Laboratoire de Génie Informatique et d’Automatique de l’Artois

Logistic regression is a well-established classification model, whose monotonicity has contributed to its popularity. However, it has at least two limitations. First, it lacks self-awareness, that is, an ability to represent the ignorance (aka epistemic or reducible uncertainty) involved in its predictions, which is crucial in safety-critical classification problems. Recently, an extension of logistic regression was introduced to remedy this issue and was applied to the problem of classifier calibration. This extension is formalised within evidence theory and relies in particular on a sound method for statistical inference and prediction developed in this framework. The first contribution of this thesis is to study the interest of this extension for active learning in the context of classifier calibration. An uncertainty sampling strategy based on ignorance is proposed and validated experimentally. A second limitation of logistic regression is that it lacks flexibility, that is, an ability to model nonlinear dependencies between the predictors. To address this issue, an elegant generalisation of logistic regression based on the Choquet
integral, called choquistic regression, was proposed. It preserves the monotonicity of logistic regression whilst alleviating its linearity. However, much as logistic regression, it lacks self-awareness. The second contribution of this thesis is to palliate this problem by deriving an extension of choquistic regression based on evidence theory, similar to the evidential extension of logistic regression. The usefulness of the obtained approach is confirmed empirically in classification problems where cautiousness in decision-making is allowed.

As part of the ELSAT2020 (VUMOPE) regional project, this thesis is partially funded by the ELSAT2020 project, which is co-financed by the European Union with the European Regional Development Fund, the French State and the Hauts-de-France Regional Council.