Related papers: Convex Imprecise Previsions: Basic Issues and Appl…

We investigate how basic probability inequalities can be extended to an imprecise framework, where (precise) probabilities and expectations are replaced by imprecise probabilities and lower/upper previsions. We focus on inequalities giving…

We consider composite loss functions for multiclass prediction comprising a proper (i.e., Fisher-consistent) loss over probability distributions and an inverse link function. We establish conditions for their (strong) convexity and explore…

In this paper we explore relaxations of (Williams) coherent and convex conditional previsions that form the families of $n$-coherent and $n$-convex conditional previsions, at the varying of $n$. We investigate which such previsions are the…

We study prediction and estimation problems using empirical risk minimization, relative to a general convex loss function. We obtain sharp error rates even when concentration is false or is very restricted, for example, in heavy-tailed…

This paper generalizes results concerning strong convexity of two-stage mean-risk models with linear recourse to distortion risk measures. Introducing the concept of (restricted) partial strong convexity, we conduct an in-depth analysis of…

Graphical models trained using maximum likelihood are a common tool for probabilistic inference of marginal distributions. However, this approach suffers difficulties when either the inference process or the model is approximate. In this…

This paper proves, in very general settings, that convex risk minimization is a procedure to select a unique conditional probability model determined by the classification problem. Unlike most previous work, we give results that are general…

This expository paper discusses Bayesian decision analysis perspectives on problems of constrained forecasting. Foundational and pedagogic discussion contrasts decision analytic approaches with the traditional, but typically inappropriate,…

In performative prediction, a predictive model impacts the distribution that generates future data, a phenomenon that is being ignored in classical supervised learning. In this closed-loop setting, the natural measure of performance named…

We consider spline estimates which preserve prescribed piecewise convex properties of the unknown function. A robust version of the penalized likelihood is given and shown to correspond to a variable halfwidth kernel smoother where the…

We give sufficient conditions for the expected excess and the upper semideviation of recourse functions to be strongly convex. This is done in the setting of two-stage stochastic programs with complete linear recourse and random right-hand…

Based on supermodularity ordering properties, we show that convex risk measures of credit losses are nondecreasing w.r.t. credit-credit and, in a wrong-way risk setup, credit-market, covariances of elliptically distributed latent factors.…

This paper focuses on investigating an inexact stochastic model-based optimization algorithm that integrates preconditioning techniques for solving stochastic composite optimization problems. The proposed framework unifies and extends the…

In this paper, we explore a static setting for the assessment of risk in the context of mathematical finance and actuarial science that takes into account model uncertainty in the distribution of a possibly infinite-dimensional risk factor.…

We consider the Chance Constrained Model Predictive Control problem for polynomial systems subject to disturbances. In this problem, we aim at finding optimal control input for given disturbed dynamical system to minimize a given cost…

Spaces of convex and concave functions appear naturally in theory and applications. For example, convex regression and log-concave density estimation are important topics in nonparametric statistics. In stochastic portfolio theory, concave…

We examine the convexity and tractability of the two-sided linear chance constraint model under Gaussian uncertainty. We show that these constraints can be applied directly to model a larger class of nonlinear chance constraints as well as…

Estimation of convex functions finds broad applications in engineering and science, while convex shape constraint gives rise to numerous challenges in asymptotic performance analysis. This paper is devoted to minimax optimal estimation of…

In decision-making problems under uncertainty, probabilistic constraints are a valuable tool to express safety of decisions. They result from taking the probability measure of a given set of random inequalities depending on the decision…

This paper addresses the problem of estimating a convex regression function under both the sup-norm risk and the pointwise risk using B-splines. The presence of the convex constraint complicates various issues in asymptotic analysis,…