Decision tree

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# Decision tree - PowerPoint PPT Presentation

Decision tree. LING 572 Fei Xia 1/10/06. Outline. Basic concepts Main issues Advanced topics. Basic concepts. A classification problem. Classification and estimation problems. Given a finite set of (input) attributes: features Ex: District, House type, Income, Previous customer

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## Decision tree

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### Decision tree

LING 572

Fei Xia

1/10/06

Outline
• Basic concepts
• Main issues

### Basic concepts

Classification and estimation problems
• Given
• a finite set of (input) attributes: features
• Ex: District, House type, Income, Previous customer
• a target attribute: the goal
• Ex: Outcome: {Nothing, Respond}
• training data: a set of classified examples in attribute-value representation
• Ex: the previous table
• Predict the value of the goal given the values of input attributes
• The goal is a discrete variable  classification problem
• The goal is a continuous variable  estimation problem

District

Suburban

(3/5)

Urban

(3/5)

Rural

(4/4)

House type

Previous customer

Respond

Detached

(2/2)

Yes(3/3)

No (2/2)

Semi-detached

(3/3)

Nothing

Nothing

Respond

Respond

Decision tree
Decision tree representation
• Each internal node is a test:
• Theoretically, a node can test multiple attributes
• In most systems, a node tests exactly one attribute
• Each branch corresponds to test results
• A branch corresponds to an attribute value or a range of attribute values
• Each leaf node assigns
• a class: decision tree
• a real value: regression tree
What’s a best decision tree?
• “Best”: You need a bias (e.g., prefer the “smallest” tree): least depth? Fewest nodes? Which trees are the best predictors of unseen data?
• Occam's Razor: we prefer the simplest hypothesis that fits the data.

 Find a decision tree that is as small as possible and fits the data

Finding a smallest decision tree
• A decision tree can represent any discrete function of the inputs: y=f(x1, x2, …, xn)
• The space of decision trees is too big for systemic search for a smallest decision tree.
• Solution: greedy algorithm
Basic algorithm: top-down induction
• Find the “best” decision attribute, A, and assign A as decision attribute for node
• For each value of A, create new branch, and divide up training examples
• Repeat the process until the gain is small enough

### Major issues

Major issues

Q1: Choosing best attribute: what quality measure to use?

Q2: Determining when to stop splitting: avoid overfitting

Q3: Handling continuous attributes

Q4: Handling training data with missing attribute values

Q5: Handing attributes with different costs

Q6: Dealing with continuous goal attribute

Q1: What quality measure
• Information gain
• Gain Ratio
Entropy of a training set
• S is a sample of training examples
• Entropy is one way of measuring the impurity of S
• Pc is the proportion of examples in S whose target attribute has value c.
Information Gain
• Gain(S,A)=expected reduction in entropy due to sorting on A.
• Choose the A with the max information gain.

(a.k.a. choose the A with the min average entropy)

S=[9+,5-]

E=0.940

S=[9+,5-]

E=0.940

Wind

Humidity

High

Weak

Normal

Strong

[3+,4-]

[6+,2-]

[6+,1-]

[3+,3-]

An example

E=0.985

E=0.592

E=0.811

E=1.00

InfoGain(S, Humidity)

=0.940-(7/14)*0.985-(7/14)0.592

=0.151

InfoGain(S, Wind)

=0.940-(8/14)*0.811-(6/14)*1.0

=0.048

Other quality measures
• Problem of information gain:
• Information Gain prefers attributes with many values.
• An alternative: Gain Ratio

Where Si is subset of S for which A has value vi.

Q2: avoiding overfitting
• Overfitting occurs when our decision tree characterizes too much detail, or noise in our training data.
• Consider error of hypothesis h over
• Training data: ErrorTrain(h)
• Entire distribution D of data: ErrorD(h)
• A hypothesis h overfits training data if there is an alternative hypothesis h’, such that
• ErrorTrain(h) < ErrorTrain(h’), and
• ErrorD(h) > errorD(h’)
How to avoiding Overfitting
• Stop growing the tree earlier
• Ex: InfoGain < threshold
• Ex: Size of examples in a node < threshold
• Grow full tree, then post-prune

 In practice, the latter works better than the former.

Post-pruning
• Split data into training and validation set
• Do until further pruning is harmful:
• Evaluate impact on validation set of pruning each possible node (plus those below it)
• Greedily remove the ones that don’t improve the performance on validation set
• Produces a smaller tree with best performance measure
Performance measure
• Accuracy:
• on validation data
• K-fold cross validation
• Misclassification cost: Sometimes more accuracy is desired for some classes than others.
• MDL: size(tree) + errors(tree)
Rule post-pruning
• Convert tree to equivalent set of rules
• Prune each rule independently of others
• Sort final rules into desired sequence for use
• Perhaps most frequently used method (e.g., C4.5)
Q3: handling numeric attributes
• Continuous attribute  discrete attribute
• Example
• Original attribute: Temperature = 82.5
• New attribute: (temperature > 72.3) = t, f

 Question: how to choose thresholds?

Choosing thresholds for a continuous attribute
• Sort the examples according to the continuous attribute.
• Identify adjacent examples that differ in their target classification  a set of candidate thresholds
• Choose the candidate with the highest information gain.
Q4: Unknown attribute values
• Assume an attribute can take the value “blank”.
• Assign most common value of A among training data at node n.
• Assign most common value of A among training data at node n which have the same target class.
• Assign prob pi to each possible value vi of A
• Assign a fraction (pi) of example to each descendant in tree
• This method is used in C4.5.
Q5: Attributes with cost
• Consider medical diagnosis (e.g., blood test) has a cost
• Question: how to learn a consistent tree with low expected cost?
• One approach: replace gain by
• Tan and Schlimmer (1990)
• A variant of decision trees
• Estimation problem: approximate real-valued functions: e.g., the crime rate
• A leaf node is marked with a real value or a linear function: e.g., the mean of the target values of the examples at the node.
• Measure of impurity: e.g., variance, standard deviation, …
Summary of Major issues

Q1: Choosing best attribute: different quality measure.

Q2: Determining when to stop splitting: stop earlier or post-pruning

Q3: Handling continuous attributes: find the breakpoints

Summary of major issues (cont)

Q4: Handling training data with missing attribute values: blank value, most common value, or fractional count

Q5: Handing attributes with different costs: use a quality measure that includes the cost factors.

Q6: Dealing with continuous goal attribute: various ways of building regression trees.

ID3
• Proposed by Quinlan (so is C4.5)
• Can handle basic cases: discrete attributes, no missing information, etc.
• Information gain as quality measure
C4.5
• An extension of ID3:
• Several quality measures
• Incomplete information (missing attribute values)
• Numerical (continuous) attributes
• Pruning of decision trees
• Rule derivation
• Random mood and batch mood
CART
• CART (classification and regression tree)
• Proposed by Breiman et. al. (1984)
• Constant numerical values in leaves
• Variance as measure of impurity
Strengths of decision tree methods
• Ability to generate understandable rules
• Ease of calculation at classification time
• Ability to handle both continuous and categorical variables
• Ability to clearly indicate best attributes
The weaknesses of decision tree methods
• Greedy algorithm: no global optimization
• Error-prone with too many classes: numbers of training examples become smaller quickly in a tree with many levels/branches.
• Expensive to train: sorting, combination of attributes, calculating quality measures, etc.
• Trouble with non-rectangular regions: the rectangular classification boxes that may not correspond well with the actual distribution of records in the decision space.

Combining multiple models
• The inherent instability of top-down decision tree induction: different training datasets from a given problem domain will produce quite different trees.
• Techniques:
• Bagging
• Boosting
Bagging
• Introduced by Breiman
• It first creates multiple decision trees based on different training sets.
• Then, it compares each tree and incorporates the best features of each.
• This addresses some of the problems inherent in regular ID3.
Boosting
• Introduced by Freund and Schapire
• It examines the trees that incorrectly classify an instance and assign them a weight.
• These weights are used to eliminate hypotheses or refocus the algorithm on the hypotheses that are performing well.
Summary
• Basic case:
• Discrete input attributes
• Discrete goal attribute
• No missing attribute values
• Same cost for all tests and all kinds of misclassification.
• Extended cases:
• Continuous attributes
• Real-valued goal attribute
• Some examples miss some attribute values
• Some tests are more expensive than others.
• Some misclassifications are more serious than others.
Summary (cont)
• Basic algorithm:
• greedy algorithm
• top-down induction
• Bias for small trees
• Major issues:
Uncovered issues
• Incremental decision tree induction?
• How can a decision relate to other decisions? what's the order of making the decisions? (e.g., POS tagging)
• What's the difference between decision tree and decision list?