Related papers: Counting Process Based Dimension Reduction Methods…

Sufficient dimension reduction [J. Amer. Statist. Assoc. 86 (1991) 316-342] has long been a prominent issue in multivariate nonparametric regression analysis. To uncover the central dimension reduction space, we propose in this paper an…

Compression techniques for deep neural network models are becoming very important for the efficient execution of high-performance deep learning systems on edge-computing devices. The concept of model compression is also important for…

In this work we present strategies for (optimal) measurement selection in model-based sequential diagnosis. In particular, assuming a set of leading diagnoses being given, we show how queries (sets of measurements) can be computed and…

In this study, we propose a new statical approach for high-dimensionality reduction of heterogenous data that limits the curse of dimensionality and deals with missing values. To handle these latter, we propose to use the Random Forest…

In this letter, we propose a simple yet effective singular value decomposition (SVD) based strategy to reduce the optimization problem dimension in data-enabled predictive control (DeePC). Specifically, in the case of linear time-invariant…

State estimation is key to both analyzing physical mechanisms and enabling real-time control of fluid flows. A common estimation approach is to relate sensor measurements to a reduced state governed by a reduced-order model (ROM). (When…

We propose a semiparametric model to study the effect of covariates on the distribution of a censored event time while making minimal assumptions about the censoring mechanism. The result is a partially identified model, in the sense that…

Coupled problems with various combinations of multiple physics, scales, and domains are found in numerous areas of science and engineering. A key challenge in the formulation and implementation of corresponding coupled numerical models is…

We use statistical mechanics techniques, viz. the replica method, to model the effect of censoring on overfitting in Cox's proportional hazards model, the dominant regression method for time-to-event data. In the overfitting regime, Maximum…

Semiparametric accelerated failure time (AFT) models are a useful alternative to Cox proportional hazards models, especially when the assumption of constant hazard ratios is untenable. However, rank-based criteria for fitting AFT models are…

Machine learning holds tremendous promise for transforming the fundamental practice of scientific discovery by virtue of its data-driven nature. With the ever-increasing stream of research data collection, it would be appealing to…

The reduced density matrix (RDM) is crucial in quantum many-body systems for understanding physical properties, including all local physical quantity information. This study aims to minimize various error constraints that causes challenges…

We propose a novel approach to sufficient dimension reduction in regression, based on estimating contour directions of negligible variation for the response surface. These directions span the orthogonal complement of the minimal space…

With the availability of high dimensional genetic biomarkers, it is of interest to identify heterogeneous effects of these predictors on patients' survival, along with proper statistical inference. Censored quantile regression has emerged…

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…

To go beyond standard first-order asymptotics for Cox regression, we develop parametric bootstrap and second-order methods. In general, computation of $P$-values beyond first order requires more model specification than is required for the…

We provide new theoretical results in the field of inverse regression methods for dimension reduction. Our approach is based on the study of some empirical processes that lie close to a certain dimension reduction subspace, called the…

Gradient-based dimension reduction decreases the cost of Bayesian inference and probabilistic modeling by identifying maximally informative (and informed) low-dimensional projections of the data and parameters, allowing high-dimensional…

We present a collection of algorithms which utilize dimensional reduction to perform mesh refinement and study possibly singular solutions of time-dependent partial differential equations. The algorithms are inspired by constructions used…

We present a method for computing reduced-order models of parameterized partial differential equation solutions. The key analytical tool is the singular value expansion of the parameterized solution, which we approximate with a singular…