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A novel two-phase molecule inference framework, mol-infer, has recently been developed to infer chemical graphs with prescribed abstract structures and desired property values through mixed integer linear programming (MILP) under the…
We consider the problem of learning a mixture of linear regressions (MLRs). An MLR is specified by $k$ nonnegative mixing weights $p_1, \ldots, p_k$ summing to $1$, and $k$ unknown regressors $w_1,...,w_k\in\mathbb{R}^d$. A sample from the…
We present a Mixed Integer Linear Program (MILP) approach in order to model the nonlinear problem of minimizing the tire noise. We first take more industrial constraints into account than in a former work of the authors. Then, we associate…
We consider regression models involving multilayer perceptrons (MLP) with one hidden layer and a Gaussian noise. The estimation of the parameters of the MLP can be done by maximizing the likelihood of the model. In this framework, it is…
Mixed Integer Programming (MIP) is one of the most widely used modeling techniques for combinatorial optimization problems. In many applications, a similar MIP model is solved on a regular basis, maintaining remarkable similarities in model…
Several recent publications report advances in training optimal decision trees (ODT) using mixed-integer programs (MIP), due to algorithmic advances in integer programming and a growing interest in addressing the inherent suboptimality of…
We investigate the problem of machine learning with mislabeled training data. We try to make the effects of mislabeled training better understood through analysis of the basic model and equations that characterize the problem. This includes…
Mixed-integer programming (MIP) technology offers a generic way of formulating and solving combinatorial optimization problems. While generally reliable, state-of-the-art MIP solvers base many crucial decisions on hand-crafted heuristics,…
Mixed Integer Programming (MIP) solvers rely on an array of sophisticated heuristics developed with decades of research to solve large-scale MIP instances encountered in practice. Machine learning offers to automatically construct better…
We study the problem of learning a linear model to set the reserve price in an auction, given contextual information, in order to maximize expected revenue from the seller side. First, we show that it is not possible to solve this problem…
A standard tool for modelling real-world optimisation problems is mixed-integer programming (MIP). However, for many of these problems, information about the relationships between variables is either incomplete or highly complex, making it…
Multiple kernel methods less consider the intrinsic manifold structure of multiple kernel data and estimate the consensus kernel matrix with quadratic number of variables, which makes it vulnerable to the noise and outliers within multiple…
Mixed-Integer Linear Programming (MILP) is a foundational tool for complex decision-making problems. However, the NP-hard nature of MILP presents a significant computational challenge, motivating the development of machine learning-based…
Training large language models (LLMs) efficiently while preserving model quality poses significant challenges, particularly with subbyte precision supported by state-of-the-art GPUs. Current mixed-precision training approaches either apply…
Large Neighbourhood Search (LNS) is a powerful heuristic framework for solving Mixed-Integer Programming (MIP) problems. However, designing effective variable selection strategies in LNS remains challenging, especially for diverse sets of…
Mixture of Experts (MoE) are successful models for modeling heterogeneous data in many statistical learning problems including regression, clustering and classification. Generally fitted by maximum likelihood estimation via the well-known…
The iteration dynamics of the coupled cluster equations exhibits a synergistic relationship among the cluster amplitudes. The iteration scheme may be viewed as a multivariate discrete-time propagation of nonlinearly coupled equations, which…
Recent advances in mathematical programming have made Mixed Integer Optimization a competitive alternative to popular regularization methods for selecting features in regression problems. The approach exhibits unquestionable foundational…
In this paper we propose novel methodologies to construct Support Vector Machine -based classifiers that takes into account that label noises occur in the training sample. We propose different alternatives based on solving Mixed Integer…
This applied research article explores the application of Mixed-Integer Linear Programming (MILP) to address line-balancing challenges in the garment industry, focusing on optimizing production processes under multiple constraints. By…