Related papers: A Huber loss-based super learner with applications…

This paper addresses the scalar regression problem through a novel solution to exactly optimize the Huber loss in a general semi-supervised setting, which combines multi-view learning and manifold regularization. We propose a principled…

We propose a generalized formulation of the Huber loss. We show that with a suitable function of choice, specifically the log-exp transform; we can achieve a loss function which combines the desirable properties of both the absolute and the…

Recent developments on deep learning established some theoretical properties of deep neural networks estimators. However, most of the existing works on this topic are restricted to bounded loss functions or (sub)-Gaussian or bounded input.…

We propose an extended generalization of the pseudo Huber loss formulation. We show that using the log-exp transform together with the logistic function, we can create a loss which combines the desirable properties of the strictly convex…

Transfer learning has become an essential technique for utilizing information from source datasets to improve the performance of the target task. However, in the context of high-dimensional data, heterogeneity arises due to heteroscedastic…

All machine learning algorithms use a loss, cost, utility or reward function to encode the learning objective and oversee the learning process. This function that supervises learning is a frequently unrecognized hyperparameter that…

As one of the triumphs and milestones of robust statistics, Huber regression plays an important role in robust inference and estimation. It has also been finding a great variety of applications in machine learning. In a parametric setup, it…

This paper proposes an adaptive penalized weighted mean regression for outlier detection of high-dimensional data. In comparison to existing approaches based on the mean shift model, the proposed estimators demonstrate robustness against…

Federated learning systems are susceptible to adversarial attacks. To combat this, we introduce a novel aggregator based on Huber loss minimization, and provide a comprehensive theoretical analysis. Under independent and identically…

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…

Accurately estimating parameters in complex nonlinear systems is crucial across scientific and engineering fields. We present a novel approach for parameter estimation using a neural network with the Huber loss function. This method taps…

Most value function learning algorithms in reinforcement learning are based on the mean squared (projected) Bellman error. However, squared errors are known to be sensitive to outliers, both skewing the solution of the objective and…

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…

In this paper, we construct a parameter estimation framework for robust low-rank tensor regression based on a truncation method and Huber loss, specifically focusing on models with random noise having only finite second-order moments.…

Robust estimation has played an important role in statistical and machine learning. However, its applications to functional linear regression are still under-developed. In this paper, we focus on Huber's loss with a diverging robustness…

The literature has proposed various robust alternatives to empirical risk minimisation to address failure modes such as distribution shift, label noise and finite-sample degeneracies. Examples include distributionally robust optimization,…

We investigate robust nonparametric regression in the presence of heavy-tailed noise, where the hypothesis class may contain unbounded functions and robustness is ensured via a robust loss function $\ell_\sigma$. Using Huber regression as a…

Federated learning has attracted significant attention as a privacy-preserving framework for training personalised models on multi-source heterogeneous data. However, most existing approaches are unable to handle scenarios where subgroup…

We develop a new approach to solving classification problems, which is bases on the theory of coherent measures of risk and risk sharing ideas. The proposed approach aims at designing a risk-averse classifier. The new approach allows for…

Robust loss minimization is an important strategy for handling robust learning issue on noisy labels. Current robust loss functions, however, inevitably involve hyperparameter(s) to be tuned, manually or heuristically through cross…