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The Neural Basis ofThe Neural Basis ofThought and LanguageThought and Language
Week 11Week 11
Metaphor and Bayes NetsMetaphor and Bayes Nets
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
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.
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?
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
The Commercial-Transaction schema
schema Commercial-Transactionsubcase of Exchangeroles
customer participant1vendor participant2money entity1 : Moneygoods entity2goods-transfer transfer1 money-transfer transfer2
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?
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)
<TARGET> is <SOURCE>
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
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.
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.
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
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
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?
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
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?
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
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
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)
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?
Simulation-based Understanding
Analysis Process
“Harry walked into the cafe.”Utterance
CAFESimulation
Belief State
General Knowledg
e
Constructions
SemanticSpecificatio
n
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
What exactly is simulation?
• Belief update plus X-schema execution
hungry meeting
cafe
time of day
readystart
ongoingfinish
done
iterate
WALK
at goal
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
Review: Probability
• Random Variables
– Boolean/Discrete
• True/false
• Cloudy/rainy/sunny
– Continuous
• [0,1] (i.e. 0.0 <= x <= 1.0)
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 23 in size
– Full Joint is a joint of all variables in model
• Probability Density Function
– Continuous variables• E.g. Uniform, Gaussian, Poisson…
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)
Y X
Inference
Toothache Cavity Catch Prob
False False False .576
False False True .144
False True False .008
False True True .072
True False False .064
True False True .016
True True False .012
True True True .108
P(Toothache=T)?P(Toothache=T, Cavity=T)? P(Toothache=T | Cavity=T)?
Bayes NetsBayes Nets
B E P(A|…)
TTFF
TFTF
0.950.940.290.001
Burglary Earthquake
Alarm
MaryCallsJohnCalls
P(B)
0.001
P(E)
0.002
A P(J|…)
TF
0.900.05
A P(M|…)
TF
0.700.01
Independence
X Y Z X Y Z
X
Y
Z X
Y
Z
X
Y
Z X
Y
Z
X independent of Z?X independent of Z? X conditionally independent of Z given Y?X conditionally independent of Z given Y?
NoNo
NoNo
NoNo
YesYes
YesYes
YesYes
Or below
Markov Blanket
X
X is independentof everything else given:
Parents, Children, Parents of Children
Reference: Joints
• Representation of entire network
• P(X1=x1 X2=x2 ... Xn=xn) =P(x1, ..., xn) = i=1..n P(xi|parents(Xi))
• How? Chain Rule
– P(x1, ..., xn) = P(x1|x2, ..., xn) P(x2, ..., xn) =... = i=1..n P(xi|xi-1, ..., x1)
– Now use conditional independences to simplify
Reference: Joint, cont.
P(x1, ..., x6) =P(x1) *P(x2|x1) *P(x3|x2, x1) *P(x4|x3, x2, x1) *P(x5|x4, x3, x2, x1) *P(x6|x5, x4, x3, x2, x1)
X2
X1
X3
X4
X6
X5
Reference: Joint, cont.
P(x1, ..., x6) =P(x1) *P(x2|x1) *P(x3|x2, x1) *P(x4|x3, x2, x1) *P(x5|x4, x3, x2, x1) *P(x6|x5, x4, x3, x2, x1)
X2
X1
X3
X4
X6
X5
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)
Reference: Inference, cont.
Q = {X1}, E = {X6}
R = X \ Q,E
P(x1, ..., x6) =P(x1) * P(x2|x1) * P(x3|x1) * P(x4|x2) *P(x5|x3) * P(x6|x5, x2)
X2
X1
X3
X4
X6
X5
P(x1, x6) = ∑x2 ∑x3 ∑x4 ∑x5 P(x1) P(x2|x1) P(x3|x1) P(x4|x2) P(x5|x3) P(x6|x5, x2)
= P(x1) ∑x2 P(x2|x1) ∑x3 P(x3|x1) ∑x4 P(x4|x2) ∑x5 P(x5|x3) P(x6|x5, x2)
= P(x1) ∑x2 P(x2|x1) ∑x3 P(x3|x1) ∑x4 P(x4|x2) m5(x2, x3)
= P(x1) ∑x2 P(x2|x1) ∑x3 P(x3|x1) m5(x2, x3) ∑x4 P(x4|x2) = ...
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
Stochastic SimulationStochastic Simulation
RainSprinkler
Cloudy
WetGrass1. 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)
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?
Dynamic Bayes Nets