Related papers: Data-driven polynomial ridge approximation using v…
Ridge functions have recently emerged as a powerful set of ideas for subspace-based dimension reduction. In this paper we begin by drawing parallels between ridge subspaces, sufficient dimension reduction and active subspaces, contrasting…
Multivariate functions encountered in high-dimensional uncertainty quantification problems often vary most strongly along a few dominant directions in the input parameter space. We propose a gradient-based method for detecting these…
This paper presents a novel learning-based approach to construct a surrogate problem that approximates a given parametric nonconvex optimization problem. The surrogate function is designed to be the minimum of a finite set of functions,…
Many of the input-parameter-to-output-quantity-of-interest maps that arise in computational science admit a surprising low-dimensional structure, where the outputs vary primarily along a handful of directions in the high-dimensional input…
We introduce a method for the nonlinear dimension reduction of a high-dimensional function $u:\mathbb{R}^d\rightarrow\mathbb{R}$, $d\gg1$. Our objective is to identify a nonlinear feature map $g:\mathbb{R}^d\rightarrow\mathbb{R}^m$, with a…
We address the challenge of correlated predictors in high-dimensional GLMs, where regression coefficients range from sparse to dense, by proposing a data-driven random projection method. This is particularly relevant for applications where…
Subsampling is a popular approach to alleviating the computational burden for analyzing massive datasets. Recent efforts have been devoted to various statistical models without explicit regularization. In this paper, we develop an efficient…
These notes are about ridge functions. Recent years have witnessed a flurry of interest in these functions. Ridge functions appear in various fields and under various guises. They appear in fields as diverse as partial differential…
Response surfaces are common surrogates for expensive computer simulations in engineering analysis. However, the cost of fitting an accurate response surface increases exponentially as the number of model inputs increases, which leaves…
We are concerned with an approximation problem for a symmetric positive semidefinite matrix due to motivation from a class of nonlinear machine learning methods. We discuss an approximation approach that we call {matrix ridge…
We investigate the feature compression of high-dimensional ridge regression using the optimal subsampling technique. Specifically, based on the basic framework of random sampling algorithm on feature for ridge regression and the A-optimal…
This paper introduces a surrogate modeling scheme based on Grassmannian manifold learning to be used for cost-efficient predictions of high-dimensional stochastic systems. The method exploits subspace-structured features of each solution by…
We present an algorithm for minimizing a sum of functions that combines the computational efficiency of stochastic gradient descent (SGD) with the second order curvature information leveraged by quasi-Newton methods. We unify these…
Building prediction models from mass-spectrometry data is challenging due to the abundance of correlated features with varying degrees of zero-inflation, leading to a common interest in reducing the features to a concise predictor set with…
We propose a Randomised Subspace Gauss-Newton (R-SGN) algorithm for solving nonlinear least-squares optimization problems, that uses a sketched Jacobian of the residual in the variable domain and solves a reduced linear least-squares on…
In this paper we analyze a zeroth-order proximal stochastic gradient method suitable for the minimization of weakly convex stochastic optimization problems. We consider nonsmooth and nonlinear stochastic composite problems, for which…
One method to solve expensive black-box optimization problems is to use a surrogate model that approximates the objective based on previous observed evaluations. The surrogate, which is cheaper to evaluate, is optimized instead to find an…
Surrogate models are used to alleviate the computational burden in engineering tasks, which require the repeated evaluation of computationally demanding models of physical systems, such as the efficient propagation of uncertainties. For…
We consider approximations formed by the sum of a linear combination of given functions enhanced by ridge functions -- a Linear/Ridge expansion. For an explicitly or implicitly given function, we reformulate finding a best Linear/Ridge…
The paper is devoted to the solution of a weighted nonlinear least-squares problem for low-rank signal estimation, which is related to Hankel structured low-rank approximation problems. A modified weighted Gauss-Newton method, which uses…