What is Sliced inverse regression?

Sliced inverse regression is a tool for dimensionality reduction in the field of multivariate statistics.

In statistics, regression analysis is a way of studying the relationship between a response variable y and its explanatory 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 , reducing the number of dimensions can make the operation computable. Dimensionality reduction aims to achieve this by showing only the most important directions of the data. SIR uses the inverse regression curve, E {\displaystyle E} , to perform a weighted principal component analysis.