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Dynamic Partial Sufficient Dimension Reduction
Sufficient dimension reduction aims for reduction of dimensionality of a...
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Simultaneous Variable Selection, Clustering, and Smoothing in Function on Scalar Regression
We address the problem of multicollinearity in a function-on-scalar regr...
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Impossibility of dimension reduction in the nuclear norm
Let S_1 (the Schatten--von Neumann trace class) denote the Banach space ...
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Supervised Coarse-Graining of Composite Objects
We consider supervised dimension reduction for regression with composite...
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A framework for streamlined statistical prediction using topic models
In the Humanities and Social Sciences, there is increasing interest in a...
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Supporting Multi-point Fan Design with Dimension Reduction
Motivated by the idea of turbomachinery active subspace performance maps...
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A New Covariance Estimator for Sufficient Dimension Reduction in High-Dimensional and Undersized Sample Problems
The application of standard sufficient dimension reduction methods for r...
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Sufficient Dimension Reduction for Interactions
Dimension reduction lies at the heart of many statistical methods. In regression, dimension reduction has been linked to the notion of sufficiency whereby the relation of the response to a set of predictors is explained by a lower dimensional subspace in the predictor space. In this paper, we consider the notion of a dimension reduction in regression on subspaces that are sufficient to explain interaction effects between predictors and another variable of interest. The motivation for this work is from precision medicine where the performance of an individualized treatment rule, given a set of pretreatment predictors, is determined by interaction effects.
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