Related papers: Dimension reduction of high-dimension categorical …
Modeling data as being sampled from a union of independent subspaces has been widely applied to a number of real world applications. However, dimensionality reduction approaches that theoretically preserve this independence assumption have…
Consider semiparametric estimation where a doubly robust estimating function for a low-dimensional parameter is available, depending on two working models. With high-dimensional data, we develop regularized calibrated estimation as a…
Dimensionality reduction (DR) of data is a crucial issue for many machine learning tasks, such as pattern recognition and data classification. In this paper, we present a quantum algorithm and a quantum circuit to efficiently perform linear…
Reduced-rank linear discriminant analysis (RRLDA) is a foundational method of dimension reduction for classification that has been useful in a wide range of applications. The goal is to identify an optimal subspace to project the…
Decentralized state estimation in a communication-constrained sensor network is considered. The exchanged estimates are dimension-reduced to reduce the communication load using a linear mapping to a lower-dimensional space. The mean squared…
We propose a reduced-order modeling approach for nonlinear, parameter-dependent ordinary differential equations (ODE). Dimensionality reduction is achieved using nonlinear maps represented by autoencoders. The resulting low-dimensional ODE…
Identifying low-dimensional sufficient structures in nonlinear sufficient dimension reduction (SDR) has long been a fundamental yet challenging problem. Most existing methods lack theoretical guarantees of exhaustiveness in identifying…
High-dimensional data can often display heterogeneity due to heteroscedastic variance or inhomogeneous covariate effects. Penalized quantile and expectile regression methods offer useful tools to detect heteroscedasticity in…
Dimension reduction is an important tool for analyzing high-dimensional data. The predictor envelope is a method of dimension reduction for regression that assumes certain linear combinations of the predictors are immaterial to the…
We develop a linear-algebraic framework for dimensional analysis in systems with constraints, particularly when variables are numerous or related by implicit relations so that direct elimination is impractical. By expressing both…
Large-scale numerical simulations often produce high-dimensional gridded data that is challenging to process for downstream applications. A prime example is numerical weather prediction, where atmospheric processes are modeled using…
There has been a lot of interest in sufficient dimension reduction (SDR) methodologies as well as nonlinear extensions in the statistics literature. In this note, we use classical results regarding metric spaces and positive definite…
The continuing advances of omic technologies mean that it is now more tangible to measure the numerous features collectively reflecting the molecular properties of a sample. When multiple omic methods are used, statistical and computational…
Given a set of response observations for a parametrized dynamical system, we seek a parametrized dynamical model that will yield uniformly small response error over a range of parameter values yet has low order. Frequently, access to…
Classification models are a key component of structural digital twin technologies used for supporting asset management decision-making. An important consideration when developing classification models is the dimensionality of the input, or…
How does one find dimensions in multivariate data that are reliably expressed across repetitions? For example, in a brain imaging study one may want to identify combinations of neural signals that are reliably expressed across multiple…
Sufficient dimension reduction is a powerful tool to extract core information hidden in the high-dimensional data and has potentially many important applications in machine learning tasks. However, the existing nonlinear sufficient…
High-dimensional data is common in multiple areas, such as health care and genomics, where the number of features can be tens of thousands. In such scenarios, the large number of features often leads to inefficient learning. Constraint…
To estimate casual treatment effects, we propose a new matching approach based on the reduced covariates obtained from sufficient dimension reduction. Compared to the original covariates and the propensity score, which are commonly used for…
It is important to make robust inference of the conditional average treatment effect from observational data, but this becomes challenging when the confounder is multivariate or high-dimensional. In this article, we propose a double…