AI::DecisionTree - Automatically Learns Decision Trees

  use AI::DecisionTree;
  my $dtree = new AI::DecisionTree;

  # A set of training data for deciding whether to play tennis
  $dtree->add_instance
    (attributes => {outlook     => 'sunny',
                    temperature => 'hot',
                    humidity    => 'high'},
     result => 'no');

  $dtree->add_instance
    (attributes => {outlook     => 'overcast',
                    temperature => 'hot',
                    humidity    => 'normal'},
     result => 'yes');

  ... repeat for several more instances, then:
  $dtree->train;

  # Find results for unseen instances
  my $result = $dtree->get_result
    (attributes => {outlook     => 'sunny',
                    temperature => 'hot',
                    humidity    => 'normal'});

The AI::DecisionTree module automatically creates so-called "decision trees" to explain a set of training data. A decision tree is a kind of categorizer that use a flowchart-like process for categorizing new instances. For instance, a learned decision tree might look like the following, which classifies for the concept "play tennis":

                   OUTLOOK
                   /  |  \
                  /   |   \
                 /    |    \
           sunny/  overcast \rainy
               /      |      \
          HUMIDITY    |       WIND
          /  \       *no*     /  \
         /    \              /    \
    high/      \normal      /      \
       /        \    strong/        \weak
     *no*      *yes*      /          \
                        *no*        *yes*

(This example, and the inspiration for the AI::DecisionTree module, come directly from Tom Mitchell's excellent book "Machine Learning", available from McGraw Hill.)

A decision tree like this one can be learned from training data, and then applied to previously unseen data to obtain results that are consistent with the training data.

The usual goal of a decision tree is to somehow encapsulate the training data in the smallest possible tree. This is motivated by an "Occam's Razor" philosophy, in which the simplest possible explanation for a set of phenomena should be preferred over other explanations. Also, small trees will make decisions faster than large trees, and they are much easier for a human to look at and understand. One of the biggest reasons for using a decision tree instead of many other machine learning techniques is that a decision tree is a much more scrutable decision maker than, say, a neural network.

The current implementation of this module uses an extremely simple method for creating the decision tree based on the training instances. It uses an Information Gain metric (based on expected reduction in entropy) to select the "most informative" attribute at each node in the tree. This is essentially the ID3 algorithm, developed by J. R. Quinlan in 1986. The idea is that the attribute with the highest Information Gain will (probably) be the best attribute to split the tree on at each point if we're interested in making small trees.

new(...parameters...)

Creates a new decision tree object and returns it. Accepts the following parameters:

noise_mode

Controls the behavior of the train() method when "noisy" data is encountered. Here "noisy" means that two or more training instances contradict each other, such that they have identical attributes but different results.

If noise_mode is set to fatal (the default), the train() method will throw an exception (die). If noise_mode is set to pick_best, the most frequent result at each noisy node will be selected.

prune

A boolean prune parameter which specifies whether the tree should be pruned after training. This is usually a good idea, so the default is to prune. Currently we prune using a simple minimum-description-length criterion.

verbose

If set to a true value, some status information will be output while training a decision tree. Default is false.

purge

If set to a true value, the do_purge() method will be invoked during train(). The default is true.

max_depth

Controls the maximum depth of the tree that will be created during train(). The default is 0, which means that trees of unlimited depth can be constructed.

add_instance(attributes => \%hash, result => $string, name => $string)

Adds a training instance to the set of instances which will be used to form the tree. An attributes parameter specifies a hash of attribute-value pairs for the instance, and a result parameter specifies the result.

An optional name parameter lets you give a unique name to each training instance. This can be used in coordination with the set_results() method below.

train()

Builds the decision tree from the list of training instances. If a numeric max_depth parameter is supplied, the maximum tree depth can be controlled (see also the new() method).

get_result(attributes => \%hash)

Returns the most likely result (from the set of all results given to add_instance()) for the set of attribute values given. An attributes parameter specifies a hash of attribute-value pairs for the instance. If the decision tree doesn't have enough information to find a result, it will return undef.

do_purge()

Purges training instances and their associated information from the DecisionTree object. This can save memory after training, and since the training instances are implemented as C structs, this turns the DecisionTree object into a pure-perl data structure that can be more easily saved with Storable.pm, for instance.

purge()

Returns true or false depending on the value of the tree's purge property. An optional boolean argument sets the property.

copy_instances(from => $other_tree)

Allows two trees to share the same set of training instances. More commonly, this lets you train one tree, then re-use its instances in another tree (possibly changing the instance result values using set_results()), which is much faster than re-populating the second tree's instances from scratch.

set_results(\%results)

Given a hash that relates instance names to instance result values, change the result values as specified.

instances()

Returns a reference to an array of the training instances used to build this tree.

nodes()

Returns the number of nodes in the trained decision tree.

depth()

Returns the depth of the tree. This is the maximum number of decisions that would need to be made to classify an unseen instance, i.e. the length of the longest path from the tree's root to a leaf. A tree with a single node would have a depth of zero.

rule_tree()

Returns a data structure representing the decision tree. For instance, for the tree diagram above, the following data structure is returned:

 [ 'outlook', {
     'rain' => [ 'wind', {
         'strong' => 'no',
         'weak' => 'yes',
     } ],
     'sunny' => [ 'humidity', {
         'normal' => 'yes',
         'high' => 'no',
     } ],
     'overcast' => 'yes',
 } ]

This is slightly remniscent of how XML::Parser returns the parsed XML tree.

Note that while the ordering in the hashes is unpredictable, the nesting is in the order in which the criteria will be checked at decision-making time.

rule_statements()

Returns a list of strings that describe the tree in rule-form. For instance, for the tree diagram above, the following list would be returned (though not necessarily in this order - the order is unpredictable):

  if outlook='rain' and wind='strong' -> 'no'
  if outlook='rain' and wind='weak' -> 'yes'
  if outlook='sunny' and humidity='normal' -> 'yes'
  if outlook='sunny' and humidity='high' -> 'no'
  if outlook='overcast' -> 'yes'

This can be helpful for scrutinizing the structure of a tree.

Note that while the order of the rules is unpredictable, the order of criteria within each rule reflects the order in which the criteria will be checked at decision-making time.

as_graphviz()

Returns a GraphViz object representing the tree. Requires that the GraphViz module is already installed, of course. The object returned will allow you to create PNGs, GIFs, image maps, or whatever graphical representation of your tree you might want.

A leaf_color argument can specify a fill color for each leaf node in the tree. The keys of the hash should be the same as the strings appearing as the result parameters given to add_instance(), and the values should be any GraphViz-style color specification.

Any additional arguments given to as_graphviz() will be passed on to GraphViz's new() method. See the GraphViz docs for more info.

A few limitations exist in the current version. All of them could be removed in future versions - especially with your help. =)

No continuous attributes

In the current implementation, only discrete-valued attributes are supported. This means that an attribute like "temperature" can have values like "cool", "medium", and "hot", but using actual temperatures like 87 or 62.3 is not going to work. This is because the values would split the data too finely - the tree-building process would probably think that it could make all its decisions based on the exact temperature value alone, ignoring all other attributes, because each temperature would have only been seen once in the training data.

The usual way to deal with this problem is for the tree-building process to figure out how to place the continuous attribute values into a set of bins (like "cool", "medium", and "hot") and then build the tree based on these bin values. Future versions of AI::DecisionTree may provide support for this. For now, you have to do it yourself.

All the stuff in the LIMITATIONS section. Also, revisit the pruning algorithm to see how it can be improved.

Ken Williams, ken@mathforum.org

Mitchell, Tom (1997). Machine Learning. McGraw-Hill. pp 52-80.

Quinlan, J. R. (1986). Induction of decision trees. Machine Learning, 1(1), pp 81-106.

perl, GraphViz