Alternate loss functions and regression models that achieve robustness to outliers by modulating the learning rate

• URL: http://arxiv.org/abs/2606.22068v2
• Date: Tue, 23 Jun 2026 10:36:32 GMT
• Title: Alternate loss functions and regression models that achieve robustness to outliers by modulating the learning rate
• Abstract summary: Most real-world training datasets are contaminated with data and outliers leading to large prediction errors.<n>This paper proposes a new robustness for achieving where the learning approach is modulated by a factor that is sensitive to outliers.
• Score: 5.974437898820796
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Most real-world datasets used for training supervised learning models are contaminated with noisy data and outliers leading to large prediction errors. This paper proposes a new approach for achieving robustness where the learning rate is modulated by a factor that is sensitive to outliers. In this approach a reduction of the learning rate is shown to be achieved by using alternate loss functions that are infinitely differentiable, strictly convex or quasiconvex and more closely approximate the absolute error than Huber and log-cosh losses. A comparison of the performance of regression models trained with different loss functions on a wide variety of benchmarks and datasets is presented to demonstrate the superior performance of the Square Root Loss (SRL) and Smooth Mean Absolute Error (SMAE) losses proposed in this paper. Two new robust linear regression models are presented. Highly vectorized robust parameter update formulae that take advantage of modern GPUs for both stochastic and batch gradient descent are presented.

Related papers

• Variational Rectification Inference for Learning with Noisy Labels [74.85528327499662]
  We propose variational rectification inference (VRI) to formulate the adaptive rectification for loss functions.<n>VRI is constructed as a hierarchical Bayes by treating the rectifying vector as a latent variable.<n>By introducing the variational term in VRI, the conditional posterior is estimated accurately and avoids collapsing to a Dirac delta function.
  arXiv  Detail & Related papers  (2026-03-18T01:25:08Z)
• Convex Loss Functions for Support Vector Machines (SVMs) and Neural Networks [0.0]
  We propose a new convex loss for Support Vector Machines, both for the binary classification and for the regression models.<n>We show the mathematical derivation of the dual problems and we experiment with them on several small datasets.
  arXiv  Detail & Related papers  (2026-01-29T06:47:51Z)
• Rectifying Regression in Reinforcement Learning [51.28909745713678]
  We show that mean absolute error is a better prediction objective than the traditional mean squared error for controlling the learned policy's suboptimality gap.<n>We present results that different loss functions are better aligned with these different regression objectives.
  arXiv  Detail & Related papers  (2025-10-01T13:32:07Z)
• A Simplified Analysis of SGD for Linear Regression with Weight Averaging [64.2393952273612]
  Recent work bycitetzou 2021benign provides sharp rates for SGD optimization in linear regression using constant learning rate.<n>We provide a simplified analysis recovering the same bias and variance bounds provided incitepzou 2021benign based on simple linear algebra tools.<n>We believe our work makes the analysis of gradient descent on linear regression very accessible and will be helpful in further analyzing mini-batching and learning rate scheduling.
  arXiv  Detail & Related papers  (2025-06-18T15:10:38Z)
• Robust Capped lp-Norm Support Vector Ordinal Regression [85.84718111830752]
  Ordinal regression is a specialized supervised problem where the labels show an inherent order. Support Vector Ordinal Regression, as an outstanding ordinal regression model, is widely used in many ordinal regression tasks. We introduce a new model, Capped $ell_p$-Norm Support Vector Ordinal Regression(CSVOR), that is robust to outliers.
  arXiv  Detail & Related papers  (2024-04-25T13:56:05Z)
• On the Performance of Empirical Risk Minimization with Smoothed Data [59.3428024282545]
  Empirical Risk Minimization (ERM) is able to achieve sublinear error whenever a class is learnable with iid data. We show that ERM is able to achieve sublinear error whenever a class is learnable with iid data.
  arXiv  Detail & Related papers  (2024-02-22T21:55:41Z)
• Robust Learning with Progressive Data Expansion Against Spurious Correlation [65.83104529677234]
  We study the learning process of a two-layer nonlinear convolutional neural network in the presence of spurious features. Our analysis suggests that imbalanced data groups and easily learnable spurious features can lead to the dominance of spurious features during the learning process. We propose a new training algorithm called PDE that efficiently enhances the model's robustness for a better worst-group performance.
  arXiv  Detail & Related papers  (2023-06-08T05:44:06Z)
• Theoretical Characterization of the Generalization Performance of Overfitted Meta-Learning [70.52689048213398]
  This paper studies the performance of overfitted meta-learning under a linear regression model with Gaussian features. We find new and interesting properties that do not exist in single-task linear regression. Our analysis suggests that benign overfitting is more significant and easier to observe when the noise and the diversity/fluctuation of the ground truth of each training task are large.
  arXiv  Detail & Related papers  (2023-04-09T20:36:13Z)
• Alternate Loss Functions for Classification and Robust Regression Can Improve the Accuracy of Artificial Neural Networks [6.452225158891343]
  This paper shows that training speed and final accuracy of neural networks can significantly depend on the loss function used to train neural networks. Two new classification loss functions that significantly improve performance on a wide variety of benchmark tasks are proposed.
  arXiv  Detail & Related papers  (2023-03-17T12:52:06Z)
• Boosting Differentiable Causal Discovery via Adaptive Sample Reweighting [62.23057729112182]
  Differentiable score-based causal discovery methods learn a directed acyclic graph from observational data. We propose a model-agnostic framework to boost causal discovery performance by dynamically learning the adaptive weights for the Reweighted Score function, ReScore.
  arXiv  Detail & Related papers  (2023-03-06T14:49:59Z)
• Soft-SVM Regression For Binary Classification [0.0]
  We introduce a new exponential family based on a convex relaxation of the hinge loss function using softness and class-separation parameters. This new family, denoted Soft-SVM, allows us to prescribe a generalized linear model that effectively bridges between logistic regression and SVM classification.
  arXiv  Detail & Related papers  (2022-05-24T03:01:35Z)
• X-model: Improving Data Efficiency in Deep Learning with A Minimax Model [78.55482897452417]
  We aim at improving data efficiency for both classification and regression setups in deep learning. To take the power of both worlds, we propose a novel X-model. X-model plays a minimax game between the feature extractor and task-specific heads.
  arXiv  Detail & Related papers  (2021-10-09T13:56:48Z)
• Variation-Incentive Loss Re-weighting for Regression Analysis on Biased Data [8.115323786541078]
  We aim to improve the accuracy of the regression analysis by addressing the data skewness/bias during model training. We propose a Variation-Incentive Loss re-weighting method (VILoss) to optimize the gradient descent-based model training for regression analysis.
  arXiv  Detail & Related papers  (2021-09-14T10:22:21Z)
• Good Classifiers are Abundant in the Interpolating Regime [64.72044662855612]
  We develop a methodology to compute precisely the full distribution of test errors among interpolating classifiers. We find that test errors tend to concentrate around a small typical value $varepsilon*$, which deviates substantially from the test error of worst-case interpolating model. Our results show that the usual style of analysis in statistical learning theory may not be fine-grained enough to capture the good generalization performance observed in practice.
  arXiv  Detail & Related papers  (2020-06-22T21:12:31Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.