CS 182Sections 103 - 104

slides created by Eva Mok (emok@icsi.berkeley.edu)

modified by jgm

April 13, 2005

Announcements

• a8 out, due Monday April 19th, 11:59pm

• BBS articles are assigned for the final paper:

– Arbib, Michael A. (2002). The mirror system, imitation, and the evolution of language.

– Hurford, James R. (2003). The neural basis of predicate-argument structure.

– Grush, Rick (2004). The emulation theory of representation: motor control, imagery, and perception.

• Skim through them and let us know, as part of a8, which article you plan to use.

Schedule

• Last Week

– Inference in Bayes Net

– Metaphor understanding using KARMA

• This Week

– Formal Grammar and Parsing

– Construction Grammar, ECG

• Next Week

– Psychological model of sentence processing

– Grammar Learning

Quiz

1. How are the source and target domains represented in KARMA?

2. How does the source domain information enter KARMA? How should it?

3. What does SHRUTI buy us?

4. How are bindings propagated in a structured connectionist framework?

Quiz

1. How are the source and target domains represented in KARMA?

2. How does the source domain information enter KARMA? How should it?

3. What does SHRUTI buy us?

4. How are bindings propagated in a structured connectionist framework?

KARMA

• DBN to represent target domain knowledge

• Metaphor maps link target and source domain

• X-schema to represent source domain knowledge

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

Dynamic Bayes Nets

Metaphor Maps

1. map entities and objects between embodied and abstract domains

2. invariantly map the aspect of the embodied domain event onto the target domain

by setting the evidence for the status variable based on controller state (event structure metaphor)

3. project x-schema parameters onto the target domain

Where does the domain knowledge come from?

• Both domains are structured by frames

• Frames have:

– List of roles (participants, frame elements)

– Relations between roles

– Scenario structure

DBN for the target domain

T0 T1

Economic State

Goal

Policy

Outcome

Difficulty

[Liberalization, Protectionism]

[free trade, protection ]

[success, failure]

[present, absent]

[recession,nogrowth,lowgrowth,higrowth]

Let’s try a different domain

• I didn’t quite catch what he was saying

• His slides are packed with information

• He sent the audience a clear message

9/11 Commission Public Hearing, Monday, March 31, 2003

When we can get a good flow of information from the streets of our cities across to, whether it is an investigating magistrate in France or an intelligence operative in the Middle East, and begin to assemble that kind of information and analyze it and repackage it and send it back out to users, whether it's a policeman on the beat or a judge in Italy or a Special Forces Team in Afghanistan, then we will be getting close to the kind of capability we need to deal with this kind of problem. That's going to take a couple, a few years.

Target domain belief net (T-1)

Metaphor Map (conduit metaphor)

Ideas are

objects

Words are

containers

Sendersare

speakers

Receiversare

addressees

sendis

talk

receiveis

hear

Target domain belief net (T) (communication frame)

speaker addressee action outcomedegree of

understanding

Source domain f-structs (transfer)

X-Schema representation

sender receiver means force rate

transfersend receive

pack

Quiz

1. How are the source and target domains represented in KARMA?

2. How does the source domain information enter KARMA? How should it?

3. What does SHRUTI buy us?

4. How are bindings propagated in a structured connectionist framework?

How do the source domain f-structs get parameterized?

• In the KARMA system, they are hand-coded.

• In general, you need analysis of sentences:

– syntax

– semanticsSyntax captures:

• constraints on word order

• constituency (units of words)

• grammatical relations (e.g. subject, object)

• subcategorization & dependency (e.g. transitive, intransitive, subject-verb agreement)

Quiz

1. How are the source and target domains represented in KARMA?

2. How does the source domain information enter KARMA? How should it?

3. What does SHRUTI buy us?

4. How are bindings propagated in a structured connectionist framework?

SHRUTI

• A connectionist model of reflexive processing

Reflexive reasoning

automatic, extremely fast (~300ms), ubiquitous

• computation of coherent explanations and predictions• gradual learning of causal structure• episodic memory• understanding language

Reflective reasoning

conscious deliberation, slowovert consideration of alternativesexternal props (pencil + paper)

• solving logic puzzles• doing cryptarithmetic• planning a vacation

SHRUTI

• synchronous activity without using global clock

• An episode of reflexive processing is a transient propagation of rhythmic activity

• An “entity” is a phase in the above rhythmic activity.

• Bindings are synchronous firings of role and entity cells

• Rules are interconnection patterns mediated by coincidence detector circuits that allow selective propagation of activity

• Long-term memories are coincidence and coincidence-failure detector circuits

• An affirmative answer / explanation corresponds to reverberatory activity around closed loops

focal cluster

• provides locus of coordination, control and decision making

• enforce sequencing and concurrency

• initiate information seeking actions

• initiate evaluation of conditions

• initiate conditional actions

• link to other schemas, knowledge structures

Quiz

1. How are the source and target domains represented in KARMA?

2. How does the source domain information enter KARMA? How should it?

3. What does SHRUTI buy us?

4. How are bindings propagated in a structured connectionist framework?

dynamic binding example

• asserting that get(father, cup)

• father fires in phase with agent role

• cup fires in phase with patient role

+ - ? agt pat

+e +v ?e ?v

+ ?

get

cup

my-father

type

entity

predicate

Active Schemas in SHRUTI

• active schemas require control and coordination, dynamic role binding and parameter setting

• schemas are interconnected networks of focal clusters

• bindings are encoded and propagated using temporal synchrony

• scalar parameters are encoded using rate-encoding

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)?

Independence

•Rainy Cloudy

•Sunny Windy

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)

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, Cavity=T)?

Inference

Toothache Cavity Prob

False False .72

False True 0.08

True False 0.08

True True 0.12

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)