This article discusses the determination of risk capital based on “aversion” functions. Aversion functions weigh different outcomes according to perceived severity. Many practical and popular risk measures are usefully viewed in terms of aversion functions including those arising from distortion operators and risk margin loadings. The approach of this paper builds on, unifies,and extends existi...

We propose a meta-learning technique for offline discovery of physics-informed neural network (PINN) loss functions. extend earlier works on meta-learning, and develop gradient-based algorithm addressing diverse task distributions based parametrized partial differential equations (PDEs) that are solved with PINNs. Furthermore, new theory we identify two desirable properties meta-learned losses ...

Loss functions engineering and the assessment of prediction performances are two crucial intertwined aspects supervised machine learning. This paper focuses on binary classification to introduce a class loss that defined probabilistic confusion matrices allow an automatic priori maximization skill scores. These tested in various experiments, which show probability distribution function associat...

This paper studies loss functions for finite sets. For a given set S, we give sum-of-square type of minimum degree. When S is the vertex standard simplex, show such have no spurious minimizers (i.e., every local minimizer global one). Up to transformations, similar without general approximately by sample T, how get solving quadratic optimization problem. Numerical experiments and applications a...

Margin maximizing properties play an important role in the analysis of classi£cation models, such as boosting and support vector machines. Margin maximization is theoretically interesting because it facilitates generalization error analysis, and practically interesting because it presents a clear geometric interpretation of the models being built. We formulate and prove a suf£cient condition fo...

We develop a general correspondence between a family of loss functions that act as surrogates to 0-1 loss, and the class of Ali-Silvey or f -divergence functionals. This correspondence provides the basis for choosing and evaluating various surrogate losses frequently used in statistical learning (e.g., hinge loss, exponential loss, logistic loss); conversely, it provides a decision-theoretic fr...

In this paper, we discuss the statistical inference on the unknown parameters and reliability function of type-II extreme value (EVII) distribution when the observed data are progressively type-II censored. By applying EM algorithm, we obtain maximum likelihood estimates (MLEs). We also suggest approximate maximum likelihood estimators (AMLEs), which have explicit expressions. We provide Bayes ...