# learnDT.py - Learning a binary decision tree # AIFCA Python3 code Version 0.9.3 Documentation at http://aipython.org # Download the zip file and read aipython.pdf for documentation # Artificial Intelligence: Foundations of Computational Agents http://artint.info # Copyright David L Poole and Alan K Mackworth 2017-2021. # This work is licensed under a Creative Commons # Attribution-NonCommercial-ShareAlike 4.0 International License. # See: http://creativecommons.org/licenses/by-nc-sa/4.0/deed.en from learnProblem import Learner, squared_error, absolute_error, log_loss, mean from learnNoInputs import Predict import math class DT_learner(Learner): def __init__(self, dataset, split_to_optimize=log_loss, # to minimize for at each split leaf_prediction=Predict.mean, # what to use for point prediction at leaves train=None, # used for cross validation min_number_examples=10): self.dataset = dataset self.target = dataset.target self.split_to_optimize = split_to_optimize self.leaf_prediction = leaf_prediction self.min_number_examples = min_number_examples if train is None: self.train = self.dataset.train else: self.train = train def learn(self): return self.learn_tree(self.dataset.input_features, self.train) def learn_tree(self, input_features, data_subset): """returns a decision tree for input_features is a set of possible conditions data_subset is a subset of the data used to build this (sub)tree where a decision tree is a function that takes an example and makes a prediction on the target feature """ if (input_features and len(data_subset) >= self.min_number_examples): first_target_val = self.target(data_subset[0]) allagree = all(self.target(inst)==first_target_val for inst in data_subset) if not allagree: split, partn = self.select_split(input_features, data_subset) if split: # the split succeeded in splitting the data false_examples, true_examples = partn rem_features = [fe for fe in input_features if fe != split] self.display(2,"Splitting on",split.__doc__,"with examples split", len(true_examples),":",len(false_examples)) true_tree = self.learn_tree(rem_features,true_examples) false_tree = self.learn_tree(rem_features,false_examples) def fun(e): if split(e): return true_tree(e) else: return false_tree(e) #fun = lambda e: true_tree(e) if split(e) else false_tree(e) fun.__doc__ = ("if "+split.__doc__+" then ("+true_tree.__doc__+ ") else ("+false_tree.__doc__+")") return fun # don't expand the trees but return a point prediction prediction = self.leaf_prediction(self.target(e) for e in data_subset) def leaf_fun(e): return prediction leaf_fun.__doc__ = "{:.7f}".format(prediction) return leaf_fun def select_split(self, input_features, data_subset): """finds best feature to split on. input_features is a non-empty list of features. returns feature, partition where feature is an input feature with the smallest error as judged by split_to_optimize or feature==None if there are no splits that improve the error partition is a pair (false_examples, true_examples) if feature is not None """ best_feat = None # best feature # best_error = float("inf") # infinity - more than any error best_error = training_error(self.dataset.target, data_subset, self.split_to_optimize, self.leaf_prediction) best_partition = None for feat in input_features: false_examples, true_examples = partition(data_subset,feat) if false_examples and true_examples: #both partitons are non-empty err = (training_error(self.dataset.target, false_examples, self.split_to_optimize, self.leaf_prediction) + training_error(self.dataset.target, true_examples, self.split_to_optimize, self.leaf_prediction)) self.display(3," split on",feat.__doc__,"has error=",err, "splits into",len(true_examples),":",len(false_examples)) if err < best_error: best_feat = feat best_error=err best_partition = false_examples, true_examples self.display(3,"best split is on",best_feat.__doc__, "with err=",best_error) return best_feat, best_partition def partition(data_subset,feature): """partitions the data_subset by the feature""" true_examples = [] false_examples = [] for example in data_subset: if feature(example): true_examples.append(example) else: false_examples.append(example) return false_examples, true_examples def training_error(target, data_subset, eval_critereon, leaf_prediction): """returns training error for dataset on the target (with no more splits) We make a single prediction using leaf_prediction It is evaluated using eval_critereon for each example """ prediction = leaf_prediction(target(e) for e in data_subset) error = sum(eval_critereon(prediction, target(e)) for e in data_subset) return error from learnProblem import Data_set, Data_from_file def testDT(data, print_tree=True, selections = Predict.all): """Prints errors and the trees for various evaluation criteria and ways to select leaves. """ evaluation_criteria = [squared_error, absolute_error, log_loss] print("Split Choice","Leaf Choice",'\t'.join(ecrit.__doc__ for ecrit in evaluation_criteria),sep="\t") for crit in evaluation_criteria: for leaf in selections: tree = DT_learner(data, split_to_optimize=crit, leaf_prediction=leaf).learn() print(crit.__doc__, leaf.__doc__, "\t".join("{:.7f}".format(data.evaluate_dataset(data.test, tree, ecrit)) for ecrit in evaluation_criteria),sep="\t") if print_tree: print(tree.__doc__) if __name__ == "__main__": print("SPECT.csv"); testDT(data=Data_from_file('data/SPECT.csv', target_index=0), print_tree=False) # print("carbool.csv"); testDT(data = Data_from_file('data/carbool.csv', target_index=-1)) # print("mail_reading.csv"); testDT(data = Data_from_file('data/mail_reading.csv', target_index=-1)) # print("holiday.csv"); testDT(data = Data_from_file('data/holiday.csv', num_train=19, target_index=-1))