1. Learning from Observations
Chapter 18
Section 1 – 4

2. Outline Learning agents Inductive learning Decision tree learning
Boosting
This is about the best “off-the-shelves” classification algorithm!
(and you’ll get to know it)

3. Learning agents
Sometimes we want to invest time and effort to observe the feedback
from our environment to our actions in order to improve these actions
so we can more effectively optimize our utility in the future.

4. Learning element Design of a learning element is affected by
Which components of the performance element are to be learned (e.g. learn to stop for traffic light)
What feedback is available to learn these components (e.g. visual feedback form camera)
What representation is used for the components
(e.g. logic, probabilistic descriptions, attributes,...)
Type of feedback:
Supervised learning: correct answers for each example (label).
Unsupervised learning: correct answers not given.
Reinforcement learning: occasional rewards

5. Two Examples of Learning Object Categories.
Here is your training set (2 classes):

6. Here is your test set:
Does it belong to one of the above classes?

7. Learning from 1 Example Copied from P. Perona talk slides.
Having said that, we all know that the human visual system can do much better than today’s computer vision algorithms. We learn a vast number of different objects and object categories in our life time. In many cases we never had the luxury of hundreds of training examples.
For example, here I show a member of a new object category that most of you have never seen. Now let’s see if you are able to find another member of this new category in the following picture.
Copied from P. Perona
talk slides.
S. Savarese, 2003

8. P. Buegel, 1562

9. Inductive learning such that h ≈ f given a training set of examples
Simplest form: learn a function from examples
f is the target function
An example is a pair (x, f(x))
Problem: find a hypothesis h
such that h ≈ f
given a training set
of examples

10. Inductive learning method
Construct/adjust h to agree with f on training set
(h is consistent if it agrees with f on all examples)
E.g., curve fitting:

11. Inductive learning method
Construct/adjust h to agree with f on training set
(h is consistent if it agrees with f on all examples)
E.g., curve fitting:

12. Inductive learning method

13. Inductive learning method

14. Inductive learning method
which curve is best?

15. Inductive learning method
Ockham’s razor: prefer the simplest hypothesis consistent with data

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

17. Attribute-based representations
Examples described by attribute values (Boolean, discrete, continuous)
E.g., situations where I will/won't wait for a table:
Classification of examples is positive (T) or negative (F)
General form for data: a number N of instances, each with attributes (x1,x2,x3,...xd) and target value y.

18. Decision trees One possible representation for hypotheses
We imagine someone taking a sequence of decisions.
E.g., here is the “true” tree for deciding whether to wait:
Note you can use the same
attribute more than once.

19. Expressiveness
Decision trees can express any function of the input attributes.
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 (unless f nondeterministic in x) but it probably won't generalize to new examples
Prefer to find more compact decision trees: we don’t want to memorize the data, we want to find structure in the data!

20. 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
n=2: 2^2 = 4 rows. For each row we can choose T or F: 2^4 functions.

21. Decision tree learning
If there are so many possible trees, can we actually search this space? (solution: greedy search).
Aim: find a small tree consistent with the training examples
Idea: (recursively) choose "most significant" attribute as root of (sub)tree.

22. Choosing an attribute
Idea: a good attribute splits the examples into subsets that are (ideally) "all positive" or "all negative"
Patrons or type?
To wait or not to wait is still at 50%.

23. Using information theory
Entropy measures the amount of uncertainty
in a probability distribution:
Consider tossing a biased coin.
If you toss the coin VERY often,
the frequency of heads is, say, p,
and hence the frequency of tails is
1-p. (fair coin p=0.5).
The uncertainty in any actual outcome
is given by the entropy:
Note, the uncertainty is zero if p=0 or 1
and maximal if we have p=0.5.

24. Using information theory
If there are more than two states s=1,2,..n we have (e.g. a die):

25. Using information theory
Imagine we have p examples which are true (positive) and n examples which are false (negative).
Our best estimate of true or false is given by:
Hence the entropy is given by:

26. Using Information Theory
How much information do we gain if we disclose the value of some attribute?
Answer:
uncertainty before minus uncertainty after

27. Example Before: Entropy = - ½ log(1/2) – ½ log(1/2)=log(2) = 1 bit:
There is “1 bit of information to be discovered”.
After: for Type: If we go into branch “French” we have 1 bit, similarly for the others.
French: 1bit
Italian: 1 bit
Thai: 1 bit
Burger: 1bit
After: for Patrons: In branch “None” and “Some” entropy = 0!,
In “Full” entropy = -1/3log(1/3)-2/3log(2/3).
So Patrons gains more information!
On average: 1 bit ! We gained nothing!

28. Information Gain How do we combine branches:
1/6 of the time we enter “None”, so we weight“None” with 1/6.
Similarly: “Some” has weight: 1/3 and “Full” has weight ½.
entropy for each branch.
weight for each branch

29. Information gain
Information Gain (IG) or reduction in entropy from the attribute test:
Choose the attribute with the largest IG

30. Information gain
For the training set, p = n = 6, I(6/12, 6/12) = 1 bit
Patrons has the highest IG of all attributes and so is chosen by the DTL algorithm as the root

31. 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

32. What to Do if... In some leaf there are no examples:
Choose True or False according to the number of positive/negative examples at your parent.
There are no attributes left
Two or more examples have the same attributes but different label: we have an error/noise. Stop and use majority vote.
Demo:

33. Boosting
Main idea:
train classifiers (e.g. decision trees) in a sequence.
a new classifier should focus on those cases which were incorrectly classified in the last round.
combine the classifiers by letting them vote on the final prediction.
each classifier could be (should be) very “weak”,
e.g. a DT, with only one node: decision stump.

34. Example this line is one simple classifier saying that
everything to the left + and everything to the right
is -

35. Decision Stump Data: {(X1,Y1),(X2,Y2),....,(Xn,Yn)}
label (e.g. True or False,
0 or 1
-1 or +1)
attributes (e.g. temperature outside) +1 Xi -1
threshold

36. The Algorithm in Detail
(Z,H) = AdaBoost[Xtrain,Ytrain,Rounds]
weights = 1/N; (N = # datacases)
For r=1 to Rounds Do
H[r] = LearnWeakClassifier[Xtrain,Ytrain,weights];
error = 0;
For i=1 to N Do
If H[r,Xtrain(i)]=Ytrain(i) error = error + weight(i);
If H[r,Xtrain(i)]=Ytrain(i)  weight(i)=weight(i) error/(1-error);
Normalize Weights
Z[r] = log[(1-error)/error]
Final classifier:

37. And in a Picture training case correctly classified training case
has large weight
in this round
this DT has
a strong vote.

38. And in animation
Original Training set : Equal Weights to all training samples
Taken from “A Tutorial on Boosting” by Yoav Freund and Rob Schapire

39. AdaBoost(Example)
ROUND 1

40. AdaBoost(Example)
ROUND 2

41. AdaBoost(Example)
ROUND 3

42. AdaBoost(Example)

43. k-Nearest Neighbors Another simple classification algorithm
Idea: Look around you too see how your neighbors classify data.
Classify a new data-point according to a majority vote of your k-nearest neighbors.

44. k-NN
decision line

45. Distance Metric How do we measure what it means to be “close”?
Depending on the problem we should choose an appropriate distance metric.

46. Algorithm in Detail For a new test example:
Find the k closest neighbors
Each neighbor predicts the class to be it sown class
Take majority vote.
Demo:
Demo: MATLAB

47. Logistic Regression / Perceptron
Fits a soft decision boundary between the classes.
2 dimensions
1 dimension

48. The logit / sigmoid Determines the offset Determines the angle
and the steepness.

49. Objective
We interpret f(x) as the probability of classifying a data case as positive.
We want to maximize the total probability of the data-vectors:

50. Algorithm in detail Repeat until convergence (gradient descend):
(Or better: Newton steps)

51. Cross-validation
You are ultimately interested in good performance on new (unseen) test data.
To estimate that, split of a (smallish) subset of the training data (called validation set).
Train without validation data and “test” on validation data.
This will give an indication of how long to run boosting.

52. Project
Demo
For this project I will obtain data from a company who want to predict activity of a chemical compound.
Training data will be provided
Test data will not!
May the best win this competition.

53. Summary 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 + boosting
Learning performance = prediction accuracy measured on test set