Publications related to Convergences of Regularized Algorithms and Stochastic Gradient Methods with Random Projections

Optimal Rates for Spectral Algorithms with Least-Squares Regression over Hilbert Spaces

In this paper, we study regression problems over a separable Hilbert space with the square loss, covering non-parametric regression over a reproducing kernel Hilbert space. We investigate a class of spectral/regularized algorithms, including ridge regressi ...

2018

Smoothing Alternating Direction Methods for Fully Nonsmooth Constrained Convex Optimization

Volkan Cevher, Quoc Tran Dinh

We propose two new alternating direction methods to solve “fully” nonsmooth constrained convex problems. Our algorithms have the best known worst-case iteration-complexity guarantee under mild assumptions for both the objective residual and feasibility gap ...

Springer2018

A Functional Framework for Enhanced Ultrasound Imaging

Ultrasound systems are cheap, portable, and fast, which have become impressively popular over the last decades. State-of art imaging is however known to be sub-optimal. Most attempts to improve it formulate the problem on a discrete spatial grid and suffer ...

2017

Harder, Better, Faster, Stronger Convergence Rates for Least-Squares Regression

Nicolas Henri Bernard Flammarion, Aymeric Daphnis Kévin Dieuleveut

We consider the optimization of a quadratic objective function whose gradients are only accessible through a stochastic oracle that returns the gradient at any given point plus a zero-mean finite variance random error. We present the first algorithm that a ...

2017

Fixed Points For Bounded Orbits In Hilbert Spaces

Nicolas Monod, Maxime Gheysens

Consider the following property of a topological group G: every continuous affine G-action on a Hilbert space with a bounded orbit has a fixed point. We prove that this property characterizes amenability for locally compact a-compact groups (e.g., countabl ...

Elsevier2017

A generalized mountain-pass theorem: the existence of multiple critical points

Hans-Jörg Ruppen

We analyse the existence of multiple critical points for an even functional J : H -> R in the following context: the Hilbert space H can be split into an orthogonal sum H = Y circle plus Z in such a way that inf{J(u) : u is an element of Z and parallel to ...

Springer Heidelberg2016

On low-rank approximability of solutions to high-dimensional operator equations and eigenvalue problems

Daniel Kressner, André Uschmajew

Low-rank tensor approximation techniques attempt to mitigate the overwhelming complexity of linear algebra tasks arising from high-dimensional applications. In this work, we study the low-rank approximability of solutions to linear systems and eigenvalue p ...

Elsevier Science Inc2016

Principal component component analysis of persistent homology rank functions with case studies of spatial point patterns, sphere packing and colloids

Katharine Felicity Turner

Persistent homology, while ostensibly measuring changes in topology, captures multiscale geometrical information. It is a natural tool for the analysis of point patterns. In this paper we explore the statistical power of the persistent homology rank functi ...

Elsevier2016

Discrete least squares polynomial approximation with random evaluations − application to parametric and stochastic elliptic PDEs

Fabio Nobile, Giovanni Migliorati

Motivated by the numerical treatment of parametric and stochastic PDEs, we analyze the least-squares method for polynomial approximation of multivariate functions based on random sampling according to a given probability measure. Recent work has shown that ...

2015

A New Identity for the Least-square Solution of Overdetermined Set of Linear Equations

Afsaneh Asaei, Mohammadjavad Taghizadeh, Saeid Haghighatshoar

In this paper, we prove a new identity for the least-square solution of an over-determined set of linear equation

Ax=b

, where

A

is an

m\times n

full-rank matrix,

b

is a column-vector of dimension

m

, and

m

(the number of equations) is larger tha ...

2015

Convergences of Regularized Algorithms and Stochastic Gradient Methods with Random Projections

Graph Chatbot

Chat with Graph Search

Optimal Rates for Spectral Algorithms with Least-Squares Regression over Hilbert Spaces

Smoothing Alternating Direction Methods for Fully Nonsmooth Constrained Convex Optimization

A Functional Framework for Enhanced Ultrasound Imaging

Harder, Better, Faster, Stronger Convergence Rates for Least-Squares Regression

Fixed Points For Bounded Orbits In Hilbert Spaces

A generalized mountain-pass theorem: the existence of multiple critical points

On low-rank approximability of solutions to high-dimensional operator equations and eigenvalue problems

Principal component component analysis of persistent homology rank functions with case studies of spatial point patterns, sphere packing and colloids

Discrete least squares polynomial approximation with random evaluations − application to parametric and stochastic elliptic PDEs

A New Identity for the Least-square Solution of Overdetermined Set of Linear Equations

Optimal Rates for Spectral Algorithms with Least-Squares Regression over Hilbert Spaces

Smoothing Alternating Direction Methods for Fully Nonsmooth Constrained Convex Optimization

A generalized mountain-pass theorem: the existence of multiple critical points

Discrete least squares polynomial approximation with random evaluations − application to parametric and stochastic elliptic PDEs

A New Identity for the Least-square Solution of Overdetermined Set of Linear Equations

Fixed Points For Bounded Orbits In Hilbert Spaces

On low-rank approximability of solutions to high-dimensional operator equations and eigenvalue problems

A Functional Framework for Enhanced Ultrasound Imaging

Principal component component analysis of persistent homology rank functions with case studies of spatial point patterns, sphere packing and colloids

Harder, Better, Faster, Stronger Convergence Rates for Least-Squares Regression