CSC242: Intro to AI. Lecture 21

Transcription

1 CSC242: Intro to AI Lecture 21

2 Quiz Stop Time: 2:15

3

4 Learning (from Examples)

5 Learning

6 Learning gives computers the ability to learn without being explicitly programmed (Samuel, 1959)... agents that can improve their behavior through diligent study of their own experiences (Russell & rvig) Improving one s performance on future tasks after making observations about the world

7 Why Learn? Can t anticipate all possible situations that the agent might find themselves in Cannot anticipate all changes that might occur over time Don t know how to program it other than by learning!

8 What To Learn? Inferring properties of the world (state) from perceptions Choosing which action to do in a given state Results of possible actions How the world evolves in time Utilities of states

9 What To Learn? Numbers (e.g., probabilities) Functions (e.g., continuous distributions, functional relations between variables) Rules (e.g., All (most) X s are Y s, Under these conditions, do this action, discrete distributions)

10 Types of Learning Unsupervised (no feedback) Semi-supervised Supervised (labelled examples) Reinforcement (feedback is reward)

11 Learning Why? Improve without programming What? Probabilities, distributions, rules,... How? Unsupervised Supervised

12 Learning Functions from Examples

13 Function Learning There is some function y = f(x) Hypothesis We don t know f We want to learn a function h that approximates the true function f

14 Function Learning There is some function y = f(x) Hypothesis We don t know f We want to learn a function h that approximates the true function f Learning is a search through the space of possible hypotheses for one that will perform well

15 Supervised Learning Given a training set of N example inputoutput pairs: (x1, y1), (x2, y2),..., (xn, yn) where each yj = f(xj) Discover function h that approximates f Search through the space of possible hypotheses for one that will perform well

16 f(x)=y Training Data x y h(x)=?

17 Evaluating Accuracy Training set: (x 1, y 1 ), (x 2, y 2 ),..., (x N, y N ) Test set: Additional (xj, yj) pairs distinct from training set Test accuracy of h by comparing h(xj) to yj for (xj, yj) from training set

18 f(x)=y Training Data x y h(x)=? Testing Data x y f(x)=y h(x)=y?

19 Generalization A hypothesis (function) generalizes well if it correctly predicts the value of y for novel examples x

20 Supervised Function Learning Search through the space of possible hypotheses (functions) For a hypothesis that generalizes well Using the training data for guidance Evaluating performance using the testing data

21 Hypothesis Space

22 Hypothesis Space The class of functions that are acceptable as solutions, e.g. Linear functions y = mx + b Polynomials (of some degree) Java programs? Turing machines?

23 f(x) (a) x y = -0.4x+3

24 f(x) f(x) (a) x (b) x y = -0.4x+3 y = c 7 x 7 + c 6 x c 1 x + c 0 = 7X c i x i i=0

25 f(x) (c) x y = c 6 x 6 + c 5 x c 1 x + c 0 y = mx + b ax + b + c sin(x)

26 f(x) f(x) (c) x (d) x y = c 6 x 6 + c 5 x c 1 x + c 0 y = mx + b ax + b + c sin(x)

27 Occam s Razor William of Occam (or Ockham) 14th c.

28 Hypotheses There is a tradeoff between complex hypotheses that fit the training data and simpler hypotheses that may generalize better There is a tradeoff between the expressiveness of a hypothesis space and the complexity of finding a good hypothesis within it

29 Learning Decision Trees

30 Classification Output y = f(x) is one of a finite set of values (classes, categories,...) Boolean classification: yes/no or true/false Input is vector x of values for attributes Factored representation

31 Example Going out to dinner with Stuart Russell Restaurants often busy in SF; sometimes have to wait for a table Decision: Do we wait or do something else?

32 Attributes Alternate : is there a suitable alternative nearby Bar: does it have a comfy bar FriSat: is it a Friday or Saturday Hungry: are we hungry Patrons: ne, Some, Full Price: $,$$,$$$ Raining: is it raining outside Reservation: do we have a reservation Type: French, Italian, Thai, burger,... WaitEstimate: 0-10, 10-30, 30-60, >60

33 Decision Making If the host/hostess says you ll have to wait: Then if there s no one in the restaurant you don t want to be there either; But if there are a few people but it s not full, then you should wait Otherwise you need to consider how long he/she told you the wait would be...

34 Patrons? ne Some Full WaitEstimate? > Alternate? Hungry? Reservation? Fri/Sat? Alternate? Bar? Raining?

35 Decision Tree Each node in the tree represents a test on a single attribute Children of the node are labelled with the possible values of the attribute Each path represents a series of tests, and the leaf node gives the value of the function when the input passes those tests

36 Patrons? ne Some Full WaitEstimate? > Alternate? Hungry? Reservation? Fri/Sat? Alternate? Bar? Raining?

37 Patrons? ne Some Full WaitEstimate? > Alternate? Hungry? Reservation? Fri/Sat? Alternate? Bar? Raining?

38 Input Attributes Alt Bar Fri Hun Pat Price Rain Res Type Est Will Wait x1 Some $$$ French 0-10 y1=yes x2 Full $ Thai y2=no x3 Some $ Burger 0-10 y3=yes x4 Full $ Thai y4=yes x5 Full $$$ French >60 y5=no x6 Some $$ Italian 0-10 y6=yes x7 ne $ Burger 0-10 y7=no x8 Some $$ Thai 0-10 y8=yes x9 Full $ Burger >60 y9=no x10 Full $$$ Italian y10=no x11 ne $ Thai 0-10 y11=no x12 Full $ Burger y12=yes

39 Inducing Decision Trees From Examples Examples: (x,y) where x is a vector of values for the input attributes and y is a single Boolean value (yes/no, true/false)

40 Input Attributes Alt Bar Fri Hun Pat Price Rain Res Type Est Will Wait x1 Some $$$ French 0-10 y1=yes x2 Full $ Thai y2=no x3 Some $ Burger 0-10 y3=yes x4 Full $ Thai y4=yes x5 Full $$$ French >60 y5=no x6 Some $$ Italian 0-10 y6=yes x7 ne $ Burger 0-10 y7=no x8 Some $$ Thai 0-10 y8=yes x9 Full $ Burger >60 y9=no x10 Full $$$ Italian y10=no x11 ne $ Thai 0-10 y11=no x12 Full $ Burger y12=yes

41 Inducing Decision Trees From Examples Examples: (x,y) Want a shallow tree (short paths, fewer tests) Greedy algorithm (AIMA Fig 18.5) Always test the most important attribute first Makes the most difference to classification of an example

42 Input Attributes Alt Bar Fri Hun Pat Price Rain Res Type Est Will Wait x1 Some $$$ French 0-10 y1=yes x2 Full $ Thai y2=no x3 Some $ Burger 0-10 y3=yes x4 Full $ Thai y4=yes x5 Full $$$ French >60 y5=no x6 Some $$ Italian 0-10 y6=yes x7 ne $ Burger 0-10 y7=no x8 Some $$ Thai 0-10 y8=yes x9 Full $ Burger >60 y9=no x10 Full $$$ Italian y10=no x11 ne $ Thai 0-10 y11=no x12 Full $ Burger y12=yes

43 Input Attributes Alt Bar Fri Hun Pat Price Rain Res Type Est Will Wait x1 Some $$$ French 0-10 y1=yes x2 Full $ Thai y2=no x3 Some $ Burger 0-10 y3=yes x4 Full $ Thai y4=yes x5 Full $$$ French >60 y5=no x6 Some $$ Italian 0-10 y6=yes x7 ne $ Burger 0-10 y7=no x8 Some $$ Thai 0-10 y8=yes x9 Full $ Burger >60 y9=no x10 Full $$$ Italian y10=no x11 ne $ Thai 0-10 y11=no x12 Full $ Burger y12=yes

44 Type? French Italian Thai Burger (a)

45 Input Attributes Alt Bar Fri Hun Pat Price Rain Res Type Est Will Wait x1 Some $$$ French 0-10 y1=yes x2 Full $ Thai y2=no x3 Some $ Burger 0-10 y3=yes x4 Full $ Thai y4=yes x5 Full $$$ French >60 y5=no x6 Some $$ Italian 0-10 y6=yes x7 ne $ Burger 0-10 y7=no x8 Some $$ Thai 0-10 y8=yes x9 Full $ Burger >60 y9=no x10 Full $$$ Italian y10=no x11 ne $ Thai 0-10 y11=no x12 Full $ Burger y12=yes

46 Input Attributes Alt Bar Fri Hun Pat Price Rain Res Type Est Will Wait x1 Some $$$ French 0-10 y1=yes x2 Full $ Thai y2=no x3 Some $ Burger 0-10 y3=yes x4 Full $ Thai y4=yes x5 Full $$$ French >60 y5=no x6 Some $$ Italian 0-10 y6=yes x7 ne $ Burger 0-10 y7=no x8 Some $$ Thai 0-10 y8=yes x9 Full $ Burger >60 y9=no x10 Full $$$ Italian y10=no x11 ne $ Thai 0-10 y11=no x12 Full $ Burger y12=yes

47 Input Attributes Alt Bar Fri Hun Pat Price Rain Res Type Est Will Wait x1 Some $$$ French 0-10 y1=yes x2 Full $ Thai y2=no x3 Some $ Burger 0-10 y3=yes x4 Full $ Thai y4=yes x5 Full $$$ French >60 y5=no x6 Some $$ Italian 0-10 y6=yes x7 ne $ Burger 0-10 y7=no x8 Some $$ Thai 0-10 y8=yes x9 Full $ Burger >60 y9=no x10 Full $$$ Italian y10=no x11 ne $ Thai 0-10 y11=no x12 Full $ Burger y12=yes

48 Patrons? ne Some Full Hungry?

49 Patrons? ne Some Full Hungry?

50 Patrons? ne Some Full Hungry? (b)

51 Uncertainty Examples have same description in terms of input attributes but different classification results Error or noise in the data ndeterministic domain We can t observe the attribute that would distinguish the examples

52 Patrons? ne Some Full Hungry? Type? French Italian Thai Burger Fri/Sat?

53 Patrons? ne Some Full Patrons? ne Some Full WaitEstimate? Hungry? > Alternate? Reservation? Fri/Sat? Bar? Hungry? Alternate? Raining? Type? French Italian Thai Burger Fri/Sat?

54 Learning lets the data speak for itself

55 Learning Improving one s performance on future tasks after making observations about the world

56 Types of Learning Unsupervised (no feedback) Semi-supervised Supervised (labelled examples) Reinforcement (feedback is reward)

57 Supervised Learning Given a training set of N example inputoutput pairs: (x1, y1), (x2, y2),..., (xn, yn) where each yj = f(xj) Discover function h that approximates f

58 Evaluating Accuracy Training set: (x 1, y 1 ), (x 2, y 2 ),..., (x N, y N ) Test set: Additional (xj, yj) pairs distinct from training set Test accuracy of h by comparing h(xj) to yj for (xj, yj) from training set

59 Hypotheses There is a tradeoff between complex hypotheses that fit the training data and simpler hypotheses that may generalize better There is a tradeoff between the expressiveness of a hypothesis space and the complexity of finding a good hypothesis within it

60 Learning Decision Trees Each node tests a single attribute Child nodes for each possible value Each path represents a series of tests, and the leaf node gives the value of the function when the input passes those tests Test most discriminating attributes first Shallower tree

61 Patrons? ne Some Full Patrons? ne Some Full WaitEstimate? Hungry? > Alternate? Reservation? Fri/Sat? Bar? Hungry? Alternate? Raining? Type? French Italian Thai Burger Fri/Sat?

62 Project 4: Learning programming! Do homeworks 19 & 20 (this class & next) Due in BB Mon 15 Apr 23:00 Posters: Tue 23 Apr & Thu 25 Apr

63 For Next Time: AIMA 18.6; fyi