Related papers: Riemannian information gradient methods for the pa…

Riemannian optimization has drawn a lot of attention due to its wide applications in practice. Riemannian stochastic first-order algorithms have been studied in the literature to solve large-scale machine learning problems over Riemannian…

Feature attribution methods, or saliency maps, are one of the most popular approaches for explaining the decisions of complex machine learning models such as deep neural networks. In this study, we propose a stochastic optimization approach…

This paper focus on investigating the distributed Riemannian stochastic optimization problem on the Stiefel manifold for multi-agent systems, where all the agents work collaboratively to optimize a function modeled by the average of their…

Bayesian experimental design (BED) is to answer the question that how to choose designs that maximize the information gathering. For implicit models, where the likelihood is intractable but sampling is possible, conventional BED methods…

In this paper, we dive into the reliability concerns of Integrated Gradients (IG), a prevalent feature attribution method for black-box deep learning models. We particularly address two predominant challenges associated with IG: the…

Optimal experimental design (OED) seeks experiments expected to yield the most useful data for some purpose. In practical circumstances where experiments are time-consuming or resource-intensive, OED can yield enormous savings. We pursue…

Differential equations (DEs) are crucial for modeling the evolution of natural or engineered systems. Traditionally, the parameters in DEs are adjusted to fit data from system observations. However, in fields such as politics, economics,…

Stochastic gradient descent (SGD) is a powerful method for large-scale optimization problems in the area of machine learning, especially for a finite-sum formulation with numerous variables. In recent years, mini-batch SGD gains great…

The Mutual Information (MI) is an often used measure of dependency between two random variables utilized in information theory, statistics and machine learning. Recently several MI estimators have been proposed that can achieve parametric…

Stochastic gradient descent (SGD) is a promising method for solving large-scale inverse problems, due to its excellent scalability with respect to data size. In this work, we analyze a new data-driven regularized stochastic gradient descent…

In this paper, we present a multilevel Monte Carlo (MLMC) version of the Stochastic Gradient (SG) method for optimization under uncertainty, in order to tackle Optimal Control Problems (OCP) where the constraints are described in the form…

Deep Learning (DL) methods have been used for electrocardiogram (ECG) processing in a wide variety of tasks, demonstrating good performance compared with traditional signal processing algorithms. These methods offer an efficient framework…

Magnetic resonance imaging is a powerful, non invasive tool for medical diagnosis. The low sensitivity for detecting the nuclear spin signals, typically limits the image resolution to several tens of micrometers in preclinical systems and…

The development of EEG decoding algorithms confronts challenges such as data sparsity, subject variability, and the need for precise annotations, all of which are vital for advancing brain-computer interfaces and enhancing the diagnosis of…

Recent work has demonstrated that imaging systems can be evaluated through the information content of their measurements alone, enabling application-agnostic optical design that avoids computational decoding challenges. Information-Driven…

In recent years, Riemannian stochastic gradient descent (R-SGD), Riemannian stochastic variance reduction (R-SVRG) and Riemannian stochastic recursive gradient (R-SRG) have attracted considerable attention on Riemannian optimization. Under…

In this contribution, we present a numerical analysis of the continuous stochastic gradient (CSG) method, including applications from topology optimization and convergence rates. In contrast to standard stochastic gradient optimization…

In many applications involving large dataset or online updating, stochastic gradient descent (SGD) provides a scalable way to compute parameter estimates and has gained increasing popularity due to its numerical convenience and memory…

Adaptive stochastic gradient algorithms in the Euclidean space have attracted much attention lately. Such explorations on Riemannian manifolds, on the other hand, are relatively new, limited, and challenging. This is because of the…

This paper presents enhancement strategies for the Hermitian and skew-Hermitian splitting method based on gradient iterations. The spectral properties are exploited for the parameter estimation, often resulting in a better convergence. In…