Parallel Computing for Sliced Inverse Regression with Projection Pursuit

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  • 射影追跡層別逆回帰法における並列計算について
  • シャエイ ツイセキソウ ベツ ギャクカイキホウ ニ オケル ヘイレツ ケイサン ニ ツイテ

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Abstract

In the paper, we propose an SIRPP implementation on parallel processing with PVM, Parallel Virtual Machine.<BR>In regression analysis, a lot of explanatory variables sometimes make data analysis harder. When some explanatory variables are useless for predicting the value of response variable, the explanatory variable selection is very useful. But, if all of the explanatory variables are related to the response variable, we will search linear combinations of explanatory variables with projection pursuit regression and ACE (Alternating Conditional Expectations). These two methods are assumed special models.<BR>Sliced Inverse Regression (Li, 1991) is one of the approaches to reduce the number of explanatory variables in regression analysis. SIR does not get rid of some explanatory variables themselves but may reduce the dimension of a space of explanatory variables. It is based on the model (SIR model)<BR>y=f(β1x, β2x, …, βkx, ε), <BR>where x is the vector of p explanatory variables, βk(k=1, 2, …, K) are unknown row vectors, ε is independent of x, and f is an arbitrary unknown function on R[K+1].<BR>Mizuta (1999) proposed an algorithm for SIR model with projection pursuit, named SIRPP (Sliced Inverse Regression with Projection Pursuit). SIRPP has excellent performance in finding {βk}. However, the algorithm requires more computing power. It is a part of projection pursuit that the algorithm takes much time. In order to overcome the defect, we use PVM for SIRPP. We offer its effectiveness through numerical examples.

Journal

  • Ouyou toukeigaku

    Ouyou toukeigaku 30 (2), 81-90, 2001

    Japanese Society of Applied Statistics

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