1. Machine Learning: Decision Trees Homework 4 assigned
courtesy: Geoffrey Hinton, Yann LeCun, Tan, Steinbach, Kumar

2. What is machine learning?
It is very hard to write programs that solve problems like recognizing a face.
We don’t know what program to write because we don’t know how its done.
Even if we had a good idea about how to do it, the program might be horrendously complicated.
Instead of writing a program by hand, we collect lots of examples that specify the correct output for a given input.
A machine learning algorithm then takes these examples and produces a program that does the job.
The program produced by the learning algorithm may look very different from a typical hand-written program. It may contain millions of numbers.
If we do it right, the program works for new cases as well as the ones we trained it on.

4. Handwriting/face recognition/detection

5. Visual object/action recognition
Aeroplanes
Bicycles
Birds
Boats
Buses
Cars
Cats
Trains
Cows
Chairs
Dogs
Horses

6. Different types of learning
Supervised Learning: given training examples of inputs and corresponding outputs, produce the “correct” outputs for new inputs. Example: character recognition.
Unsupervised Learning: given only inputs as training, find structure in the world: discover clusters, manifolds, characterize the areas of the space to which the observed inputs belong
Reinforcement Learning: an agent takes inputs from the environment, and takes actions that affect the environment. Occasionally, the agent gets a scalar reward or punishment. The goal is to learn to produce action sequences that maximize the expected reward.

7. Applications
handwriting recognition, OCR: reading checks and zip codes, handwriting recognition for tablet PCs.
speech recognition, speaker recognition/verification
security: face detection and recognition, event detection in videos.
text classification: indexing, web search.
computer vision: object detection and recognition.
diagnosis: medical diagnosis (e.g. pap smears processing)
adaptive control: locomotion control for legged robots, navigation for mobile robots, minimizing pollutant emissions for chemical plants, predicting consumption for utilities...
fraud detection: e.g. detection of “unusual” usage patterns for credit cards or calling cards.
database marketing: predicting who is more likely to respond to an ad campaign. (...and the antidote) spam filtering.
games (e.g. backgammon).
Financial prediction (many people on Wall Street use machine learning).

8. Learning ≠ memorization
rote learning is easy: just memorize all the training examples and their corresponding outputs.
when a new input comes in, compare it to all the memorized samples, and produce the output associated with the matching sample.
PROBLEM: in general, new inputs are different from training samples. The ability to produce correct outputs or behavior on previously unseen inputs is called GENERALIZATION.
rote learning is memorization without generalization.
The big question of Learning Theory (and practice): how to get good generalization with a limited number of examples.

9. Look ahead Supervised learning Decision trees Linear models
Neural networks
Unsupervised learning
K-means clustering
Full text in PDF

10. Learning from examples

11. Examples of Classification Task
Handwriting recognition
Face detection
Speech recognition
Object recognition

12. Learning from examples

13. Uses different biases in predicting Russel’s waiting habbits
Decision Trees
--Examples are used to
--Learn topology
--Order of questions
K-nearest
neighbors
If patrons=full and day=Friday
then wait (0.3/0.7)
If wait>60 and Reservation=no
then wait (0.4/0.9)
Association rules
--Examples are used to
--Learn support and
confidence of association
rules
SVMs
Neural Nets
--Examples are used to
--Learn topology
--Learn edge weights
Naïve bayes
(bayesnet learning)
--Examples are used to
--Learn topology
--Learn CPTs

15. Decision Tree Classification Task

16. Apply Model to Test Data
Start from the root of tree.
Refund
MarSt
TaxInc
YES NO
Yes No
Married
Single, Divorced
< 80K
> 80K

17. Apply Model to Test Data
Refund
MarSt
TaxInc
YES NO
Yes No
Married
Single, Divorced
< 80K
> 80K

18. Apply Model to Test Data
Refund
Yes No NO
MarSt
Single, Divorced
Married
TaxInc NO
< 80K
> 80K NO
YES

19. Apply Model to Test Data
Refund
Yes No NO
MarSt
Single, Divorced
Married
TaxInc NO
< 80K
> 80K NO
YES

20. Apply Model to Test Data
Refund
Yes No NO
MarSt
Single, Divorced
Married
TaxInc NO
< 80K
> 80K NO
YES

21. Apply Model to Test Data
Refund
Yes No NO
MarSt
Married
Assign Cheat to “No”
Single, Divorced
TaxInc NO
< 80K
> 80K NO
YES

22. Decision Tree Classification Task

23. Decision Tree Induction
Many Algorithms:
Hunt’s Algorithm (one of the earliest)
CART
ID3, C ml/dtrees/c4.5/tutorial.html
SLIQ,SPRINT

24. Tree Induction Greedy strategy.
Split the records based on an attribute test that optimizes certain criterion.
Issues
Determine how to split the records
How to specify the attribute test condition?
How to determine the best split?
Determine when to stop splitting

25. Tree Induction Greedy strategy.
Split the records based on an attribute test that optimizes certain criterion.
Issues
Determine how to split the records
How to specify the attribute test condition?
How to determine the best split?
Determine when to stop splitting

26. How to Specify Test Condition?
Depends on attribute types
Nominal
Ordinal
Continuous
Depends on number of ways to split
2-way split
Multi-way split

27. Splitting Based on Nominal Attributes
Multi-way split: Use as many partitions as distinct values.
Binary split: Divides values into two subsets Need to find optimal partitioning.
CarType
Family
Sports
Luxury
CarType
{Sports, Luxury}
{Family}
CarType
{Family, Luxury}
{Sports} OR

28. Splitting Based on Continuous Attributes
Different ways of handling
Discretization to form an ordinal categorical attribute
Static – discretize once at the beginning
Dynamic – ranges can be found by equal interval bucketing, equal frequency bucketing (percentiles), or clustering.
Binary Decision: (A < v) or (A  v)
consider all possible splits and finds the best cut
can be more compute intensive

29. Tree Induction Greedy strategy.
Split the records based on an attribute test that optimizes certain criterion.
Issues
Determine how to split the records
How to specify the attribute test condition?
How to determine the best split?
Determine when to stop splitting

30. How to determine the Best Split
Greedy approach:
Nodes with homogeneous class distribution are preferred
Need a measure of node impurity:
Non-homogeneous,
High degree of impurity
Homogeneous,
Low degree of impurity

31. Entropy
The entropy of a random variable V with values vk, each with probability P(vk) is:
𝐻 𝑉 =− 𝑘 𝑃( 𝑣 𝑘 ) 𝑙𝑜𝑔 2 𝑃 (𝑣 𝑘 )

32. Splitting Criteria based on INFO
Entropy at a given node t:
(NOTE: p( j | t) is the relative frequency of class j at node t).
Measures homogeneity of a node.
Maximum (log nc) when records are equally distributed among all classes implying least information
Minimum (0.0) when all records belong to one class, implying most information

33. How to Find the Best Split
Before Splitting: M0 A? B?
Yes No
Yes No
Node N1
Node N2
Node N3
Node N4 M1 M2 M3 M4
M12
M34
Gain = M0 – M12 vs M0 – M34

34. Examples for computing Entropy
P(C1) = 0/6 = P(C2) = 6/6 = 1
Entropy = – 0 log 0 – 1 log 1 = – 0 – 0 = 0
P(C1) = 1/ P(C2) = 5/6
Entropy = – (1/6) log2 (1/6) – (5/6) log2 (1/6) = 0.65
P(C1) = 2/ P(C2) = 4/6
Entropy = – (2/6) log2 (2/6) – (4/6) log2 (4/6) = 0.92

35. Splitting Based on INFO...
Information Gain:
Parent Node, p is split into k partitions;
ni is number of records in partition i
Measures Reduction in Entropy achieved because of the split. Choose the split that achieves most reduction (maximizes GAIN)
Used in ID3 and C4.5

36. S The Information Gain Computation P+ : N+ /(N++N-) P- : N- /(N++N-)
I(P+ ,, P-) = -P+ log(P+) - P- log(P- ) N+ N-
N1+
N1-
N2+
N2-
Nk+
Nk-
Splitting on
feature f
The difference
is the information
gain
So, pick the feature
with the largest Info Gain
I.e. smallest residual info
I(P1+ ,, P1-)
I(P2+ ,, P2-)
I(Pk+ ,, Pk-) S
[Ni+ + Ni- ]/[N+ + N-] I(Pi+ ,, Pi-)
i=1 k
Given k mutually exclusive and exhaustive
events E1….Ek whose probabilities are
p1….pk
The “information” content (entropy) is defined as
S i -pi log2 pi
A split is good if it reduces the entropy..

37. V(M) = 2/4 * I(1/2,1/2) + 2/4 * I(1/2,1/2)
A simple example
I(1/2,1/2) = -1/2 *log 1/2 -1/2 *log 1/2
= 1/2 + 1/2 =1
I(1,0) = 1*log * log 0 = 0
V(M) = 2/4 * I(1/2,1/2) + 2/4 * I(1/2,1/2)
= 1
V(A) = 2/4 * I(1,0) + 2/4 * I(0,1)
= 0
V(N) = 2/4 * I(1/2,1/2) + 2/4 * I(1/2,1/2)
So Anxious is the best attribute to split on
Once you split on Anxious, the problem is solved

38. Decision Tree Based Classification
Advantages:
Inexpensive to construct
Extremely fast at classifying unknown records
Easy to interpret for small-sized trees
Accuracy is comparable to other classification techniques for many simple data sets

39. Tree Induction Greedy strategy.
Split the records based on an attribute test that optimizes certain criterion.
Issues
Determine how to split the records
How to specify the attribute test condition?
How to determine the best split?
Determine when to stop splitting

40. Underfitting and Overfitting
Underfitting: when model is too simple, both training and test errors are large

41. Overfitting due to Noise
Decision boundary is distorted by noise point

42. Notes on Overfitting
Overfitting results in decision trees that are more complex than necessary
Training error no longer provides a good estimate of how well the tree will perform on previously unseen records
Need new ways for estimating errors

43. How to Address Overfitting
Pre-Pruning (Early Stopping Rule)
Stop the algorithm before it becomes a fully-grown tree
Typical stopping conditions for a node:
Stop if all instances belong to the same class
Stop if all the attribute values are the same
More restrictive conditions:
Stop if number of instances is less than some user-specified threshold
Stop if class distribution of instances are independent of the available features (e.g., using  2 test)
Stop if expanding the current node does not improve impurity measures (e.g., Gini or information gain).

44. How to Address Overfitting…
Post-pruning
Grow decision tree to its entirety
Trim the nodes of the decision tree in a bottom-up fashion
If generalization error improves after trimming, replace sub-tree by a leaf node.
Class label of leaf node is determined from majority class of instances in the sub-tree

45. Decision Boundary
Border line between two neighboring regions of different classes is known as decision boundary
Decision boundary is parallel to axes because test condition involves a single attribute at-a-time

46. Oblique Decision Trees
x + y < 1
Class = +
Class =
Test condition may involve multiple attributes
More expressive representation
Finding optimal test condition is computationally expensive