Three kinds of learning Supervised learning
Learning some mapping from inputs to outputs
Unsupervised learning Given “data”, what kinds of patterns
can you find? Reinforcement learning
Learn from positive negative reinforcement
Categorical data example
Example from Ross Quinlan, Decision Tree Induction; graphics from Tom Mitchell, Machine Learning
Decision Tree Classification
Which feature to split on?
Try to classify as many as possible with each split(This is a good split)
Which feature to split on?
These are bad splits – no classifications obtained
Improving a good split
Decision Tree Algorithm Framework
Use splitting criterion to decide on best attribute to split
Each child is new decision tree – recurse with parent feature removed
If all data points in child node are same class, classify node as that class
If no attributes left, classify by majority rule If no data points left, no such example
seen: classify as majority class from entire dataset
How do we know which splits are good?
Want nodes as “pure” as possible How do we quantify “randomness”
of a node? Want All elements +: “randomness” = 0 All elements –: “randomness” = 0 Half +, half -: “randomness” = 1 Draw plot
What should “randomness” function look like?
Typical solution: Entropy pp = proportion of + examples pn = proportion of – examples
A collection with low entropy is good.
NNPP ppppEntropy lglg
ID3 Criterion Split on feature with most
information gain. Gain = entropy in original node –
weighted sum of entropy in child nodes
child
childEntropyparentofsize
childofsize
parentEntropysplitGain
)(
)()(
How good is this split?
985.7
4log
7
4
7
3log
7
322 592.0
7
1log
7
1
7
6log
7
622
789.0)592(.14
7)985(.
14
7average Weighted
940.14
5log
14
5
14
9log
14
922
151.789.940. Gain
How good is this split?
971.5
3log
5
3
5
2log
5
222
694.0)971(.14
5)0(
14
4)971(.
14
5average Weighted
940.14
5log
14
5
14
9log
14
922
246.694.940. Gain
04
0log
4
0
4
4log
4
422 971.
5
2log
5
2
5
3log
5
322
The big picture Start with root Find attribute to split on with most
gain Recurse
Assessment How do I know how well my
decision tree works? Training set: data that you use to
build decision tree Test set: data that you did not use
for training that you use to assess the quality of decision tree
Issues on training and test sets
Do you know the correct classification for the test set?
If you do, why not include it in the training set to get a better classifier?
If you don’t, how can you measure the performance of your classifier?
Cross Validation Tenfold cross-validation
Ten iterations Pull a different tenth of the dataset out
each time to act as a test set Train on the remaining training set Measure performance on the test set
Leave one out cross-validation Similar, but leave only one point out
each time, then count correct vs. incorrect
Noise and Overfitting Can we always obtain a decision tree
that is consistent with the data? Do we always want a decision tree that
is consistent with the data? Example: Predict Carleton students who
become CEOs Features: state/country of origin, GPA letter,
major, age, high school GPA, junior high GPA, ...
What happens with only a few features? What happens with many features?
Overfitting Fitting a classifier “too closely” to
the data finding patterns that aren’t really there
Prevented in decision trees by pruning When building trees, stop recursion on
irrelevant attributes Do statistical tests at node to
determine if should continue or not
Examples of decision treesusing Weka
Preventing overfitting by cross validation
Another technique to prevent overfitting (is this valid)? Keep on recursing on decision tree as
long as you continue to get improved accuracy on the test set
Ensemble Methods Many “weak” learners, when
combined together, can perform more strongly than any one by itself
Bagging & Boosting: many different learners, voting on which classification Multiple algorithms, or different
features, or both
Bagging / Boosting Bagging: vote to determine answer
Run one algorithm on random subsets of data to obtain multiple classifiers
Boosting: weighted vote to determine answer Each iteration, weight more heavily data that
learner got wrong What does it mean to “weight more heavily” for
k-nn? For decision trees? AdaBoost is recent (1997) and has become
popular, fast
Computational Learning Theory
Chapter 20 up next Moving on to Chapter 20:
statistical learning methods Skipping to: will revisit earlier
topics (perhaps) near end of course 20.5: Neural Networks 20.6: Support vector machines