Related papers: Stochastic Multi-Dimensional Deconvolution
Many interesting tasks in image restoration can be cast as linear inverse problems. A recent family of approaches for solving these problems uses stochastic algorithms that sample from the posterior distribution of natural images given the…
Microgrids are recognized as a relevant tool to absorb decentralized renewable energies in the energy mix. However, the sequential handling of multiple stochastic productions and demands, and of storage, make their management a delicate…
The dynamic mode decomposition (DMD) is a data-driven approach that extracts the dominant features from spatiotemporal data. In this work, we introduce sparse-mode DMD, a new variant of the optimized DMD framework that specifically…
An important theme in modern inverse problems is the reconstruction of time-dependent data from only finitely many measurements. To obtain satisfactory reconstruction results in this setting it is essential to strongly exploit temporal…
Multidimensional Scaling (MDS) is one of the most popular methods for dimensionality reduction and visualization of high dimensional data. Apart from these tasks, it also found applications in the field of geometry processing for the…
We analyze in a closed form the learning dynamics of stochastic gradient descent (SGD) for a single-layer neural network classifying a high-dimensional Gaussian mixture where each cluster is assigned one of two labels. This problem provides…
Dynamic Mode Decomposition (DMD) is an equation-free method that aims at reconstructing the best linear fit from temporal datasets. In this paper, we show that DMD does not provide accurate approximation for datasets describing oscillatory…
Dynamic Mode Decomposition (DMD) is a data-driven and model-free decomposition technique. It is suitable for revealing spatio-temporal features of both numerically and experimentally acquired data. Conceptually, DMD performs a…
Multidimensional imaging, capturing image data in more than two dimensions, has been an emerging field with diverse applications. Due to the limitation of two-dimensional detectors in obtaining the high-dimensional image data, computational…
We propose a new method for computing Dynamic Mode Decomposition (DMD) evolution matrices, which we use to analyze dynamical systems. Unlike the majority of existing methods, our approach is based on a variational formulation consisting of…
Interactive image restoration aims to generate restored images by adjusting a controlling coefficient which determines the restoration level. Previous works are restricted in modulating image with a single coefficient. However, real images…
Classical metric and non-metric multidimensional scaling (MDS) variants are widely known manifold learning (ML) methods which enable construction of low dimensional representation (projections) of high dimensional data inputs. However,…
This paper introduces two variational inference approaches for infinite-dimensional inverse problems, developed through gradient descent with a constant learning rate. The proposed methods enable efficient approximate sampling from the…
With the rapid increase of big data, distributed Machine Learning (ML) has been widely applied in training large-scale models. Stochastic Gradient Descent (SGD) is arguably the workhorse algorithm of ML. Distributed ML models trained by SGD…
Sample-based Bayesian inference provides a route to uncertainty quantification in the geosciences, and inverse problems in general, though is very computationally demanding in the naive form that requires simulating an accurate computer…
The stability and generalization of stochastic gradient-based methods provide valuable insights into understanding the algorithmic performance of machine learning models. As the main workhorse for deep learning, stochastic gradient descent…
We present a multilevel stochastic gradient descent method for the optimal control of systems governed by partial differential equations under uncertain input data. The gradient descent method used to find the optimal control leverages a…
This paper presents a novel adaptive-sparse polynomial dimensional decomposition (PDD) method for stochastic design optimization of complex systems. The method entails an adaptive-sparse PDD approximation of a high-dimensional stochastic…
Stochastic gradient descent (SGD) is a fundamental optimization algorithm widely used in modern machine learning. In this paper, we propose Factor-Augmented SGD (FSGD), a new optimization method that leverages latent factor representations…
Dynamic mode decomposition (DMD) is a powerful data-driven technique for construction of reduced-order models of complex dynamical systems. Multiple numerical tests have demonstrated the accuracy and efficiency of DMD, but mostly for…