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The study of a machine learning problem is in many ways is difficult to separate from the study of the loss function being used. One avenue of inquiry has been to look at these loss functions in terms of their properties as scoring rules…

Virtually all machine learning tasks are characterized using some form of loss function, and "good performance" is typically stated in terms of a sufficiently small average loss, taken over the random draw of test data. While optimizing for…

Recent works have revealed an essential paradigm in designing loss functions that differentiate individual losses vs. aggregate losses. The individual loss measures the quality of the model on a sample, while the aggregate loss combines…

Choosing a suitable loss function is essential when learning by empirical risk minimisation. In many practical cases, the datasets used for training a classifier may contain incorrect labels, which prompts the interest for using loss…

The class of $\alpha$-stable distributions received much interest for modelling impulsive phenomena occur in engineering, economics, insurance, and physics. The lack of non-analytical form for probability density function is considered as…

We consider supervised learning problems in which set predictions provide explicit uncertainty estimates. Using Choquet integrals (a.k.a. Lov{\'a}sz extensions), we propose a convex loss function for nondecreasing subset-valued functions…

We revisit logistic regression and its nonlinear extensions, including multilayer feedforward neural networks, by showing that these classifiers can be viewed as converting input or higher-level features into Dempster-Shafer mass functions…

Designing proper loss functions for vision tasks has been a long-standing research direction to advance the capability of existing models. For object detection, the well-established classification and regression loss functions have been…

In this work, we study a new class of risks defined in terms of the location and deviation of the loss distribution, generalizing far beyond classical mean-variance risk functions. The class is easily implemented as a wrapper around any…

Robust regression aims to develop methods for estimating an unknown regression function in the presence of outliers, heavy-tailed distributions, or contaminated data, which can severely impact performance. Most existing theoretical results…

This work proposes a wavelet shrinkage rule under asymmetric LINEX loss function and a mixture of a point mass function at zero and the logistic distribution as prior distribution to the wavelet coefficients in a nonparametric regression…

In this paper, we develop a novel efficient and robust nonparametric regression estimator under a framework of feedforward neural network. There are several interesting characteristics for the proposed estimator. First, the loss function is…

Modern analysis on parton distribution functions (PDFs) requires calculations of the log-likelihood functions from thousands of experimental data points, and scans of multi-dimensional parameter space with tens of degrees of freedom. In…

Despite its empirical success, deep learning still lacks a comprehensive theoretical understanding of model fitting and generalization. This paper proposes the probability distribution (PD) learning framework to analyze the optimization and…

Mining large datasets and obtaining calibrated predictions from tem is of immediate relevance and utility in reliable deep learning. In our work, we develop methods for Deep neural networks based inferences in such datasets like the Gene…

Measuring the accuracy of cross-sectional predictions is a subjective problem. Generally, this problem is avoided. In contrast, this paper confronts subjectivity up front by eliciting an impartial decision-maker's preferences. These…

Most classification models can be considered as the process of matching templates. However, when intra-class uncertainty/variability is not considered, especially for datasets containing unbalanced classes, this may lead to classification…

In the domain of machine learning, the significance of the loss function is paramount, especially in supervised learning tasks. It serves as a fundamental pillar that profoundly influences the behavior and efficacy of supervised learning…

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…

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…