and detecting single periodicity robustly.
result The proposed algorithm outperforms other methods for both single and multiple periodicity detection.
A robust Gaussian process model using Huber likelihood for outlier resistance.
problem Outliers in observational data sets affect Gaussian process regression's robustness.
method Proposes a Gaussian process model with Huber likelihood and weights based on projection statistics.
result Demonstrates improved statistical efficiency and robustness to outliers.
In this paper, we develop connections between two seemingly disparate, but central, models in robust statistics: Huber's epsilon-contamination model and the heavy-tailed noise model. We provide conditions under which this connection provides near-statistically-optimal estimators. Building on this connection, we provide…
The paper extends Huber's theorem to higher dimensions using n-Laplace equations.
problem Proving finite point conformal compactification for general dimensions.
method Using n-Laplace equations and strengthened Arsove-Huber's theorem.
result Established finite point conformal compactification theorem for manifolds.
We study Empirical Risk Minimizers (ERM) and Regularized Empirical Risk Minimizers (RERM) for regression problems with convex and L L L -Lipschitz loss functions. We consider a setting where $|\cO|$ malicious outliers contaminate the labels. In that case, under a local Bernstein condition, we show that the L 2 L_2 L 2 -error rat…
In this paper, we generalize Huber's criterion to multichannel sparse recovery problem of complex-valued measurements where the objective is to find good recovery of jointly sparse unknown signal vectors from the given multiple measurement vectors which are different linear combinations of the same known elementary vec…
Efficiently estimates mean of symmetric distributions without moments.
problem Estimating mean of symmetric distributions without moment assumptions.
method Generalization of filtering technique, Huber-loss-based techniques, SoS proofs.
result Achieves optimal error bounds for various symmetric distributions.
Estimates error for robust M-estimators with convex penalties.
problem Estimating out-of-sample error for robust M-estimators in high-dimensional linear regression.
method Proposes a generic out-of-sample error estimate for robust M M M -estimators with convex penalties, using observed data and derivatives. result The out-of-sample error estimate has a relative error of order n − 1 / 2 n^{-1/2} n − 1/2 under certain conditions. Supervised learning is an active research area, with numerous applications in diverse fields such as data analytics, computer vision, speech and audio processing, and image understanding. In most cases, the loss functions used in machine learning assume symmetric noise models, and seek to estimate the unknown function …
RHPSVM improves SVM performance with robust loss function.
problem Outliers and resampling instability in SVM models.
method RHPSVM uses a rescaled Huberized pinball loss function.
result RHPSVM outperforms existing SVM models in noisy and small-sample scenarios.
Develops efficient estimators for PCA and sparse regression in the presence of oblivious outliers.
problem Estimation of PCA and sparse regression in the presence of a small fraction of corrupted data.
method Designs efficient estimators using Huber loss with non-smooth regularizers like the ℓ1 norm or nuclear norm.
result Achieves consistent estimation error approaching zero as the number of observations grows.
New theorems in 2D and 4D for metrics with curvature or singularity.
problem Proving new versions of Huber theorem in dimensions 2 and 4.
method Using Coulomb frames and Bach tensor conditions to construct conformal metrics.
result Constructs conformal metrics with regularity across singularities in 4D.
Study minimax rates for density estimation under Huber contamination and Besov IPM losses.
problem Minimax convergence rates of nonparametric density estimation under Huber contamination model with outliers.
method Re-scaled thresholding wavelet series estimator and GAN architectures.
result Achieves minimax optimal convergence rates under Besov IPM losses.
This paper improves robust cluster enumeration for RES data.
problem Challenges in determining optimal clusters in noisy data.
method Generalizes robust Bayesian cluster enumeration for RES mixtures.
result Significant robustness improvement over existing methods.
Near-optimal algorithms for mean estimation and linear regression with Gaussian covariates and Huber contamination.
problem Gaussian mean estimation and linear regression with Gaussian covariates in the presence of Huber contamination.
method Near-optimal algorithms with optimal error guarantees, achieving sample complexity n = i l d e O ( d / ε 2 ) n = ilde{O}(d/ε^2) n = i l d e O ( d / ε 2 ) and almost linear runtime. result First sample near-optimal and almost linear-time algorithms with optimal error guarantees for both problems.
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 ℓ 1 \ell_1 ℓ 1 -penalized Huber regression method. result Error bound identical to Gaussian case for L L L -subexponential covariates. A new method quantizes conditional probability measures using deep learning.
problem Quantizing conditional probability measures efficiently.
method DCMQ method using Huber-energy kernel and deep neural network.
result Promising results on various examples.
New RESK distributions improve robust clustering of skewed data.
problem Robustly clustering non-symmetric, heavy-tailed data clusters.
method Proposes RESK distributions and an EM algorithm with robust skew-Huber M-estimator.
result Numerical experiments confirm the effectiveness of the proposed methods.