1. The Neural Basis of Thought and Language Week 11 Metaphor and Bayes Nets

2. Schedule Assignment 7 extension, due Wednesday night Last Week –Aspect and Tense –Event Structure Metaphor This Week –Frames & how it maps to X-schemas –Inference, KARMA: Knowledge-based Action Representations for Metaphor and Aspect Next Week –Grammar

3. Announcement Panel: "Cruise Control": Careers in Artificial Intelligence. Friday, April 16th from 3-4:30 in Bechtel Hall 120A/B. The panel is an informal session, where professionals in the field of AI will answer general questions about their entry into the field, trends, etc. Panelists will be: –Peter Norvig from Google –Charlie Ortiz of Teambotics at SRI –Nancy Chang from ICSI. Moderator will be: –Barbara Hightower, CS advisor.

4. Quiz 1.What are metaphors? Give two examples of Primary Metaphors and sentences using them. 2.What are Event Structure Metaphors? Give an example. 3.How do Bayes Nets fit into the simulation story? What are the benefits of that model? 4.What are Dynamic Bayesian Networks?

5. Going from motor control to abstract reasoning The sensory-motor system is directly engaged in abstract reasoning Both the physical domain and abstract domain are structured by schemas and frames, i.e. there are –semantic roles, and –relation between semantic roles schemas generally refer to embodied, “universal” knowledge, whereas frames are generally culturally specific

6. Frames and FrameNet Formalizes links between semantics and syntax FrameNet –For every target word (ideally word sense) Describes underlying frames or conceptual structures Semantic frames are schemas –Frame elements (roles) Participants, props, etc... Event Frames –Temporal structure –Constraints on before/during/after –E.g. Commercial Transaction

7. The Commercial-Transaction schema schema Commercial-Transaction subcase of Exchange roles customer  participant1 vendor  participant2 money  entity1 : Money goods  entity2 goods-transfer  transfer1 money-transfer  transfer2

8. Quiz 1.What are metaphors? Give two examples of Primary Metaphors and sentences using them. 2.What are Event Structure Metaphors? Give an example. 3.How do Bayes Nets fit into the simulation story? What are the benefits of that model? 4.What are Dynamic Bayesian Networks?

9. Metaphors metaphors are mappings from a source domain to a target domain metaphor maps specify the correlation between source domain entities / relation and target domain entities / relation they also allow inference to transfer from source domain to target domain (possibly, but less frequently, vice versa) is

10. Primary Metaphors The key thing to remember about primary metaphors is that they have an experiential basis Affection Is Warmth Important is Big Happy is Up Intimacy is Closeness Bad is Stinky Difficulties are Burdens More is Up Categories are Containers Similarity is Closeness Linear Scales are Paths Organization is Physical Structure Help is Support Time Is Motion Relationships are Enclosures Control is Up Knowing is Seeing Understanding is Grasping Seeing is Touching

11. Affection is Warmth Subjective Judgment: Affection Sensory-Motor Domain: Temperature Example: They greeted me warmly. Primary Experience: Feeling warm while being held affectionately. more examples: –She gave me a cold shoulder –Now that I've known such-and-such for a while, he's finally warming up to me.

12. Important is Big Subjective Judgment: Importance Sensory-Motor Domain: Size Example: Tomorrow is a big day. Primary experience: As a child, important things in your environment are often big, e.g., parents, but also large things that exert a force on you more examples: –Don't sweat the small stuff. –I'll have a meeting with the big boss today.

13. How are these metaphors developed? Conflation Hypothesis: Children hypothesize an early meaning for a source domain word that conflates meanings in both the literal and metaphorical senses –experiencing warmth and affection when being held as a child –observing a higher water level when there's more water in a cup

18. The Dual Metaphors for Time Time is stationary and we move through it –It takes a long time to write a book –We are behind schedule schedules are landmarks on this landscape that we have to be at by a certain time Time is a moving object –The deadline is approaching –He is forever chasing his past the past is an object that has come by and moved past him

19. A different experiment by Boroditsky & Ramscar, 2002 “Next Wednesday's meeting has been moved forward two days. What day is the meeting now that it has been rescheduled?” Is the meeting Monday? or Friday?

20. Results of the experiment two spatial primes: A.participant sitting in an office chair moving through space. (ego-moving prime) B.participant pulling an office chair towards himself with a rope. (time-moving prime) results: A.more likely to say Friday B.more likely to say Monday

21. Quiz 1.What are metaphors? Give two examples of Primary Metaphors and sentences using them. 2.What are Event Structure Metaphors? Give an example. 3.How do Bayes Nets fit into the simulation story? What are the benefits of that model? 4.What are Dynamic Bayesian Networks?

22. Event Structure Metaphor Target Domain: event structure Source Domain: physical space States are Locations Changes are Movements Causes are Forces Causation is Forced Movement Actions are Self-propelled Movements Purposes are Destinations Means are Paths Difficulties are Impediments to Motion External Events are Large, Moving Objects Long-term Purposeful Activities are Journeys

23. The Dual of the ESM Attributes are possessions Changes are Movements of Possessions (acquisitions or losses) Causes are forces Causation is Transfer of Possessions (giving or taking) Purposes are Desired Objects Achieving a Purpose Is Acquiring a Desired Object

24. Examples of the Dual I have a headache. I got a headache. My headache went away. The noise gave me a headache. The aspirin took away my headache. I'm in trouble. (Location ESM) The programming assignment gave me much trouble. (Object ESM)

25. Quiz 1.What are metaphors? Give two examples of Primary Metaphors and sentences using them. 2.What are Event Structure Metaphors? Give an example. 3.How do Bayes Nets fit into the simulation story? What are the benefits of that model? 4.What are Dynamic Bayesian Networks?

26. Simulation-based Understanding Analysis Process “Harry walked into the cafe.” Utterance CAFE Simulation Belief State General Knowledge Constructions Semantic Specification

27. Semantic Analysis Takes in constructions –pairing of form and meaning –Form pole = syntax –Meaning pole = frames and other schemas Spits out semantic specification –schemas with bound roles

28. What exactly is simulation? Belief update plus X-schema execution hungrymeeting cafe time of day ready start ongoing finish done iterate WALK at goal

29. Bayes Nets: Take away points Computational technique to capture best fit –Probabilistic –Approximation to neural spreading activation Easy to write down (intuitive) –Nodes in terms of explicit causal relations Efficient –Much smaller than full joint... Known mechanisms to do inference

30. Review: Probability Random Variables –Boolean/Discrete True/false Cloudy/rainy/sunny –Continuous [0,1] (i.e. 0.0 <= x <= 1.0)

31. Priors/Unconditional Probability Probability Distribution –In absence of any other info –Sums to 1 –E.g. P(Sunny=T) =.8 (thus, P(Sunny=F) =.2) This is a simple probability distribution Joint Probability –P(Sunny, Umbrella, Bike) Table 2 3 in size –Full Joint is a joint of all variables in model Probability Density Function –Continuous variables E.g. Uniform, Gaussian, Poisson…

32. Conditional Probability P(Y | X) is probability of Y given that all we know is the value of X –E.g. P(cavity=T | toothache=T) =.8 thus P( cavity=F | toothache=T) =.2 Product Rule –P(Y | X) = P(X Y) / P(X)(normalizer to add up to 1 ) YX

33. Inference ToothacheCavityCatchProb False.576 False True.144 FalseTrueFalse.008 FalseTrue.072 TrueFalse.064 TrueFalseTrue.016 True False.012 True.108 P(Toothache=T)? P(Toothache=T, Cavity=T)? P(Toothache=T | Cavity=T)?

34. Bayes Nets BEP(A| … ) TTFFTTFF TFTFTFTF 0.95 0.94 0.29 0.001 BurglaryEarthquake Alarm MaryCallsJohnCalls P(B) 0.001 P(E) 0.002 AP(J|…) TFTF 0.90 0.05 AP(M|…) TFTF 0.70 0.01

35. Graphical Models P(Y | X) = P(X | Y) P(Y) P(X) What is P(Y=F|X=T)? What is P(X=T|Y=F)? What does it mean to have evidence? X Y Sneezing Cold P(X=T) =.3 P(Y=T|X=T) =.7 P(Y=T|X=F) =.2

36. Independence XYZXYZ X Y ZX Y Z X Y ZX Y Z X independent of Z?X conditionally independent of Z given Y? X independent of Z?X conditionally independent of Z given Y? No No No Yes Yes Yes Or below

37. Markov Blanket X X is independent of everything else given: Parents, Children, Parents of Children

38. Reference: Joints Representation of entire network P(X 1 =x 1  X 2 =x 2 ... X n =x n ) = P(x 1,..., x n ) =  i=1..n P(x i |parents(X i )) How? Chain Rule –P(x 1,..., x n ) = P(x 1 |x 2,..., x n ) P(x 2,..., x n ) =... =  i=1..n P(x i |x i-1,..., x 1 ) –Now use conditional independences to simplify

39. Reference: Joint, cont. P(x 1,..., x 6 ) = P(x 1 ) * P(x 2 |x 1 ) * P(x 3 |x 2, x 1 ) * P(x 4 |x 3, x 2, x 1 ) * P(x 5 |x 4, x 3, x 2, x 1 ) * P(x 6 |x 5, x 4, x 3, x 2, x 1 ) X2X2 X1X1 X3X3 X4X4 X6X6 X5X5

40. Reference: Joint, cont. P(x 1,..., x 6 ) = P(x 1 ) * P(x 2 |x 1 ) * P(x 3 |x 2, x 1 ) * P(x 4 |x 3, x 2, x 1 ) * P(x 5 |x 4, x 3, x 2, x 1 ) * P(x 6 |x 5, x 4, x 3, x 2, x 1 ) X2X2 X1X1 X3X3 X4X4 X6X6 X5X5

41. Reference: Inference General case –Variable Eliminate –P(Q | E) when you have P(R, Q, E) –P(Q | E) = ∑ R P(R, Q, E) / ∑ R,Q P(R, Q, E) ∑ R P(R, Q, E) = P(Q, E) ∑ Q P(Q, E) = P(E) P(Q, E) / P(E) = P(Q | E)

42. Reference: Inference, cont. Q = {X 1 }, E = {X 6 } R = X \ Q,E P(x 1,..., x 6 ) = P(x 1 ) * P(x 2 |x 1 ) * P(x 3 |x 1 ) * P(x 4 |x 2 ) * P(x 5 |x 3 ) * P(x 6 |x 5, x 2 ) X2X2 X1X1 X3X3 X4X4 X6X6 X5X5 P(x 1, x 6 )= ∑ x2 ∑ x3 ∑ x4 ∑ x5 P(x 1 ) P(x 2 |x 1 ) P(x 3 |x 1 ) P(x 4 |x 2 ) P(x 5 |x 3 ) P(x 6 |x 5, x 2 ) = P(x 1 ) ∑ x2 P(x 2 |x 1 ) ∑ x3 P(x 3 |x 1 ) ∑ x4 P(x 4 |x 2 ) ∑ x5 P(x 5 |x 3 ) P(x 6 |x 5, x 2 ) = P(x 1 ) ∑ x2 P(x 2 |x 1 ) ∑ x3 P(x 3 |x 1 ) ∑ x4 P(x 4 |x 2 ) m 5 (x 2, x 3 ) = P(x 1 ) ∑ x2 P(x 2 |x 1 ) ∑ x3 P(x 3 |x 1 ) m 5 (x 2, x 3 ) ∑ x4 P(x 4 |x 2 )=...

43. Approximation Methods Simple –no evidence Rejection –just forget about the invalids Likelihood Weighting –only valid, but not necessarily useful MCMC –Best: only valid, useful, in proportion

44. Stochastic Simulation Rain Sprinkler Cloudy WetGrass 1. Repeat N times: 1.1. Guess Cloudy at random 1.2. For each guess of Cloudy, guess Sprinkler and Rain, then WetGrass 2. Compute the ratio of the # runs where WetGrass and Cloudy are True over the # runs where Cloudy is True P(WetGrass|Cloudy)? P(WetGrass|Cloudy) = P(WetGrass  Cloudy) / P(Cloudy)

45. Quiz 1.What are metaphors? Give two examples of Primary Metaphors and sentences using them. 2.What are Event Structure Metaphors? Give an example. 3.How do Bayes Nets fit into the simulation story? What are the benefits of that model? 4.What are Dynamic Bayesian Networks?

46. DBNs Explicit causal relations + full joint table  Bayes Nets Sequence of full joint states over time  HMM HMM + BN  DBNs DBNs are a generalization of HMMs which capture sparse causal relationships of full joint

47. Dynamic Bayes Nets