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Purpose: To develop a deep learning method on a nonlinear manifold to explore the temporal redundancy of dynamic signals to reconstruct cardiac MRI data from highly undersampled measurements. Methods: Cardiac MR image reconstruction is…

Image and Video Processing · Electrical Eng. & Systems 2021-04-05 Ziwen Ke , Zhuo-Xu Cui , Wenqi Huang , Jing Cheng , Sen Jia , Haifeng Wang , Xin Liu , Hairong Zheng , Leslie Ying , Yanjie Zhu , Dong Liang

We introduce a novel and highly tractable supervised learning approach based on neural networks that can be applied for the computation of model-free price bounds of, potentially high-dimensional, financial derivatives and for the…

Computational Finance · Quantitative Finance 2022-12-15 Ariel Neufeld , Julian Sester

Deep auto-encoders (DAEs) have achieved great success in learning data representations via the powerful representability of neural networks. But most DAEs only focus on the most dominant structures which are able to reconstruct the data…

Machine Learning · Computer Science 2020-07-14 Zhao Kang , Xiao Lu , Jian Liang , Kun Bai , Zenglin Xu

Optimal experimental design is a well studied field in applied science and engineering. Techniques for estimating such a design are commonly used within the framework of parameter estimation. Nonetheless, in recent years parameter…

Machine Learning · Statistics 2025-01-13 Md Shahriar Rahim Siddiqui , Arman Rahmim , Eldad Haber

This paper studies the performative prediction problem where a learner aims to minimize the expected loss with a decision-dependent data distribution. Such setting is motivated when outcomes can be affected by the prediction model, e.g., in…

Optimization and Control · Mathematics 2024-05-24 Haitong Liu , Qiang Li , Hoi-To Wai

In this paper, we present a novel method for achieving dexterous manipulation of complex objects, while simultaneously securing the object without the use of passive support surfaces. We posit that a key difficulty for training such…

Developing agents that can perform challenging complex tasks is the goal of reinforcement learning. The model-free reinforcement learning has been considered as a feasible solution. However, the state of the art research has been to develop…

Machine Learning · Computer Science 2020-08-24 MyungJae Shin , Joongheon Kim

A novel derivative-free algorithm, optimization by moving ridge functions (OMoRF), for unconstrained and bound-constrained optimization is presented. This algorithm couples trust region methodologies with output-based dimension reduction to…

Optimization and Control · Mathematics 2021-01-07 James C. Gross , Geoffrey T. Parks

We study the problem of zero-order optimization of a strongly convex function. The goal is to find the minimizer of the function by a sequential exploration of its values, under measurement noise. We study the impact of higher order…

Machine Learning · Computer Science 2022-11-28 Arya Akhavan , Massimiliano Pontil , Alexandre B. Tsybakov

Many applications in machine learning or signal processing involve nonsmooth optimization problems. This nonsmoothness brings a low-dimensional structure to the optimal solutions. In this paper, we propose a randomized proximal gradient…

Optimization and Control · Mathematics 2020-04-29 Dmitry Grishchenko , Franck Iutzeler , Jérôme Malick

Large models and enormous data are essential driving forces of the unprecedented successes achieved by modern algorithms, especially in scientific computing and machine learning. Nevertheless, the growing dimensionality and model…

Machine Learning · Computer Science 2023-10-04 Yijun Dong

Robust optimization has been established as a leading methodology to approach decision problems under uncertainty. To derive a robust optimization model, a central ingredient is to identify a suitable model for uncertainty, which is called…

Optimization and Control · Mathematics 2021-09-10 Marc Goerigk , Jannis Kurtz

The Manifold Hypothesis is a widely accepted tenet of Machine Learning which asserts that nominally high-dimensional data are in fact concentrated near a low-dimensional manifold, embedded in high-dimensional space. This phenomenon is…

Methodology · Statistics 2025-03-24 Nick Whiteley , Annie Gray , Patrick Rubin-Delanchy

Unsupervised deep metric learning (UDML) focuses on learning a semantic representation space using only unlabeled data. This challenging problem requires accurately estimating the similarity between data points, which is used to supervise a…

Computer Vision and Pattern Recognition · Computer Science 2024-03-25 Shubhang Bhatnagar , Narendra Ahuja

This article discusses a newly developed online manifold learning method, subspace iteration using reduced models (SIRM), for the dimensionality reduction of dynamical systems. This method may be viewed as subspace iteration combined with a…

Dynamical Systems · Mathematics 2014-07-24 Liqian Peng , Kamran Mohseni

In reward-free reinforcement learning (RL), an agent explores the environment first without any reward information, in order to achieve certain learning goals afterwards for any given reward. In this paper we focus on reward-free RL under…

Machine Learning · Computer Science 2023-03-21 Yuan Cheng , Ruiquan Huang , Jing Yang , Yingbin Liang

Sampling-based algorithms are widely used for motion planning in high-dimensional configuration spaces. However, due to low sampling efficiency, their performance often diminishes in complex configuration spaces with narrow corridors.…

Robotics · Computer Science 2025-07-22 Lu Huang , Lingxiao Meng , Jiankun Wang , Xingjian Jing

We study the problem of learning classification functions from noiseless training samples, under the assumption that the decision boundary is of a certain regularity. We establish universal lower bounds for this estimation problem, for…

Functional Analysis · Mathematics 2021-12-28 Philipp Petersen , Felix Voigtlaender

The discovering of low-dimensional manifolds in high-dimensional data is one of the main goals in manifold learning. We propose a new approach to identify the effective dimension (intrinsic dimension) of low-dimensional manifolds. The scale…

Statistics Theory · Mathematics 2008-03-17 Xiaohui Wang , J. S. Marron

Solving optimization problems with unknown parameters often requires learning a predictive model to predict the values of the unknown parameters and then solving the problem using these values. Recent work has shown that including the…

Machine Learning · Computer Science 2020-10-23 Kai Wang , Bryan Wilder , Andrew Perrault , Milind Tambe