Related papers: Functional Gradient Flows for Constrained Sampling

Variational inference is computationally challenging in models that contain both conjugate and non-conjugate terms. Methods specifically designed for conjugate models, even though computationally efficient, find it difficult to deal with…

Recent advances in the application of physics-informed learning into the field of fluid mechanics have been predominantly grounded in the Newtonian framework, primarly leveraging Navier-Stokes Equation or one of its various derivative to…

In this paper, we propose a new numerical scheme for a spatially discrete model of constrained total variation flows, which are total variation flows whose values are constrained in a Riemannian manifold. The difficulty of this problem is…

Retinal vessel segmentation serves as a critical prerequisite for automated diagnosis of retinal pathologies. While recent advances in Convolutional Neural Networks (CNNs) have demonstrated promising performance in this task, significant…

In this paper we propose a splitting scheme which hybridizes generalized conditional gradient with a proximal step which we call CGALP algorithm, for minimizing the sum of three proper convex and lower-semicontinuous functions in real…

Many tasks in machine learning and signal processing can be solved by minimizing a convex function of a measure. This includes sparse spikes deconvolution or training a neural network with a single hidden layer. For these problems, we study…

Sampling theory in fractional Fourier Transform (FrFT) domain has been studied extensively in the last decades. This interest stems from the ability of the FrFT to generalize the traditional Fourier Transform, broadening the traditional…

Gradient clipping is commonly used in training deep neural networks partly due to its practicability in relieving the exploding gradient problem. Recently, \citet{zhang2019gradient} show that clipped (stochastic) Gradient Descent (GD)…

Medical image segmentation plays an important role in accurately identifying and isolating regions of interest within medical images. Generative approaches are particularly effective in modeling the statistical properties of segmentation…

Many core problems in robotics can be framed as constrained optimization problems. Often on these problems, the robotic system has uncertainty, or it would be advantageous to identify multiple high quality feasible solutions. To enable…

This paper introduces a novel approach to compute the numerical fluxes at the cell boundaries for a cell-centered conservative numerical scheme. Explicit gradients used in deriving the reconstruction polynomials are replaced by high-order…

In many sequential decision-making problems one is interested in minimizing an expected cumulative cost while taking into account \emph{risk}, i.e., increased awareness of events of small probability and high consequences. Accordingly, the…

We focus on the problem of semantic segmentation based on RGB-D data, with emphasis on analyzing cluttered indoor scenes containing many instances from many visual categories. Our approach is based on a parametric figure-ground intensity…

We propose a variational form of the BDF2 method as an alternative to the commonly used minimizing movement scheme for the time-discrete approximation of gradient flows in abstract metric spaces. Assuming uniform semi-convexity --- but no…

Since its discovery over the last decade, Compressed Sensing (CS) has been successfully applied to Magnetic Reso- nance Imaging (MRI). It has been shown to be a powerful way to reduce scanning time without sacrificing image quality. MR…

We propose a method for efficiently incorporating constraints into a stochastic gradient Langevin framework for the training of deep neural networks. Constraints allow direct control of the parameter space of the model. Appropriately…

We introduce a theoretical and practical framework for efficient importance sampling of mini-batch samples for gradient estimation from single and multiple probability distributions. To handle noisy gradients, our framework dynamically…

Although deep neural networks (NNs) have achievedstate-of-the-art accuracy in many visual recognition tasks,the growing computational complexity and energy con-sumption of networks remains an issue, especially for ap-plications on platforms…

Power system networks are often modeled as homogeneous graphs, which limits the ability of graph neural network (GNN) to capture individual generator features at the same nodes. By introducing the proposed virtual node-splitting strategy,…

In this paper, we study a Markov chain-based stochastic gradient algorithm in general Hilbert spaces, aiming at approximating the optimal solution of a quadratic loss function. We establish probabilistic upper bounds on its convergence. We…