Publications related to Optimal Rates of Sketched-regularized Algorithms for Least-Squares Regression over Hilbert Spaces

Case Study of Data Assimilation Methods with the LWR-Proteus Phase II Experimental Campaign

Andreas Pautz, Mathieu Hursin, Daniel Jerôme Siefman

This paper describes the application of data assimilation methods to CASMO-5 simulations of a Proteus research reactor experiment. Its focus is a comparison and evaluation of three prominent data assimilation methods: generalized linear least squares, MOCA ...

2017

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

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

From averaging to acceleration, there is only a step-size

Nicolas Henri Bernard Flammarion

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 ...

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

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 ...

Idiap2015

Adaptive polynomial approximation by means of random discrete least squares

Giovanni Migliorati

We address adaptive multivariate polynomial approximation by means of the discrete least-squares method with random evaluations, to approximate in the L2 probability sense a smooth function depending on a random variable distributed according to a given pr ...

Springer2015

Multitask diffusion LMS with sparsity-based regularization

Ali H. Sayed, Roula Nassif

In this work, a diffusion-type algorithm is proposed to solve multitask estimation problems where each cluster of nodes is interested in estimating its own optimum parameter vector in a distributed manner. The approach relies on minimizing a global mean-sq ...

IEEE2015

MATHICSE Technical Report : 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 func- tions based on random sampling according to a given probability measure. Recent work has shown th ...

MATHICSE2014

Invariant manifolds with boundary for jump-diffusions

Damir Filipovic

We provide necessary and sufficient conditions for stochastic invariance of finite dimensional submanifolds with boundary in Hilbert spaces for stochastic partial differential equations driven by Wiener processes and Poisson random measures. ...

Univ Washington, Dept Mathematics2014

Optimal Rates of Sketched-regularized Algorithms for Least-Squares Regression over Hilbert Spaces

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Case Study of Data Assimilation Methods with the LWR-Proteus Phase II Experimental Campaign

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

From averaging to acceleration, there is only a step-size

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

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

Adaptive polynomial approximation by means of random discrete least squares

Multitask diffusion LMS with sparsity-based regularization

MATHICSE Technical Report : Discrete least squares polynomial approximation with random evaluations – application to parametric and stochastic elliptic PDES

Invariant manifolds with boundary for jump-diffusions

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

From averaging to acceleration, there is only a step-size

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

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

Adaptive polynomial approximation by means of random discrete least squares

MATHICSE Technical Report : Discrete least squares polynomial approximation with random evaluations – application to parametric and stochastic elliptic PDES

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

Multitask diffusion LMS with sparsity-based regularization

Invariant manifolds with boundary for jump-diffusions

Case Study of Data Assimilation Methods with the LWR-Proteus Phase II Experimental Campaign