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Interval linear regression analysis based on Minkowski difference – a bridge between traditional and interval linear regression models

Masahiro Inuiguchi, Tetsuzo Tanino (2006)

Kybernetika

In this paper, we extend the traditional linear regression methods to the (numerical input)-(interval output) data case assuming both the observation/measurement error and the indeterminacy of the input-output relationship. We propose three different models based on three different assumptions of interval output data. In each model, the errors are defined as intervals by solving the interval equation representing the relationship among the interval output, the interval function and the interval...

Iterative feature selection in least square regression estimation

Pierre Alquier (2008)

Annales de l'I.H.P. Probabilités et statistiques

This paper presents a new algorithm to perform regression estimation, in both the inductive and transductive setting. The estimator is defined as a linear combination of functions in a given dictionary. Coefficients of the combinations are computed sequentially using projection on some simple sets. These sets are defined as confidence regions provided by a deviation (PAC) inequality on an estimator in one-dimensional models. We prove that every projection the algorithm actually improves the performance...

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