Machine Learning: Decision Trees Chapter 18.1-18.3

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Machine Learning: Decision Trees Chapter 18.1-18.3 Some material adopted from notes by Chuck Dyer
What is learning? ,[object Object],[object Object],[object Object]
Why study learning? ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
A general model of learning agents
Major paradigms of machine learning ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
The inductive learning problem ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Supervised concept learning ,[object Object],[object Object],[object Object]
Inductive learning framework ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Inductive learning as search ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Model spaces ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Model spaces + + - - Nearest neighbor Version space Decision tree I I + + - - I + + - -
Inductive learning and bias ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Preference bias: Ockham’s Razor ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Learning decision trees ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Color Shape Size + + - Size + - + big big small small round square red green blue
Decision tree-induced partition – example I Color Shape Size + + - Size + - + big big small small round square red green blue
Expressiveness ,[object Object],[object Object],[object Object],[object Object]
Hypothesis spaces ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
R&N’s restaurant domain ,[object Object],[object Object],[object Object],[object Object],[object Object]
A decision tree from introspection
Attribute-based representations ,[object Object],[object Object],[object Object],[object Object]
ID3 Algorithm ,[object Object],[object Object],[object Object],[object Object],[object Object]
Choosing the best attribute ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Choosing an attribute ,[object Object],[object Object]
ID3-induced decision tree
Information theory 101 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Information theory 101 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Information theory II ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Huffman code ,[object Object],[object Object],[object Object],[object Object],[object Object]
Huffman code example ,[object Object],[object Object],[object Object],[object Object],[object Object],.5 .5 1 .125 .125 .25 A C B D .25 0 1 0 0 1 1 If we use this code to many messages (A,B,C or D) with this probability distribution, then, over time, the average bits/message should approach 1.75
Information for classification ,[object Object],[object Object],[object Object],[object Object],C 1 C 2 C 3 C 1 C 2 C 3 High information Low information
Information for classification II ,[object Object],[object Object],C 1 C 2 C 3 C 1 C 2 C 3 High information Low information
Information gain ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Computing information gain ,[object Object],[object Object],[object Object],Gain (Pat, T) = 1 - .47 = .53 Gain (Type, T) = 1 – 1 = 0 French Italian Thai Burger Empty Some Full Y Y Y Y Y Y N N N N N N
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
How well does it work? ,[object Object],[object Object],[object Object],[object Object]
Extensions of the decision tree learning algorithm ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Using gain ratios ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Computing gain ratio ,[object Object],[object Object],[object Object],Gain (Pat, T) =.53 Gain (Type, T) = 0 SplitInfo (Pat, T) = - (1/6 log 1/6 + 1/3 log 1/3 + 1/2 log 1/2) = 1/6*2.6 + 1/3*1.6 + 1/2*1 = 1.47 SplitInfo (Type, T) = 1/6 log 1/6 + 1/6 log 1/6 + 1/3 log 1/3 + 1/3 log 1/3 = 1/6*2.6 + 1/6*2.6 + 1/3*1.6 + 1/3*1.6 = 1.93 GainRatio (Pat, T) = Gain (Pat, T) / SplitInfo(Pat, T) = .53 / 1.47 = .36 GainRatio (Type, T) = Gain (Type, T) / SplitInfo (Type, T) = 0 / 1.93 = 0 French Italian Thai Burger Empty Some Full Y Y Y Y Y Y N N N N N N
Real-valued data ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Noisy data and overfitting ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Pruning decision trees ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],2 success 4 failure FAILURE Training Test Pruned Color 1 success 0 failure 0 success 2 failures red blue Color 1 success 3 failure 1 success 1 failure red blue
Converting decision trees to rules ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Evaluation methodology ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Performance measurement ,[object Object],[object Object],[object Object],[object Object]
Summary: Decision tree learning ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
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Machine Learning: Decision Trees Chapter 18.1-18.3