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

Predicting Individual Scores From Resting State fMRI Using Partial Least Squares Regression

Dimitri Nestor Alice Van De Ville, Stephan Morgenthaler, Thomas William Arthur Bolton, Maria Giulia Preti, Djalel Eddine Meskaldji

An important question in neuroscience is to reveal the relationship between individual performance and brain activity. This could be achieved by applying model regression techniques, in which functional connectivity derived from resting-state functional ma ...

Ieee2016

Comparing molecules and solids across structural and alchemical space

Michele Ceriotti, Sandip De

Evaluating the (dis)similarity of crystalline, disordered and molecular compounds is a critical step in the development of algorithms to navigate automatically the configuration space of complex materials. For instance, a structural similarity metric is cr ...

Royal Society of Chemistry2016

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

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

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

Estimation in Functional Lagged Regression

Lukasz Kidzinski

The paper introduces a functional time series (lagged) regression model. The impulse-response coefficients in such a model are operators acting on a separable Hilbert space, which is the function space L-2 in applications. A spectral approach to the estima ...

Wiley-Blackwell2015

Forecasting Uncertainty in Electricity Demand

Tri Kurniawan Wijaya

Generalized Additive Models (GAM) are a widely popular class of regression models to forecast electricity demand, due to their high accuracy, flexibility and interpretability. However, the residuals of the fitted GAM are typically heteroscedastic and lepto ...

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

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

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

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Predicting Individual Scores From Resting State fMRI Using Partial Least Squares Regression

Comparing molecules and solids across structural and alchemical space

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

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

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

Estimation in Functional Lagged Regression

Forecasting Uncertainty in Electricity Demand

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

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

Estimation in Functional Lagged Regression

Predicting Individual Scores From Resting State fMRI Using Partial Least Squares Regression

Forecasting Uncertainty in Electricity Demand

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

Comparing molecules and solids across structural and alchemical space

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

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

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

Multitask diffusion LMS with sparsity-based regularization