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Deep metrics have been shown effective as similarity measures in multi-modal image registration; however, the metrics are currently constructed from aligned image pairs in the training data. In this paper, we propose a strategy for learning…

Operator learning offers a robust framework for approximating mappings between infinite-dimensional function spaces. It has also become a powerful tool for solving inverse problems in the computational sciences. This chapter surveys…

Analyzing high-dimensional data with manifold learning algorithms often requires searching for the nearest neighbors of all observations. This presents a computational bottleneck in statistical manifold learning when observations of…

Deep metric learning maps visually similar images onto nearby locations and visually dissimilar images apart from each other in an embedding manifold. The learning process is mainly based on the supplied image negative and positive training…

Many real-world decision processes are modeled by optimization problems whose defining parameters are unknown and must be inferred from observable data. The Predict-Then-Optimize framework uses machine learning models to predict unknown…

The method of choice to study one-dimensional strongly interacting many body quantum systems is based on matrix product states and operators. Such method allows to explore the most relevant, and numerically manageable, portion of an…

In the rapidly evolving research on artificial intelligence (AI) the demand for fast, computationally efficient, and scalable solutions has increased in recent years. The problem of optimizing the computing resources for distributed machine…

In multi-task learning, multiple tasks are solved jointly, sharing inductive bias between them. Multi-task learning is inherently a multi-objective problem because different tasks may conflict, necessitating a trade-off. A common compromise…

In distributed optimization, the practical problem-solving performance is essentially sensitive to algorithm selection, parameter setting, problem type and data pattern. Thus, it is often laborious to acquire a highly efficient method for a…

Proximal algorithms have gained popularity in recent years in large-scale and distributed optimization problems. One such problem is the phase retrieval problem, for which proximal operators have been proposed recently. The phase retrieval…

Split Learning (SL) is a promising Distributed Learning approach in electromyography (EMG) based prosthetic control, due to its applicability within resource-constrained environments. Other learning approaches, such as Deep Learning and…

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…

Collaborative training can improve the accuracy of a model for a user by trading off the model's bias (introduced by using data from other users who are potentially different) against its variance (due to the limited amount of data on any…

In many operational applications, it is necessary to routinely find, within a very limited time window, provably good solutions to challenging mixed-integer linear programming (MILP) problems. An example is the Security-Constrained Unit…

We revisit the operator splitting schemes proposed in a recent work of [Some extensions of the operator splitting schemes based on Lagrangian and primal-dual: A unified proximal point analysis, Feng Xue, Optimization, 2022, doi:…

The proximal point algorithm is a widely used tool for solving a variety of convex optimization problems such as finding zeros of maximally monotone operators, fixed points of nonexpansive mappings, as well as minimizing convex functions.…

Mappings to structured output spaces (strings, trees, partitions, etc.) are typically learned using extensions of classification algorithms to simple graphical structures (eg., linear chains) in which search and parameter estimation can be…

Multi-Task Learning (MTL) is a foundational machine learning problem that has seen extensive development over the past decade. Recently, various optimization-based MTL approaches have been proposed to learn multiple tasks simultaneously by…

As deep learning methodologies have developed, it has been generally agreed that increasing neural network size improves model quality. However, this is at the expense of memory and compute requirements, which also need to be increased.…

We present a novel deep learning approach to approximate the solution of large, sparse, symmetric, positive-definite linear systems of equations. These systems arise from many problems in applied science, e.g., in numerical methods for…