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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
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