Related papers: Generalized Huber Loss for Robust Learning and its…
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…
Complex distributions of the healthcare expenditure pose challenges to statistical modeling via a single model. Super learning, an ensemble method that combines a range of candidate models, is a promising alternative for cost estimation and…
Huber loss, its asymmetric variants and their associated functionals (here named Huber functionals) are studied in the context of point forecasting and forecast evaluation. The Huber functional of a distribution is the set of minimizers of…
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 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…
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…
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…
Distributional Reinforcement Learning (RL) estimates return distribution mainly by learning quantile values via minimizing the quantile Huber loss function, entailing a threshold parameter often selected heuristically or via hyperparameter…
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…
Robust regression has attracted a great amount of attention in the literature recently, particularly for taking asymmetricity into account simultaneously and for high-dimensional analysis. However, the majority of research on the topics…
While the traditional formulation of machine learning tasks is in terms of performance on average, in practice we are often interested in how well a trained model performs on rare or difficult data points at test time. To achieve more…
Many results have been proved for various nuclear norm penalized estimators of the uniform sampling matrix completion problem. However, most of these estimators are not robust: in most of the cases the quadratic loss function and its…
A commonly used learning rule is to approximately minimize the \emph{average} loss over the training set. Other learning algorithms, such as AdaBoost and hard-SVM, aim at minimizing the \emph{maximal} loss over the training set. The average…
In this paper, the worst-case probability measure over the data is introduced as a tool for characterizing the generalization capabilities of machine learning algorithms. More specifically, the worst-case probability measure is a Gibbs…
We consider the problem of learning a loss function which, when minimized over a training dataset, yields a model that approximately minimizes a validation error metric. Though learning an optimal loss function is NP-hard, we present an…
We present a computational and statistical approach for fitting isotonic models under convex differentiable loss functions. We offer a recursive partitioning algorithm which provably and efficiently solves isotonic regression under any such…
In this paper, we study robust covariance estimation under the approximate factor model with observed factors. We propose a novel framework to first estimate the initial joint covariance matrix of the observed data and the factors, and then…
This paper introduces a loss-based generalized Bayesian methodology for high-dimensional robust regression with serially correlated errors and predictors. The proposed framework employs a novel scaled pseudo-Huber (SPH) loss function, which…
Robust M-estimation uses loss functions, such as least absolute deviation (LAD), quantile loss and Huber's loss, to construct its objective function, in order to for example eschew the impact of outliers, whereas the difficulty in analysing…
The standard loss functions used in the literature on probabilistic prediction are the log loss function, the Brier loss function, and the spherical loss function; however, any computable proper loss function can be used for comparison of…