NAME
AI::DecisionTree - Automatically Learns Decision Trees
SYNOPSIS
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'});
DESCRIPTION
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.
METHODS
Building and Querying the Tree
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.
Tree Introspection
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.
LIMITATIONS
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.
TO DO
All the stuff in the LIMITATIONS section. Also, revisit the pruning algorithm to see how it can be improved.
AUTHOR
Ken Williams, ken@mathforum.org
SEE ALSO
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