1. 1 Inductive Learning of Rules MushroomEdible? SporesSpots Color YN BrownN YY GreyY NY BlackY NN BrownN YN WhiteN YY BrownY YN Brown NN Red Don’t try this at home...

2. 2 Types of Learning zWhat is learning? yImproved performance over time/experience yIncreased knowledge zSpeedup learning yNo change to set of theoretically inferable facts yChange to speed with which agent can infer them zInductive learning yMore facts can be inferred

3. 3 Mature Technology zMany Applications yDetect fraudulent credit card transactions yInformation filtering systems that learn user preferences yAutonomous vehicles that drive public highways (ALVINN) yDecision trees for diagnosing heart attacks ySpeech synthesis (correct pronunciation) (NETtalk) zData mining: huge datasets, scaling issues

4. 4 Defining a Learning Problem zExperience: zTask: zPerformance Measure: A program is said to learn from experience E with respect to task T and performance measure P, if it’s performance at tasks in T, as measured by P, improves with experience E.

5. 5 Example: Checkers zTask T: yPlaying checkers zPerformance Measure P: yPercent of games won against opponents zExperience E: yPlaying practice games against itself

6. 6 Example: Handwriting Recognition zTask T: y zPerformance Measure P: y zExperience E: y Recognizing and classifying handwritten words within images

7. 7 Example: Robot Driving zTask T: zPerformance Measure P: zExperience E: Driving on a public four-lane highway using vision sensors

8. 8 Example: Speech Recognition zTask T: zPerformance Measure P: zExperience E: Identification of a word sequence from audio recorded from arbitrary speakers... noise

9. 9 Issues zWhat feedback (experience) is available? zWhat kind of knowledge is being increased? zHow is that knowledge represented? zWhat prior information is available? zWhat is the right learning algorithm? zHow avoid overfitting?

10. 10 Choosing the Training Experience zCredit assignment problem: yDirect training examples: xE.g. individual checker boards + correct move for each yIndirect training examples : xE.g. complete sequence of moves and final result zWhich examples: yRandom, teacher chooses, learner chooses Supervised learning Reinforcement learning Unsupervised learning

11. 11 Choosing the Target Function zWhat type of knowledge will be learned? zHow will the knowledge be used by the performance program? zE.g. checkers program yAssume it knows legal moves yNeeds to choose best move ySo learn function: F: Boards -> Moves xhard to learn yAlternative: F: Boards -> R

12. 12 The Ideal Evaluation Function zV(b) = 100 if b is a final, won board zV(b) = -100 if b is a final, lost board zV(b) = 0 if b is a final, drawn board zOtherwise, if b is not final V(b) = V(s) where s is best, reachable final board Nonoperational… Want operational approximation of V: V

13. 13 How Represent Target Function zx 1 = number of black pieces on the board zx 2 = number of red pieces on the board zx 3 = number of black kings on the board zx 4 = number of red kings on the board zx 5 = number of black pieces threatened by red zx 6 = number of red pieces threatened by black V(b) = a + bx 1 + cx 2 + dx 3 + ex 4 + fx 5 + gx 6 Now just need to learn 7 numbers!

14. 14 Target Function zProfound Formulation: Can express any type of inductive learning as approximating a function zE.g., Checkers yV: boards -> evaluation zE.g., Handwriting recognition yV: image -> word zE.g., Mushrooms yV: mushroom-attributes -> {E, P} zInductive bias

15. 15 Theory of Inductive Learning

16. 16 Theory of Inductive Learning zSuppose our examples are drawn with a probability distribution Pr(x), and that we learned a hypothesis f to describe a concept C. zWe can define Error(f) to be: zwhere D are the set of all examples on which f and C disagree.

17. 17 PAC Learning zWe’re not perfect (in more than one way). So why should our programs be perfect? zWhat we want is:  Error(f) <  for some chosen  zBut sometimes, we’re completely clueless: (hopefully, with low probability). What we really want is:  Prob ( Error(f)  < .  As the number of examples grows,  and  should decrease. zWe call this Probably approximately correct.

18. 18 Definition of PAC Learnability zLet C be a class of concepts. zWe say that C is PAC learnable by a hypothesis space H if: ythere is a polynomial-time algorithm A, ya polynomial function p,  such that for every C in C, every probability distribution Pr, and  and ,  if A is given at least p(1/ , 1/  ) examples,  then A returns with probability 1-  a hypothesis whose error is less than . zk-DNF, and k-CNF are PAC learnable.

19. 19 Version Spaces: A Learning Alg. zKey idea: yMaintain most specific and most general hypotheses at every point. Update them as examples come in. zWe describe objects in the space by attributes: yfaculty, staff, student y20’s, 30’s, 40’s. ymale, female zConcepts: boolean combination of attribute- values: yfaculty, 30’s, male, yfemale, 20’s.

20. 20 Generalization and Specializ... zA concept C1 is more general than C2 if it describes a superset of the objects: yC1={20’s, faculty} is more general than C2={20’s, faculty, female}. yC2 is a specialization of C1. zImmediate specializations (generalizations). zThe version space algorithm maintains the most specific and most general boundaries at every point of the learning.

21. 21 Example T malefemale facultystudent 20’s30’s male, fac male,studfemale,facfemale,studfac,20’s fac, 30’s male,fac,20male,fac,30fem,fac,20male,stud,30