[R] Re: projection pursuit

[Liaw, Andy]

> From: Jim_Garrett at bd.com
> 
> Luis,
> 
> See the fastICA package, in particular the final example in 
> the function
> fastICA's help page.  This doesn't leave you with density 
> estimates, but
> with projection-pursuit directions; you still have to figure 
> out how to fit
> a density estimate to the rotated data.  Actually, as I understand it,
> XGobi also finds directions but does not fit a density.  However, any
> multivariate density estimator ought to be applicable.  I'm 
> not aware at
> the moment of the tools R offers for multivariate density 
> estimation, but
> I'm sure there are multiple possibilities.

I believe locfit() can handle up to 5 dimensions.


> _The Elements of Statistical Learning_ by Hastie, Tibshirani, 
> and Friedman
> mention a "trick" to use classification tools (which model class
> probabilities) to estimate density.  Fundamentally, generate 
> data from a
> reference distribution, and use the classification tool to estimate
> probability of observed data (as opposed to generated data) 
> as a function
> of the inputs.  These probabilities, normalized to integrate 
> to 1, form a
> density estimate.  Since there are so very many classification tools
> available, this trick offers a lot of flexibility.

Leo Breiman had talked about this `trick' in his early presentations on
random forest.  However, from my limited experiment, this is an extremely
poor way of estimating density.  Has anyone else tried it?

Cheers,
Andy

 
> Good luck.
> 
> Jim Garrett
> Baltimore, Maryland, USA
> 
> 
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