Related papers: Dimension Reduction Using Active Manifolds

This paper addresses the problem of mapping high-dimensional data to a low-dimensional space, in the presence of other known features. This problem is ubiquitous in science and engineering as there are often controllable/measurable features…

This paper develops the concept of the Adjacent Deviation Subspace (ADS), a novel framework for reducing infinite-dimensional functional data into finite-dimensional vector or scalar representations while preserving critical information of…

We consider convex, black-box objective functions with additive or multiplicative noise with a high-dimensional parameter space and a data space of lower dimension, where gradients of the map exist, but may be inaccessible. We investigate…

Derivative-free Riemannian optimization (DFRO) aims to minimize an objective function using only function evaluations, under the constraint that the decision variables lie on a Riemannian manifold. The rapid increase in problem dimensions…

High-dimensional representations, such as radial basis function networks or tile coding, are common choices for policy evaluation in reinforcement learning. Learning with such high-dimensional representations, however, can be expensive,…

Many scientific areas are faced with the challenge of extracting information from large, complex, and highly structured data sets. A great deal of modern statistical work focuses on developing tools for handling such data. This paper…

Randomized dimensionality reduction is a widely-used algorithmic technique for speeding up large-scale Euclidean optimization problems. In this paper, we study dimension reduction for a variety of maximization problems, including…

The vast majority of Dimensionality Reduction (DR) techniques rely on second-order statistics to define their optimization objective. Even though this provides adequate results in most cases, it comes with several shortcomings. The methods…

In this paper we develop a new machinery to study the capacity of artificial neural networks (ANNs) to approximate high-dimensional functions without suffering from the curse of dimensionality. Specifically, we introduce a concept which we…

In many experimental contexts, it is necessary to statistically remove the impact of instrumental effects in order to physically interpret measurements. This task has been extensively studied in particle physics, where the deconvolution…

The usual approach to model reduction for parametric partial differential equations (PDEs) is to construct a linear space $V_n$ which approximates well the solution manifold $\mathcal{M}$ consisting of all solutions $u(y)$ with $y$ the…

Dimensionality reduction techniques map values from a high dimensional space to one with a lower dimension. The result is a space which requires less physical memory and has a faster distance calculation. These techniques are widely used…

Diffusion Map is a spectral dimensionality reduction technique which is able to uncover nonlinear submanifolds in high-dimensional data. And, it is increasingly applied across a wide range of scientific disciplines, such as biology,…

High-dimensional data analysis has been an active area, and the main focuses have been variable selection and dimension reduction. In practice, it occurs often that the variables are located on an unknown, lower-dimensional nonlinear…

We discuss a method of parameter reduction in complex models known as the Manifold Boundary Approximation Method (MBAM). This approach, based on a geometric interpretation of statistics, maps the model reduction problem to a geometric…

Metric embeddings are a widely used method in algorithm design, where generally a ``complex'' metric is embedded into a simpler, lower-dimensional one. Historically, the theoretical computer science community has focused on bi-Lipschitz…

A common setting for scientific inference is the ability to sample from a high-fidelity forward model (simulation) without having an explicit probability density of the data. We propose a simulation-based maximum likelihood deconvolution…

This works handles the inverse reinforcement learning problem in high-dimensional state spaces, which relies on an efficient solution of model-based high-dimensional reinforcement learning problems. To solve the computationally expensive…

The goal of supervised representation learning is to construct effective data representations for prediction. Among all the characteristics of an ideal nonparametric representation of high-dimensional complex data, sufficiency, low…

This paper presents a novel non-linear model reduction method: Probabilistic Manifold Decomposition (PMD), which provides a powerful framework for constructing non-intrusive reduced-order models (ROMs) by embedding a high-dimensional system…