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Semidefinite programming (SDP) is a central topic in mathematical optimization with extensive studies on its efficient solvers. In this paper, we present a proof-of-principle sublinear-time algorithm for solving SDPs with low-rank…
Machine learning methods are commonly used to solve inverse problems, wherein an unknown signal must be estimated from few indirect measurements generated via a known acquisition procedure. In particular, neural networks perform well…
High dimension low sample size statistical analysis is important in a wide range of applications. In such situations, the highly appealing discrimination method, support vector machine, can be improved to alleviate data piling at the…
The maximum-cut problem is one of the fundamental problems in combinatorial optimization. With the advent of quantum computers, both the maximum-cut and the equivalent quadratic unconstrained binary optimization problem have experienced…
This paper investigates the asymptotic behavior of the soft-margin and hard-margin support vector machine (SVM) classifiers for simultaneously high-dimensional and numerous data (large $n$ and large $p$ with $n/p\to\delta$) drawn from a…
Deep Neural Networks and Reinforcement Learning methods have empirically shown great promise in tackling challenging combinatorial problems. In those methods a deep neural network is used as a solution generator which is then trained by…
The workflow satisfiability problem (WSP) asks whether there exists an assignment of authorised users to the steps in a workflow specification, subject to certain constraints on the assignment. (Such an assignment is called valid.) The…
A particularly interesting instance of supervised learning with kernels is when each training example is associated with two objects, as in pairwise classification (Brunner et al., 2012), and in supervised learning of preference relations…
In this work, we adopt Wyner common information framework for unsupervised multi-view representation learning. Within this framework, we propose two novel formulations that enable the development of computational efficient solvers based on…
We consider the problem of robust matrix completion, which aims to recover a low rank matrix $L_*$ and a sparse matrix $S_*$ from incomplete observations of their sum $M=L_*+S_*\in\mathbb{R}^{m\times n}$. Algorithmically, the robust matrix…
Considering the classification problem, we summarize the nonparallel support vector machines with the nonparallel hyperplanes to two types of frameworks. The first type constructs the hyperplanes separately. It solves a series of small…
This paper adapts a recently developed regularized stochastic version of the Broyden, Fletcher, Goldfarb, and Shanno (BFGS) quasi-Newton method for the solution of support vector machine classification problems. The proposed method is shown…
We consider Benders decomposition for solving two-stage stochastic programs with complete recourse based on finite samples of the uncertain parameters. We define the Benders cuts binding at the final optimal solution or the ones…
It is important to identify the change point of a system's health status, which usually signifies an incipient fault under development. The One-Class Support Vector Machine (OC-SVM) is a popular machine learning model for anomaly detection…
Multivariate data analysis techniques have the potential to improve physics analyses in many ways. The common classification problem of signal/background discrimination is one example. The Support Vector Machine learning algorithm is a…
Singular value decomposition (SVD) and matrix inversion are ubiquitous in scientific computing. Both tasks are computationally demanding for large scale matrices. Existing algorithms can approximatively solve these problems with a given…
We consider counterfactual explanations for private support vector machines (SVM), where the privacy mechanism that publicly releases the classifier guarantees differential privacy. While privacy preservation is essential when dealing with…
The support vector machine (SVM) is a well-established classification method whose name refers to the particular training examples, called support vectors, that determine the maximum margin separating hyperplane. The SVM classifier is known…
Distance metric learning aims to learn from the given training data a valid distance metric, with which the similarity between data samples can be more effectively evaluated for classification. Metric learning is often formulated as a…
In this paper we introduce the Wastewater Treatment Plant Problem, a real-world scheduling problem, and compare the performance of several tools on it. We show that, for a naive modeling, state-of-the-art SMT solvers outperform other tools…