Related papers: Sparse Polynomial Chaos Expansions: Literature Sur…

The Polynomial Chaos Expansion (PCE) technique recovers a finite second order random variable exploiting suitable linear combinations of orthogonal polynomials which are functions of a given stochas- tic quantity {\xi}, hence acting as a…

Sparse coding aims to model data vectors as sparse linear combinations of basis elements, but a majority of related studies are restricted to continuous data without spatial or temporal structure. A new model-based sparse coding (MSC)…

Software engineers often have to estimate the performance of a software system before having full knowledge of the system parameters, such as workload and operational profile. These uncertain parameters inevitably affect the accuracy of…

Compressive sampling has been widely used for sparse polynomial chaos (PC) approximation of stochastic functions. The recovery accuracy of compressive sampling highly depends on the incoherence properties of the measurement matrix. In this…

In this paper we present a basis selection method that can be used with $\ell_1$-minimization to adaptively determine the large coefficients of polynomial chaos expansions (PCE). The adaptive construction produces anisotropic basis sets…

In complex and unknown processes, global models are initially generated over the entire experimental space but often fail to provide accurate predictions in local areas. A common approach is to use local models, which requires partitioning…

Polynomial chaos expansion (PCE) is an increasingly popular technique for uncertainty propagation and quantification in systems and control. Based on the theory of Hilbert spaces and orthogonal polynomials, PCE allows for a unifying…

Polynomial chaos expansions are used to reduce the computational cost in the Bayesian solutions of inverse problems by creating a surrogate posterior that can be evaluated inexpensively. We show, by analysis and example, that when the data…

Since the introduction of the lasso in regression, various sparse methods have been developed in an unsupervised context like sparse principal component analysis (s-PCA), sparse canonical correlation analysis (s-CCA) and sparse singular…

The present work addresses the issue of accurate stochastic approximations in high-dimensional parametric space using tools from uncertainty quantification (UQ). The basis adaptation method and its accelerated algorithm in polynomial chaos…

We present a new approach for constructing a data-driven surrogate model and using it for Bayesian parameter estimation in partial differential equation (PDE) models. We first use parameter observations and Gaussian Process regression to…

This work proposes a method for sparse polynomial chaos (PC) approximation of high-dimensional stochastic functions based on non-adapted random sampling. We modify the standard l1 -minimization algorithm, originally proposed in the context…

Implementations of Markov chain Monte Carlo (MCMC) methods need to confront two fundamental challenges: accurate representation of prior information and efficient evaluation of likelihoods. Principal component analysis (PCA) and related…

We apply the Tensor Train (TT) decomposition to construct the tensor product Polynomial Chaos Expansion (PCE) of a random field, to solve the stochastic elliptic diffusion PDE with the stochastic Galerkin discretization, and to compute some…

Sparse PCA provides a linear combination of small number of features that maximizes variance across data. Although Sparse PCA has apparent advantages compared to PCA, such as better interpretability, it is generally thought to be…

This work introduces a method to equip data-driven polynomial chaos expansion surrogate models with intervals that quantify the predictive uncertainty of the surrogate. To that end, jackknife-based conformal prediction is integrated into…

Multivariate global polynomial approximations - such as polynomial chaos or stochastic collocation methods - are now in widespread use for sensitivity analysis and uncertainty quantification. The pseudospectral variety of these methods uses…

Principal Component Analysis (PCA) is a dimension reduction technique. It produces inconsistent estimators when the dimensionality is moderate to high, which is often the problem in modern large-scale applications where algorithm…

Sparse principal component analysis (sparse PCA) is a widely used technique for dimensionality reduction in multivariate analysis, addressing two key limitations of standard PCA. First, sparse PCA can be implemented in high-dimensional low…

Symbolic regression plays a crucial role in modern scientific research thanks to its capability of discovering concise and interpretable mathematical expressions from data. A key challenge lies in the search for parsimonious and…