Related papers: Riemannian information gradient methods for the pa…

In this study, we investigate stochastic optimization on Riemannian manifolds, focusing on the crucial variance reduction mechanism used in both Euclidean and Riemannian settings. Riemannian variance-reduced methods usually involve a…

The inverse Gaussian (IG) is one of the most famous and considered distributions with positive support. We propose a convenient mode-based parameterization yielding the reparametrized IG (rIG) distribution; it allows/simplifies the use of…

Although color is a fundamental feature of human visual perception, it has been largely unexplored in the reduced-reference (RR) image quality assessment (IQA) schemes. In this paper, we propose a natural scene statistic (NSS) method, which…

Inspired by dynamic programming, we propose Stochastic Virtual Gradient Descent (SVGD) algorithm where the Virtual Gradient is defined by computational graph and automatic differentiation. The method is computationally efficient and has…

By restricting the iterate on a nonlinear manifold, the recently proposed Riemannian optimization methods prove to be both efficient and effective in low rank tensor completion problems. However, existing methods fail to exploit the easily…

A challenge in high-dimensional inverse problems is developing iterative solvers to find the accurate solution of regularized optimization problems with low computational cost. An important example is computed tomography (CT) where both…

Stochastic gradient descent (SGD) and projected stochastic gradient descent (PSGD) are scalable algorithms to compute model parameters in unconstrained and constrained optimization problems. In comparison with SGD, PSGD forces its iterative…

Generative models have recently gained increasing attention in image generation and editing tasks. However, they often lack a direct connection to object geometry, which is crucial in sensitive domains such as computational anatomy,…

Many Markov Chain Monte Carlo (MCMC) methods leverage gradient information of the potential function of target distribution to explore sample space efficiently. However, computing gradients can often be computationally expensive for large…

This report concerns the problem of dimensionality reduction through information geometric methods on statistical manifolds. While there has been considerable work recently presented regarding dimensionality reduction for the purposes of…

This paper studies an acceleration technique for incremental aggregated gradient ({\sf IAG}) method through the use of \emph{curvature} information for solving strongly convex finite sum optimization problems. These optimization problems of…

Deep learning-based EEG classification is crucial for the automated detection of neurological disorders, improving diagnostic accuracy and enabling early intervention. However, the low signal-to-noise ratio of EEG signals limits model…

Stochastic-gradient sampling methods are often used to perform Bayesian inference on neural networks. It has been observed that the methods in which notions of differential geometry are included tend to have better performances, with the…

Stochastic minimax optimization on Riemannian manifolds has recently attracted significant attention due to its broad range of applications, such as robust training of neural networks and robust maximum likelihood estimation. Existing…

Importance sampling has become an indispensable strategy to speed up optimization algorithms for large-scale applications. Improved adaptive variants - using importance values defined by the complete gradient information which changes…

With rising powerful, low-cost embedded devices, the edge computing has become an increasingly popular choice. In this paper, we propose a new incremental local stochastic gradient descent (SGD) tailored on the Raspberry Pi to deal with…

Novel convergence analyses are presented of Riemannian stochastic gradient descent (RSGD) on a Hadamard manifold. RSGD is the most basic Riemannian stochastic optimization algorithm and is used in many applications in the field of machine…

Research on the use of information geometry (IG) in modern physics has witnessed significant advances recently. In this review article, we report on the utilization of IG methods to define measures of complexity in both classical and,…

Constrained optimization plays a crucial role in the fields of quantum physics and quantum information science and becomes especially challenging for high-dimensional complex structure problems. One specific issue is that of quantum process…

We consider stochastic optimization under distributional uncertainty, where the unknown distributional parameter is estimated from streaming data that arrive sequentially over time. Moreover, data may depend on the decision of the time when…