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By Leo Breiman, Jerome Friedman, Charles J. Stone, R.A. Olshen

The method used to build tree dependent ideas is the point of interest of this monograph. in contrast to many different statistical tactics, which moved from pencil and paper to calculators, this text's use of timber was once unthinkable ahead of desktops. either the sensible and theoretical aspects were built within the authors' research of tree tools. class and Regression timber displays those aspects, masking using bushes as a knowledge research process, and in a extra mathematical framework, proving a few of their basic homes.

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Extra info for Classification and regression trees

Example text

This issue is analogous to the familiar question in linear regression of how well the stepwise procedures do as compared with "best subsets" procedures. We do not address this problem. At this stage of computer technology, an overall optimal tree growing procedure does not appear feasible for any reasonably sized data set. " Con- structing a good classifier whose performance will stand up under test samples and that is useful and practical is our first priority. 6 TWO RUNNING EXAMPLES To illustrate various parts of the methodology, two models have been constructed for generating data.

It is complemented by a more complex waveform recognition model. 11). 12. Let ithdigit, i = 1, 2, ... , ... , x. "' seven-dimensional vector of zeros and ones with x,2m == "1 ) to be a if the light in the mth position is on for the ith digit, and x. 2m otherwise. The values of x, 2m C '" {I, ... 1. =0 Set IO} and let X be the set of all possible 7 -tuples (Xl' ... , x 7 ) of zeros and ones. 1 Digit Xl x2 x3 x4 x5 x5 x7 1 0 0 1 0 0 1 0 2 1 0 1 1 1 0 1 3 1 0 1 1 0 1 1 4 0 1 1 1 0 1 0 5 1 1 0 1 0 1 1 6 1 1 0 1 1 1 1 7 1 0 1 0 0 1 0 8 1 1 1 1 1 1 1 9 1 1 1 1 0 1 1 0 1 1 1 0 1 1 1 The data for the example are generated from a faulty calcu- later.

S. aa. There are not an infinite number of distinct splits of ~ dzLa. }. These are given by {Is xl ~ N' ~ N. • are taken halfway between consecutive distinct xl' For a categorical variable x • since {x E s} and {x m m generate the same split with distinct values. then 2 and t L-1 L reversed, if x t R m ~ s} takes on L m - 1 splits are . defined on the values of x m At each node the tree algorithm searches through the variables one by one, beginning with xl and continuing up to x ' For each M variable it finds the best SPlit.

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