Related papers: Mixed integer programming formulation of unsupervi…

In this paper, we explore model-based approach to training robust and interpretable binarized regression models for multiclass classification tasks using Mixed-Integer Programming (MIP). Our MIP model balances the optimization of prediction…

Mixed integer linear programming (MILP) is a powerful representation often used to formulate decision-making problems under uncertainty. However, it lacks a natural mechanism to reason about objects, classes of objects, and relations.…

Recent research on multiple kernel learning has lead to a number of approaches for combining kernels in regularized risk minimization. The proposed approaches include different formulations of objectives and varying regularization…

In this research we propose a new method for training predictive machine learning models for prescriptive applications. This approach, which we refer to as coupled validation, is based on tweaking the validation step in the standard…

The study proves the existence of an algorithm to receive all elements of a class of binary matrices without obtaining redundant elements, e. g. without obtaining binary matrices that do not belong to the class. This makes it possible to…

A wide range of machine learning algorithms iteratively add data to the training sample. Examples include semi-supervised learning, active learning, multi-armed bandits, and Bayesian optimization. We embed this kind of data addition into…

Mixed-integer linear programming (MILP) has been a fundamental problem in combinatorial optimization. Conventional MILP solving mainly relies on carefully designed heuristics embedded in the branch-and-bound framework. Driven by the strong…

Multiagent planning and coordination problems are common and known to be computationally hard. We show that a wide range of two-agent problems can be formulated as bilinear programs. We present a successive approximation algorithm that…

This paper addresses distributed consensus optimization problems with mixed-integer variables, with a specific focus on Boolean variables. We introduce a novel distributed algorithm that extends the Consensus Augmented Lagrangian…

Learning the parameters of graphical models using the maximum likelihood estimation is generally hard which requires an approximation. Maximum composite likelihood estimations are statistical approximations of the maximum likelihood…

Among the most famous algorithms for solving classification problems are support vector machines (SVMs), which find a separating hyperplane for a set of labeled data points. In some applications, however, labels are only available for a…

The study of representations invariant to common transformations of the data is important to learning. Most techniques have focused on local approximate invariance implemented within expensive optimization frameworks lacking explicit…

ML models have errors when used for predictions. The errors are unknown but can be quantified by model uncertainty. When multiple ML models are trained using the same training points, their model uncertainties may be statistically…

Machine learning methods for computational imaging require uncertainty estimation to be reliable in real settings. While Bayesian models offer a computationally tractable way of recovering uncertainty, they need large data volumes to be…

Bayesian models are a powerful tool for studying complex data, allowing the analyst to encode rich hierarchical dependencies and leverage prior information. Most importantly, they facilitate a complete characterization of uncertainty…

In this work we define and analyze the bilinear models which replace the conventional linear operation used in many building blocks of machine learning (ML). The main idea is to devise the ML algorithms which are adapted to the objects they…

Decision trees are one of the most popular methods for solving classification problems, mainly because of their good interpretability properties. Moreover, due to advances in recent years in mixed-integer optimization, several models have…

Semi-supervised learning is a setting in which one has labeled and unlabeled data available. In this survey we explore different types of theoretical results when one uses unlabeled data in classification and regression tasks. Most methods…

Training in machine learning generally consists in finding one model, whose parameters minimize a data-dependent loss. Yet, empirical work shows that ensemble learning, an approach in which multiple models are sampled, can improve…

This paper analyses the feasible sets structure of general mixed integer linear programs (MIPs) and its relationship with the existence of a finite cardinality test set which can be applied in augmentation algorithms. We derive and…