Related papers: Mixed integer programming formulation of unsupervi…
We consider the problem of optimally designing a system for repeated use under uncertainty. We develop a modeling framework that integrates design and operational phases, which are represented by a mixed-integer program and discounted-cost…
Unsupervised learning requiring only raw data is not only a fundamental function of the cerebral cortex, but also a foundation for a next generation of artificial neural networks. However, a unified theoretical framework to treat sensory…
Research efforts of the past fifty years have led to a development of linear integer programming as a mature discipline of mathematical optimization. Such a level of maturity has not been reached when one considers nonlinear systems subject…
We introduce a new paradigm to investigate unsupervised learning, reducing unsupervised learning to supervised learning. Specifically, we mitigate the subjectivity in unsupervised decision-making by leveraging knowledge acquired from prior,…
This work introduces a framework to address the computational complexity inherent in Mixed-Integer Programming (MIP) models by harnessing the potential of deep learning. By employing deep learning, we construct problem-specific heuristics…
The problem of computing an exact experimental design that is optimal for the least-squares estimation of the parameters of a regression model is considered. We show that this problem can be solved via mixed-integer linear programming…
In this paper, we present a novel approach to construct multiclass classifiers by means of arrangements of hyperplanes. We propose different mixed integer (linear and non linear) programming formulations for the problem using extensions of…
We introduce a unified framework for the study of multilevel mixed integer linear optimization problems and multistage stochastic mixed integer linear optimization problems with recourse. The framework highlights the common mathematical…
This work introduces a verification framework that provides both sound and complete guarantees for data poisoning attacks during neural network training. We formulate adversarial data manipulation, model training, and test-time evaluation…
We consider the problem of inference in higher-order undirected graphical models with binary labels. We formulate this problem as a binary polynomial optimization problem and propose several linear programming relaxations for it. We compare…
Advances in high-throughput technologies have originated an ever-increasing availability of omics datasets. The integration of multiple heterogeneous data sources is currently an issue for biology and bioinformatics. Multiple kernel…
Mixed integer Model Predictive Control (MPC) problems arise in the operation of systems where discrete and continuous decisions must be taken simultaneously to compensate for disturbances. The efficient solution of mixed integer MPC…
We consider statistical procedures for hypothesis testing of real valued functionals of matched pairs with missing values. In order to improve the accuracy of existing methods, we propose a novel multiplication combination procedure.…
Unsupervised learning in a generalized Hopfield associative-memory network is investigated in this work. First, we prove that the (generalized) Hopfield model is equivalent to a semi-restricted Boltzmann machine with a layer of visible…
In this paper we propose a technique that assigns obstacles to clusters used for collision avoidance via Mixed-Integer Programming. This strategy enables a reduction in the number of binary variables used for collision avoidance, thus…
We propose a methodology, based on machine learning and optimization, for selecting a solver configuration for a given instance. First, we employ a set of solved instances and configurations in order to learn a performance function of the…
Multi-objective integer or mixed-integer programming problems typically have disconnected feasible domains, making the task of constructing an approximation of the Pareto front challenging. The present paper shows that certain algorithms…
The restricted Boltzmann machine is a basic machine learning tool able, in principle, to model the distribution of some arbitrary dataset. Its standard training procedure appears however delicate and obscure in many respects. We bring some…
The shift design and the personnel scheduling problem is known to be a difficult problem. It is a real-world problem which has lots of applications in the organization of companies. Solutions are usually found by dividing the problem in two…
Machine Learning models are increasingly used for decision making, in particular in high-stakes applications such as credit scoring, medicine or recidivism prediction. However, there are growing concerns about these models with respect to…