An Inverse-regression Method of Dependent Variable Transformation for Dimension Reduction with Non-linear Confounding

2014 ◽  
Vol 42 (3) ◽  
pp. 760-774 ◽  
Author(s):  
Heng-Hui Lue
Keyword(s):  
Dimension Reduction ◽  
Regression Method ◽  
Inverse Regression ◽  
Variable Transformation ◽  
Non Linear

Non-linear Techniques for Dimension Reduction

2009 ◽  
pp. 1003-1007 ◽  
Author(s):  
Jian Yang ◽  
Zhong Jin ◽  
Jingyu Yang
Keyword(s):  
Dimension Reduction ◽  
Non Linear

A NEW PARAMETER ESTIMATION METHOD FOR ONLINE SOFT TISSUE CHARACTERIZATION

2016 ◽  
Vol 16 (08) ◽  
pp. 1640019 ◽  
Author(s):  
JAEHYUN SHIN ◽  
YONGMIN ZHONG ◽  
JULIAN SMITH ◽  
CHENGFAN GU
Keyword(s):  
Soft Tissue ◽  
Linear Regression ◽  
Tissue Characterization ◽  
Soft Tissues ◽  
Unscented Kalman Filter ◽  
Estimation Method ◽  
Regression Method ◽  
Linear Regression Method ◽  
Non Linear

Dynamic soft tissue characterization is of importance to robotic-assisted minimally invasive surgery. The traditional linear regression method is unsuited to handle the non-linear Hunt–Crossley (HC) model and its linearization process involves a linearization error. This paper presents a new non-linear estimation method for dynamic characterization of mechanical properties of soft tissues. In order to deal with non-linear and dynamic conditions involved in soft tissue characterization, this method improves the non-linearity and dynamics of the HC model by treating parameter [Formula: see text] as independent variable. Based on this, an unscented Kalman filter is developed for online estimation of soft tissue parameters. Simulations and comparison analysis demonstrate that the proposed method is able to estimate mechanical parameters for both homogeneous tissues and heterogeneous and multi-layer tissues, and the achieved performance is much better than that of the linear regression method.

scholarly journals Sufficient dimension reduction for compositional data

Biostatistics ◽  
2019 ◽  
Author(s):  
Diego Tomassi ◽  
Liliana Forzani ◽  
Sabrina Duarte ◽  
Ruth M Pfeiffer
Keyword(s):  
Dimension Reduction ◽  
Graphical Models ◽  
Compositional Data ◽  
Human Microbiome ◽  
Human Microbiome Project ◽  
Outcome Variable ◽  
Sufficient Dimension Reduction ◽  
Inverse Regression ◽  
Linear Combinations ◽  
Reduction Methods

Summary Recent efforts to characterize the human microbiome and its relation to chronic diseases have led to a surge in statistical development for compositional data. We develop likelihood-based sufficient dimension reduction methods (SDR) to find linear combinations that contain all the information in the compositional data on an outcome variable, i.e., are sufficient for modeling and prediction of the outcome. We consider several models for the inverse regression of the compositional vector or transformations of it, as a function of outcome. They include normal, multinomial, and Poisson graphical models that allow for complex dependencies among observed counts. These methods yield efficient estimators of the reduction and can be applied to continuous or categorical outcomes. We incorporate variable selection into the estimation via penalties and address important invariance issues arising from the compositional nature of the data. We illustrate and compare our methods and some established methods for analyzing microbiome data in simulations and using data from the Human Microbiome Project. Displaying the data in the coordinate system of the SDR linear combinations allows visual inspection and facilitates comparisons across studies.

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