Sliced inverse regression

Sliced inverse regression (SIR) is a tool for <a href="/facts/Dimension_reduction/XoRpcrB0">dimensionality reduction</a> in the field of <a href="/facts/Multivariate_statistics/tDuNcWrL">multivariate statistics</a>.
In <a href="/facts/Statistics/DNPsKGYU">statistics</a>, <a href="/facts/Regression_analysis/n6z5Tf7K">regression analysis</a> is a method of studying the relationship between a response variable y and its input variable 
 
 
 
 
 
 x
 _
 
 
 
 
 {\displaystyle {\underline {x}}}
 
, which is a p-dimensional vector. There are several approaches in the category of regression. For example, parametric methods include multiple linear regression, and non-parametric methods include local smoothing.
As the number of observations needed to use local smoothing methods scales exponentially with high-dimensional data (as p grows), reducing the number of dimensions can make the operation computable. <a href="/facts/Dimension_reduction/XoRpcrB0">Dimensionality reduction</a> aims to achieve this by showing only the most important dimension of the data. SIR uses the inverse regression curve, 
 
 
 
 E
 (
 
 
 x
 _
 
 
 
 
 |
 
 
 y
 )
 
 
 {\displaystyle E({\underline {x}}\,|\,y)}
 
, to perform a weighted principal component analysis.

Sliced inverse regression open-in-new

Sliced inverse regression