Related papers: Shared active subspace for multivariate vector-val…

Active subspaces are an emerging set of tools for identifying and exploiting the most important directions in the space of a computer simulation's input parameters; these directions depend on the simulation's quantity of interest, which we…

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…

Active subspaces can effectively reduce the dimension of high-dimensional parameter studies enabling otherwise infeasible experiments with expensive simulations. The key components of active subspace methods are the eigenvectors of a…

Estimating singular subspaces from noisy matrices is a fundamental problem with wide-ranging applications across various fields. Driven by the challenges of data integration and multi-view analysis, this study focuses on estimating shared…

We propose an algorithmic framework, that employs active subspace techniques, for scalable global optimization of functions with low effective dimension (also referred to as low-rank functions). This proposal replaces the original…

In the era of big data, integrating multi-source functional data to extract a subspace that captures the shared subspace across sources has attracted considerable attention. In practice, data collection procedures often follow…

The Active Subspace (AS) method is a widely used technique for identifying the most influential directions in high-dimensional input spaces that affect the output of a computational model. The standard AS algorithm requires a sufficient…

This work puts forth low-complexity Riemannian subspace descent algorithms for the minimization of functions over the symmetric positive definite (SPD) manifold. Different from the existing Riemannian gradient descent variants, the proposed…

Lower-dimensional subspaces that impact estimates of uncertainty are often described by Linear combinations of input variables, leading to active variables. This paper extends the derivative-based active subspace methods and…

We propose the use of the vector-valued distance to compute distances and extract geometric information from the manifold of symmetric positive definite matrices (SPD), and develop gyrovector calculus, constructing analogs of vector space…

Distributions measured in high energy physics experiments are usually distorted and/or transformed by various detector effects. A regularization method for unfolding these distributions is re-formulated in terms of the Singular Value…

Modern data analysis increasingly requires identifying shared latent structure across multiple high-dimensional datasets. A commonly used model assumes that the data matrices are noisy observations of low-rank matrices with a shared…

Covariance matrix estimation is an important problem in multivariate data analysis, both from theoretical as well as applied points of view. Many simple and popular covariance matrix estimators are known to be severely affected by model…

Most engineering models contain several parameters, and the map from input parameters to model output can be viewed as a multivariate function. An active subspace is a low-dimensional subspace of the space of inputs that explains the…

Active subspace (AS) methods are a valuable tool for understanding the relationship between the inputs and outputs of a Physics simulation. In this paper, an elegant generalization of the traditional ASM is developed to assess the…

We present a new dimension reduction method called the global active subspace method. The method uses expected values of finite differences of the underlying function to identify the important directions, and builds a surrogate model using…

We develop a model-based method for evaluating heterogeneity among several p x p covariance matrices in the large p, small n setting. This is done by assuming a spiked covariance model for each group and sharing information about the space…

The singular value decomposition (SVD) allows to write a matrix as a product of a left singular vectors matrix, a nonnegative singular values diagonal matrix and a right singular vectors matrix. Among the applications of the SVD are the…

In many areas of applied statistics and machine learning, generating an arbitrary number of independent and identically distributed (i.i.d.) samples from a given distribution is a key task. When the distribution is known only through…

We propose a multifidelity dimension reduction method to identify a low-dimensional structure present in many engineering models. The structure of interest arises when functions vary primarily on a low-dimensional subspace of the…