arXiv research

Proposes a new Huber loss combining absolute and quadratic properties.

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…

Paper introduces a new robust loss function for RL.

The paper introduces a new FOR framework using Huber and ε-insensitive losses.

Super learner with Huber loss improves cost prediction and causal effect estimation in healthcare expenditure data.

Proposes a new loss function for robust learning.

This paper solves hedging in incomplete markets using neural networks.

This paper examines how noise affects deep neural networks and improves their performance.

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.

Study minimax rates for density estimation under Huber contamination and Besov IPM losses.

New proof shows faster convergence rate for robust estimation with Lasso in adversarially contaminated outputs.

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…

Deep Huber QRNs predict Huber quantiles for house prices.

In this paper, we introduce a novel and robust approach to Quantized Matrix Completion (QMC). First, we propose a rank minimization problem with constraints induced by quantization bounds. Next, we form an unconstrained optimization problem by regularizing the rank function with Huber loss. Huber loss is leveraged to c…

A new Markov subsampling strategy based on Huber criterion improves data processing from noisy full data.

Study improves $H$-consistency bounds for regression analysis.

Paper supports robust estimation in regression with heavy-tailed errors.

Study robust linear regression with outliers, providing exact asymptotics for ERM performance.

Paper proves robust M-estimators' coordinates' normality in high dimensions.

We propose an algorithm, semismooth Newton coordinate descent (SNCD), for the elastic-net penalized Huber loss regression and quantile regression in high dimensional settings. Unlike existing coordinate descent type algorithms, the SNCD updates each regression coefficient and its corresponding subgradient simultaneousl…

Study improves robust nonparametric regression in heavy-tailed noise.

A robust loss for anomaly mitigation and unsupervised contamination classification

We present a new method for high-dimensional linear regression when a scale parameter of the additive errors is unknown. The proposed estimator is based on a penalized Huber $M$-estimator, for which theoretical results on estimation error have recently been proposed in high-dimensional statistics literature. However, t…

Robust biclustering method tackles heavy-tailed data issues.

Unified approach for robust low rank matrix estimation with adversaries.

Paper tackles robust matrix completion with heavy-tailed noise.

The paper proves deep learning can be robust with certain loss functions.

We consider new formulations and methods for sparse quantile regression in the high-dimensional setting. Quantile regression plays an important role in many applications, including outlier-robust exploratory analysis in gene selection. In addition, the sparsity consideration in quantile regression enables the explorati…

We solve robust regression and matrix completion problems with sparse and low-rank models.

Extracting the underlying trend signal is a crucial step to facilitate time series analysis like forecasting and anomaly detection. Besides noise signal, time series can contain not only outliers but also abrupt trend changes in real-world scenarios. To deal with these challenges, we propose a robust trend filtering al…

The Support Vector Machine (SVM) has been used in a wide variety of classification problems. The original SVM uses the hinge loss function, which is non-differentiable and makes the problem difficult to solve in particular for regularized SVMs, such as with $\ell_1$-regularization. This paper considers the Huberized SV…

Improved robust regression for heavy-tailed and contaminated data.

Paper proposes an algorithm for robust estimation using Huber's criterion.

New tester outperforms existing ones in uniformity testing.

Generalized Huber's theorem for specific manifold curvature types.

Gradient descent with logistic loss can interpolate deep networks with smoothed ReLU activations under certain conditions.

This paper analyzes M-estimators under infinite-variance noise in high dimensions.

Huber regression assessed for robustness in statistical learning.

New robust regression method works with fewer data points than previous methods.

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 …

We present a generalization of the Cauchy/Lorentzian, Geman-McClure, Welsch/Leclerc, generalized Charbonnier, Charbonnier/pseudo-Huber/L1-L2, and L2 loss functions. By introducing robustness as a continuous parameter, our loss function allows algorithms built around robust loss minimization to be generalized, which imp…

New algorithm recovers sparse signals robustly against Gaussian noise and adaptive adversaries.

New bounds for DeepONets reduce out-of-sample error without width dependence.

We propose sparsemax, a new activation function similar to the traditional softmax, but able to output sparse probabilities. After deriving its properties, we show how its Jacobian can be efficiently computed, enabling its use in a network trained with backpropagation. Then, we propose a new smooth and convex loss func…

The paper proves new inequalities on the unit ball in higher dimensions.

A new framework for time series forecasting that adapts to varying patterns.

Study improves data quality assessment for structural monitoring data.