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We introduce Bayesian optimization, a technique developed for optimizing time-consuming engineering simulations and for fitting machine learning models on large datasets. Bayesian optimization guides the choice of experiments during…

In this paper, we propose a new mathematical optimization model for multiclass classification based on arrangements of hyperplanes. Our approach preserves the core support vector machine (SVM) paradigm of maximizing class separation while…

Computational imaging has been revolutionized by compressed sensing algorithms, which offer guaranteed uniqueness, convergence, and stability properties. Model-based deep learning methods that combine imaging physics with learned…

We propose a new data representation method based on Quantum Cognition Machine Learning and apply it to manifold learning, specifically to the estimation of intrinsic dimension of data sets. The idea is to learn a representation of each…

Multiobjective feature selection seeks to determine the most discriminative feature subset by simultaneously optimizing two conflicting objectives: minimizing the number of selected features and the classification error rate. The goal is to…

In this work, we employ the Constraint Energy Minimizing Generalized Multiscale Finite Element Method (CEM-GMsFEM) to solve the problem of linear heterogeneous poroelasticity with coefficients of high contrast. The proposed method makes use…

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…

Efficient characterization of quantum devices is a significant challenge critical for the development of large scale quantum computers. We consider an experimentally motivated situation, in which we have a decent estimate of the…

In this paper we present a unified framework for solving a general class of problems arising in the context of set-membership estimation/identification theory. More precisely, the paper aims at providing an original approach for the…

This paper investigates the problem of image classification with limited or no annotations, but abundant unlabeled data. The setting exists in many tasks such as semi-supervised image classification, image clustering, and image retrieval.…

A topology optimization method is presented for the design of periodic microstructured materials with prescribed homogenized nonlinear constitutive properties over finite strain ranges. The mechanical model assumes linear elastic isotropic…

We consider fast deterministic algorithms to identify the "best" linearly independent terms in multivariate mixtures and use them to compute, up to a user-selected accuracy, an equivalent representation with fewer terms. One algorithm…

Computing atomic-scale properties of chemically disordered materials requires an efficient exploration of their vast configuration space. Traditional approaches such as Monte Carlo or Special Quasirandom Structures either entail sampling an…

Harmonic inpainting with optimised data is very popular for inpainting-based image compression. We improve this approach in three important aspects. Firstly, we replace the standard finite differences discretisation by a finite element…

One of the main challenges for feature representation in deep learning-based classification is the design of appropriate loss functions that exhibit strong discriminative power. The classical softmax loss does not explicitly encourage…

This paper is to give a new understanding and applications of the subspace projection method for selfadjoint eigenvalue problems. A new error estimate in the energy norm, which is induced by the stiff matrix, of the subspace projection…

We propose a construction for joint feature learning and clustering of multichannel extracellular electrophysiological data across multiple recording periods for action potential detection and discrimination ("spike sorting"). Our…

Penalized estimation can conduct variable selection and parameter estimation simultaneously. The general framework is to minimize a loss function subject to a penalty designed to generate sparse variable selection. The…

It has been a long-standing goal in machine learning, as well as in AI more generally, to develop life-long learning systems that learn many different tasks over time, and reuse insights from tasks learned, "learning to learn" as they do…

Multi-view clustering integrates multiple feature sets, which reveal distinct aspects of the data and provide complementary information to each other, to improve the clustering performance. It remains challenging to effectively exploit…