Janvier 2024


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Jeudi 18 Janvier
Heure: 10:30 - 11:30
Lieu: Salle B107, bâtiment B, Université de Villetaneuse
Résumé: Rule-based machine learning via mathematical optimization
Description: Cristina Molero del Río Rule-based machine learning models are appealing because of their simple
decision structure. In this talk, we will present two examples, decision
trees and rule sets, with special focus on the former.

Contrary to classic classification and regression trees, built in a greedy
heuristic manner, designing the tree model through an optimization problem
allows us to easily include desirable properties in Machine Learning in
addition to prediction accuracy. We present a Non-Linear Optimization
approach that is scalable with respect to the size of the training sample,
and illustrate this flexibility to model several important issues in
Explainable and Fair Machine Learning. These include sparsity, as a proxy
for interpretability, by reducing the amount of information necessary to
predict well; fairness, by aiming to avoid predictions that discriminate
against sensitive features such as gender or race; the cost-sensitivity
for groups of individuals in which prediction errors are more critical,
such as patients of a disease, by ensuring an acceptable accuracy
performance for them; local explainability, where the goal is to identify
the predictor variables that have the largest impact on the individual
predictions; as well as data complexity in the form of observations of
functional nature. The performance of our approach is illustrated on real
and synthetic data sets
Jeudi 25 Janvier
Heure: 10:30 - 11:30
Lieu: Salle B107, bâtiment B, Université de Villetaneuse
Résumé: A branch-and-bound method for multiobjective mixed integer quadratic programs based on dual relaxations
Description: Marianna De Santis Most real-world optimization problems in the areas of applied sciences, engineering and economics involve multiple, often conflicting and nonlinear, goals. In the mathematical model of these problems, under the necessity of reflecting discrete quantities, logical relationships or decisions, integer and 0-1-variables need to be introduced, leading to MultiObjective Mixed Integer Nonlinear Programming problems (MO-MINLPs). The practical relevance of MO-MINLPs is pointed out in many publications, where tailored approaches for specific applications have been proposed. MO-MINLPs are intrinsically nonconvex, implying that the design of exact and efficient solution methods is particularly challenging and requires global optimization techniques. In this talk, we present a branch-and-bound method for multiobjective mixed-integer convex quadratic programs that computes a superset of efficient integer assignments and a coverage of the nondominated set. The method relies on outer approximations of the upper image set of continuous relaxations. These outer approximations are obtained addressing the dual formulations of specific subproblems where the values of certain integer variables are fixed. The devised pruning conditions and a tailored preprocessing phase allow a fast enumeration of the nodes. Despite the fact that we do not require any boundedness of the feasible set, we are able to prove that the method stops after having explored a finite number of nodes. Numerical experiments on instances with two, three, and four objectives are presente