Related papers: A note on incremental POD algorithms for continuou…
The tensor-train (TT) decomposition is widely used to compress large tensors into a more compact form by exploiting their inherent data structures. A fundamental approach for constructing the TT format is the well-known TT-SVD method, which…
We propose new continuous-time formulations for first-order stochastic optimization algorithms such as mini-batch gradient descent and variance-reduced methods. We exploit these continuous-time models, together with simple Lyapunov analysis…
This paper introduces unified models for high-dimensional factor-based Ito process, which can accommodate both continuous-time Ito diffusion and discrete-time stochastic volatility (SV) models by embedding the discrete SV model in the…
We study the convergence of the Augmented Decomposition Algorithm (ADA) proposed in [32] for solving multi-block separable convex minimization problems subject to linear constraints. We show that the global convergence rate of the exact ADA…
Data-driven decompositions of Particle Image Velocimetry (PIV) measurements are widely used for a variety of purposes, including the detection of coherent features (e.g., vortical structures), filtering operations (e.g., outlier removal or…
Recently, researchers have investigated the relationship between proper orthogonal decomposition (POD), difference quotients (DQs), and pointwise in time error bounds for POD reduced order models of partial differential equations. In a…
This paper presents exact Semi-Definite Program (SDP) reformulations for infinite-dimensional moment optimization problems involving a new class of piecewise Sum-of-Squares (SOS)-convex functions and projected spectrahedral support sets.…
We introduce and study a discrete multi-period extension of the classical knapsack problem, dubbed generalized incremental knapsack. In this setting, we are given a set of $n$ items, each associated with a non-negative weight, and $T$ time…
Particle advection is one of the foundational algorithms for visualization and analysis and is central to understanding vector fields common to scientific simulations. Achieving efficient performance with large data in a distributed memory…
We investigate Stochastic Mirror Descent (SMD) with matrix parameters and vector-valued predictions, a framework relevant to multi-class classification and matrix completion problems. Focusing on the overparameterized regime, where the…
Aiming to provide a faster and convenient truncated SVD algorithm for large sparse matrices from real applications (i.e. for computing a few of largest singular values and the corresponding singular vectors), a dynamically shifted power…
Incremental methods are widely utilized for solving finite-sum optimization problems in machine learning and signal processing. In this paper, we study a family of incremental methods -- including incremental subgradient, incremental…
Support vector data description (SVDD) is a machine learning technique that is used for single-class classification and outlier detection. The idea of SVDD is to find a set of support vectors that defines a boundary around data. When…
Particle-optimization-based sampling (POS) is a recently developed effective sampling technique that interactively updates a set of particles. A representative algorithm is the Stein variational gradient descent (SVGD). We prove, under…
The dynamic mode decomposition (DMD) has become a leading tool for data-driven modeling of dynamical systems, providing a regression framework for fitting linear dynamical models to time-series measurement data. We present a simple…
Various Neural Networks employ time-consuming matrix operations like matrix inversion. Many such matrix operations are faster to compute given the Singular Value Decomposition (SVD). Previous work allows using the SVD in Neural Networks…
This paper introduces a high performance implementation of \texttt{Zolo-SVD} algorithm on distributed memory systems, which is based on the polar decomposition (PD) algorithm via the Zolotarev's function (\texttt{Zolo-PD}), originally…
In this paper we analyze the finite element approximation of the Stokes equations with non-smooth Dirichlet boundary data. To define the discrete solution, we first approximate the boundary datum by a smooth one and then apply a standard…
This paper presents unifying results for subspace identification (SID) and dynamic mode decomposition (DMD) for autonomous dynamical systems. We observe that SID seeks to solve an optimization problem to estimate an extended observability…
An important task when processing sensor data is to distinguish relevant from irrelevant data. This paper describes a method for an iterative singular value decomposition that maintains a model of the background via singular vectors…