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In this paper, we address the probabilistic error quantification of a general class of prediction methods. We consider a given prediction model and show how to obtain, through a sample-based approach, a probabilistic upper bound on the absolute value of the prediction error. The proposed scheme is based on a probabilistic scaling methodology in which the number of required randomized samples is independent of the complexity of the prediction model. The methodology is extended to address the case in which the probabilistic uncertain quantification is required to be valid for every member of a finite family of predictors. We illustrate the results of the paper by means of a numerical example.
In this paper, a sample-based procedure for obtaining simple and computable approximations of chance-constrained sets is proposed. The procedure allows to control the complexity of the approximating set, by defining families of simple-approximating s
Estimation of the prediction error of a linear estimation rule is difficult if the data analyst also use data to select a set of variables and construct the estimation rule using only the selected variables. In this work, we propose an asymptotically
We consider multi-agent systems where agents actions and beliefs are determined aleatorically, or by the throw of dice. This system consists of possible worlds that assign distributions to independent random variables, and agents who assign probabili
In probabilistic coherence spaces, a denotational model of probabilistic functional languages, morphisms are analytic and therefore smooth. We explore two related applications of the corresponding derivatives. First we show how derivatives allow to c
Predict a new response from a covariate is a challenging task in regression, which raises new question since the era of high-dimensional data. In this paper, we are interested in the inverse regression method from a theoretical viewpoint. Theoretical