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CS498-EA Reasoning in AI Lecture #2PowerPoint Presentation

CS498-EA Reasoning in AI Lecture #2

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CS498-EA Reasoning in AI Lecture #2

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CS498-EAReasoning in AILecture #2

Professor: Eyal Amir

Fall Semester 2009

- Applications of reasoning in AI
- Econometrics
- Social Networks
- Verification of Circuits and Programs
- Natural Language Processing
- Robotics
- Vision
- Computer Security

- What is probability of recession, when a bank(bm) goes into bankruptcy?
- Recession: Recession of a country in [0,1]
- Market[X]: Quarterly market (X) index
- Loss[X,Y]: Loss of a bank (Y) in a market (X)
- Revenue[Y]: Revenue of a bank (Y)

Example: school friendships and their effects

Friend(A,B)

Attr(A)

Measuremt(A)

shorthand for Friend(., .), Atrr(.), and Measuremt(.)

potential functions

Friend(A,C)

Attr(B)

Measuremt(B)

Friend(B,C)

Attr(C)

Measuremt(C)

hlia

blia

hjoe

htom

hbob

btom

hann

bjoe

bann

bbob

hval

bval

f

f

f

f

f

f

f

f

f

f

f

f

f

f

f

f

f

f

f

f

f

f

f

f

f

f

f

f

f

f

tom;

val

bob;

lia

lia;

tom

ann;

lia

ann;

tom

lia;

ann

val;

bob

tom;

ann

joe;

val

ann;

joe

val;

joe

tom;

lia

bob;

val

lia;

joe

bob;

tom

val;

tom

joe;

ann

ann;

bob

val;

lia

joe;

bob

tom;

bob

joe;

tom

tom;

joe

joe;

lia

bob;

ann

lia;

val

val;

ann

ann;

val

lia;

bob

bob;

joe

Figure 5: Computation time for

f3

x1

f1

not

AND

x2

f5

AND

not

f2

OR

x3

f4

Question: Can we set this boolean cirtuit to TRUE?

f5(x1,x2,x3) = a function of the input signal

f3

x1

f1

not

AND

x2

f5

AND

not

f2

OR

SAT(f5) ?

x3

f4

Question: Can we set this boolean cirtuit to TRUE?

f5(x1,x2,x3) = f3 f4 = f1 (f2 x3) =

(x1 x2) (x2 x3)

M[x1]=FALSE

M[x2]=FALSE

M[x3]=FALSE

- Questions in logical circuit verification
- Equivalence of circuits
- Arrival of the circuit to a state (required a temporal model, which gets propositionalized)
- Achieving an output from the circuit

- Logical semantics
- Probabilistic choice between meanings
- Inference over time

- Videos

- Videos

- Shortest paths

- Classic computer science problem: many algorithms, applications
- “best” generally means minimizing some sort of cost

each edge has some

cost associated with it

cost of path generally sum etc. of cost of edges along path

10

10

10

source

s

10

sink

t

- Edges fail probabilistically
- Goal: find most reliable path

Directed Acyclic Graph G

edge reliability

t

0.85

s

0.9

0.95

path reliability = 0.95 x 0.9 x 0.85 = 0.73

assumption: independent!!!

not very realistic...

- Consider a richer structure using a graphical model

(discrete) hidden variable

X

t

e3

s

e2

e1

the hidden variable allows us to model correlations and dependencies between edge failures

binary random variables:

1 if edge survives, 0 if edge fails

- Specified:
- prior probability on X
- conditional probabilities for each edge

Pr[X=1] = 0.4

Pr[X=2] = 0.1

Pr[X=3] = 0.2

Pr[X=4] = 0.3

Pr[e1 survives | X=1] = 0.9

Pr[e1 fails | X=1] = 0.1

... etc.

X

t

e3

s

e2

e1

- Graphical model defines joint distribution:
Pr[X,e1,e2,e3,...]= Pr[X] Pr[e1|X] Pr[e2|X]...

- Reliability of path is marginal Pr[e1,e2,e3]
- Can compute by summing...

X

t

e3

s

e2

e1

- Just to name a few:
- Network QoS routing[citations]

routers fail stochastically

links fail stochastically

Failures are typically correlated: if two machines run the same version of

unpatched Windows, and one gets infected by a virus...

- Just to name a few:
- Network QoS routing [citations]
- Parsing w/ weighted FSAs

FSA where edges have probabilities assigned to them

(from Smith + Eisner ACL’05 best paper)

- Just to name a few:
- Network QoS routing
- Parsing w/ weighted FSAs
- Robot navigation

e.g., DARPA Grand Challenge