Sliced Inverse Regression
Principal Hessian Direction

Ker-Chau Li

Dept. of Statistics & Dept. of Mathematics, UCLA, USA


Dimensionality is an issue that can arise in every scientific field. Generally speaking, the difficulty lies on how to visualize a high dimensional function or data set. This is an area which has become increasingly more important due to the advent of computer and graphics technology.

Sliced inverse regression (SIR) and principal Hessian direction (PHD) are two basic dimension reduction methods. They are useful for the detection of geometric information underlying noisy data of several dimensions - a crucial step in empirical model building which has been overlooked in the literature. In this series of lectures, I will review the theory of SIR/PHD and describe some ongoing research in various application areas.


  • Introduction: dynamic graphics, principal component analysis, dimension reduction.
  • SIR: basic theory and application.
  • SIR: further discussion.
  • PHD: theory and application.
  • Nonlinear Confounding: the limitation of SIR/PHD.
  • Classification: Fisher's linear discriminant analysis and SIR, hand-written digit recognition problems.
  • Tree-structured regression via PHD and a new approach to analysis of two level factorial designs.
  • Censored regression and error-in-regressor problems.
  • Nonlinear time series and multivariate SIR.
  • Other research topics and conclusion.

Software Download

SIR related

Download  Xlispstat