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() new(noise_mode => 'pick_best') Creates a new decision tree object and returns it. Accepts a parameter, "noise_mode", which 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. add_instance(attributes => \%hash, result => $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. train() Builds the decision tree from the list of training instances. 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". Tree Introspection nodes() Returns the number of nodes in the trained decision tree. 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. 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. No support for tree-trimming Most decision tree building algorithms use a two-stage building process - first a tree is built that completely fits the training data (or fits it as closely as possible if noisy data is supported), and then the tree is pruned so that it will generalize well to new instances. This might be done either by maximizing performance on a set of held-out training instances, or by pruning parts of the tree that don't seem like they'll be very valuable. Currently, we build a tree that completely fits the training data, and we don't prune it. That means that the tree may overfit the training data in many cases - i.e., you won't be able to see the forest for the trees (or, more accurately, the tree for the leaves). This is mainly a problem when you're using "real world" or noisy data. If you're using data that you know to be a result of a rule-based process and you just want to figure out what the rules are, the current implementation should work fine for you. TO DO All the stuff in the LIMITATIONS section, plus more. For instance, it would be nice to create a GraphViz (or Dot) graphical representation of the tree. 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. the perl manpage.