Learning from Observations

Chapter 18

Through 18.3.5

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Outline

• Learning agents• Inductive learning• Decision tree learning

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Learning

• Learning is essential for unknown environments,– i.e., when designer lacks omniscience

• Learning is useful as a system construction method,– i.e., designer might not know how to solve the

problem

• Learning modifies the agent's decision mechanisms to improve performance over time

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Learning element

• Design of a learning element is affected by– Which components of the performance element are to

be learned (condition-action rules; relevant properties of the world; results of possible actions; etc.)

– What feedback is available to learn these components– What representation is used for the components (this

chapter: vectors of attribute values)

• Type of feedback:– Supervised learning: correct answers for each

example– Unsupervised learning: correct answers not given– Reinforcement learning: occasional rewards

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Inductive Learning

• When the output y is one of a finite set of values, the learning problem is called classification

• When y is a number (such as earnings or tomorrow’s temperature), then the learning problem is called regression

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Inductive learning

• Simplest form: learn a function from examples

f is the target function

An example is a pair (x, f(x))

Problem: find a hypothesis hsuch that h ≈ fgiven a training set of examples

•

•

6

7

Learning decision trees

Problem: decide whether to wait for a table at a restaurant, based on the following attributes:1. Alternate: is there an alternative restaurant nearby?2. Bar: is there a comfortable bar area to wait in?3. Fri/Sat: is today Friday or Saturday?4. Hungry: are we hungry?5. Patrons: number of people in the restaurant (None, Some, Full)6. Price: price range ($, $$, $$$)7. Raining: is it raining outside?8. Reservation: have we made a reservation?9. Type: kind of restaurant (French, Italian, Thai, Burger)10. WaitEstimate: estimated waiting time (0-10, 10-30, 30-60, >60)

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Attribute-based representations

• Examples described by attribute values (Boolean, discrete, continuous)

• Classification of examples is positive (T) or negative (F)

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Decision trees

• One possible representation for hypotheses• E.g., here is the “true” tree for deciding whether to wait:

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Expressiveness• Decision trees can express any function in propositional logic • E.g., for Boolean functions, truth table row → path to leaf:

• Trivially, there is a consistent decision tree for any training set with one path to leaf for each example but it probably won't generalize to new examples

• Prefer to find more compact decision trees

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Hypothesis spaces

How many distinct decision trees with n Boolean attributes?

= number of Boolean functions

= number of distinct truth tables with 2n rows = 22n

• E.g., with 6 Boolean attributes, there are 18,446,744,073,709,551,616 trees

• We’ll do a greedy search

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Decision tree learning

• Aim: find a small tree consistent with the training examples• Idea: (recursively) choose "most significant" attribute as root of

(sub)tree

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• Example in class

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Choosing an attribute

• Idea: a good attribute splits the examples into subsets that are (ideally) "all positive" or "all negative"

• Patrons? is a better choice•

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Using information theory

• To implement Choose-Attribute in the DTL algorithm

• Information Content (Entropy):

I(P(v1), … , P(vn)) = Σi -P(vi) log2 P(vi)

• For a training set containing p positive examples and n negative examples:

np

n

np

n

np

p

np

p

np

n

np

pI

22 loglog),(

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Information gain

• A chosen attribute A divides the training set E into subsets E1, … , Ev according to their values for A, where A has v distinct values.

• Information Gain (IG) or reduction in entropy from the attribute test:

• Choose the attribute with the largest IG

v

i ii

i

ii

iii

np

n

np

pI

np

npAremainder

1

),()(

)(),()( Aremaindernp

n

np

pIAIG

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Information gain

For the training set, p = n = 6, I(6/12, 6/12) = 1 bit

Consider the attributes Patrons and Type:

Patrons has the highest IG of all attributes and so is chosen by the DTL algorithm as the root€

IG(Patrons) =1−[2

12I(0,1) +

4

12I(1,0) +

6

12I(

2

6,4

6)] = .541 bits

IG(Type) =1−[2

12I(

1

2,1

2) +

2

12I(

1

2,1

2) +

4

12I(

2

4,2

4) +

4

12I(

2

4,2

4)] = 0 bits

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Example contd.

• Decision tree learned from the 12 examples:

• Substantially simpler than “true” tree---a more complex hypothesis isn’t justified by small amount of data

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• Learning algorithm versus classifier (class)

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Performance measurement

• How do we know that h ≈ f ?1. Use theorems of computational/statistical learning theory

2. Try h on a new test set of examples

Learning curve = % correct on test set as a function of training set size

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Evaluating Inductive Hypotheses

• Accuracy of hypotheses on training data is obviously biased since the hypothesis was constructed to fit this data.

• Accuracy must be evaluated on a separate test set.• Average over multiple train/test splits to get accurate measure of

accuracy.• K-fold cross validation averages over K trials using each example

exactly once as a test case.

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K-Fold Cross Validation

Randomly partition data D into k disjoint equal-sized subsets P1…Pk

For i from 1 to k do: Use Pi for the test set and remaining data for trainingAverage results over all K folds. Accuracy: % correctFor class C:Precision: #True C & System’s answer is C/#System’s answer is C Recall: #True C & System’s answer is C / # True CF1-measure: 2 * (precision * recall / (precision + recall))

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K-Fold Cross Validation Comments

• Every example gets used as a test example once and as a training example k–1 times.

• All test sets are independent; however, training sets overlap significantly..

• Standard method is 10-fold.• If k is low, not sufficient number of train/test trials; if k is high, test

set is small and test variance is high and run time is increased.• If k=|D|, method is called leave-one-out cross validation.

Overfitting

• Overfitting can occur with any type of learner• The model describes random error or noise rather than the

underlying pattern• For decision tree induction, “pruning” is use to combat overfitting.• Starting with nodes with only examples as children, eliminate

attributes that fail a significance test. [That’s all you need to know]

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Summary

• Learning needed for unknown environments, lazy designers• Learning agent = performance element + learning element• For supervised learning, the aim is to find a simple hypothesis

approximately consistent with training examples• Decision tree learning using information gain • Learning performance = prediction accuracy measured on test set

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