Related papers: Model-based SIR for dimension reduction
The development and use of dimension reduction methods is prevalent in modern statistical literature. This paper reviews a class of dimension reduction techniques which aim to simultaneously select relevant predictors and find clusters…
In this work, we develop a new theory and method for sufficient dimension reduction (SDR) in single-index models, where SDR is a sub-field of supervised dimension reduction based on conditional independence. Our work is primarily motivated…
This article discusses a newly developed online manifold learning method, subspace iteration using reduced models (SIRM), for the dimensionality reduction of dynamical systems. This method may be viewed as subspace iteration combined with a…
In this paper we consider a semiparametric regression model involving a $d$-dimensional quantitative explanatory variable $X$ and including a dimension reduction of $X$ via an index $\beta'X$. In this model, the main goal is to estimate the…
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…
Missing data present challenges in data analysis. Naive analyses such as complete-case and available-case analysis may introduce bias and loss of efficiency, and produce unreliable results. Multiple imputation (MI) is one of the most widely…
Mutual information (MI) is a fundamental measure of statistical dependence, with a myriad of applications to information theory, statistics, and machine learning. While it possesses many desirable structural properties, the estimation of…
Sufficient dimension reduction (SDR) provides a framework for reducing the predictor space dimension in regression problems. We consider SDR in the context of deterministic functions of several variables such as those arising in computer…
Sufficient dimension reduction (SDR) in regression, which reduces the dimension by replacing original predictors with a minimal set of their linear combinations without loss of information, is very helpful when the number of predictors is…
Sufficient dimension reduction (SDR) is an effective tool for regression models, offering a viable approach to address and analyze the nonlinear nature of regression problems. This paper introduces the itdr R package, a comprehensive and…
We consider the smoothed version of sliced average variance estimation (SAVE) dimension reduction method for dealing with spatially dependent data that are observations of a strongly mixing random field. We propose kernel estimators for the…
A major family of sufficient dimension reduction (SDR) methods, called inverse regression, commonly require the distribution of the predictor $X$ to have a linear $E(X|\beta^\mathsf{T}X)$ and a degenerate $\mathrm{var}(X|\beta^\mathsf{T}X)$…
Online dimension reduction is a common method for high-dimensional streaming data processing. Online principal component analysis, online sliced inverse regression, online kernel principal component analysis and other methods have been…
In "Li, L. and Yin, X. (2008). Sliced Inverse Regression with Regularizations. Biometrics, 64(1):124--131" a ridge SIR estimator is introduced as the solution of a minimization problem and computed thanks to an alternating least-squares…
In the regression setting, dimension reduction allows for complicated regression structures to be detected via visualization in a low-dimension framework. However, some popular dimension reduction methodologies fail to achieve this aim when…
The principal support vector machines method (Li et al., 2011) is a powerful tool for sufficient dimension reduction that replaces original predictors with their low-dimensional linear combinations without loss of information. However, the…
Creating low dimensional representations of a high dimensional data set is an important component in many machine learning applications. How to cluster data using their low dimensional embedded space is still a challenging problem in…
Federated learning has become a popular tool in the big data era nowadays. It trains a centralized model based on data from different clients while keeping data decentralized. In this paper, we propose a federated sparse sliced inverse…
In this paper, we propose new sampling approaches for the Shrinkage Inverse-Wishart (SIW) distribution, a generalized family of the Inverse-Wishart distribution originally proposed by Berger et al. (2020, Annals of Statistics). It offers a…
The discovery of non-linear causal relationship under additive non-Gaussian noise models has attracted considerable attention recently because of their high flexibility. In this paper, we propose a novel causal inference algorithm called…