Module CrossValidate

loops through all possible tree roots and chooses the one which produces the best tree

**Arguments**

  - examples: the full set of examples

  - trainExamples: the training examples

  - testExamples: the testing examples

  - attrs: a list of attributes to consider in the tree building

  - nPossibleVals: a list of the number of possible values each variable can adopt

  - treeBuilder: the function to be used to actually build the tree

  - nQuantBounds: an optional list.  If present, it's assumed that the builder
    algorithm takes this argument as well (for building QuantTrees)

**Returns**

  The best tree found
  
**Notes**

  1) Trees are built using _trainExamples_

  2) Testing of each tree (to determine which is best) is done using _CrossValidate_ and
     the entire set of data (i.e. all of _examples_)

  3) _trainExamples_ is not used at all, which immediately raises the question of
     why it's even being passed in

Determines the classification error for the testExamples

**Arguments**

  - tree: a decision tree (or anything supporting a _ClassifyExample()_ method)

  - testExamples: a list of examples to be used for testing

  - appendExamples: a toggle which is passed along to the tree as it does
    the classification. The trees can use this to store the examples they
    classify locally.

**Returns**

  a 2-tuple consisting of:

    1) the percent error of the tree

    2) a list of misclassified examples
    

Driver function for building trees and doing cross validation

**Arguments**

  - examples: the full set of examples

  - attrs: a list of attributes to consider in the tree building

  - nPossibleVals: a list of the number of possible values each variable can adopt

  - holdOutFrac: the fraction of the data which should be reserved for the hold-out set
     (used to calculate the error)

  - silent: a toggle used to control how much visual noise this makes as it goes.

  - calcTotalError: a toggle used to indicate whether the classification error
    of the tree should be calculated using the entire data set (when true) or just
    the training hold out set (when false)

  - treeBuilder: the function to call to build the tree

  - lessGreedy: toggles use of the less greedy tree growth algorithm (see
    _ChooseOptimalRoot_).

  - startAt: forces the tree to be rooted at this descriptor

  - nQuantBounds: an optional list.  If present, it's assumed that the builder
    algorithm takes this argument as well (for building QuantTrees)

  - maxDepth: an optional integer.  If present, it's assumed that the builder
    algorithm takes this argument as well

**Returns**

   a 2-tuple containing:

     1) the tree

     2) the cross-validation error of the tree