Cs498 ea reasoning in ai lecture 2
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CS498-EA Reasoning in AI Lecture #2. Professor: Eyal Amir Fall Semester 2009. Today. Applications of reasoning in AI Econometrics Social Networks Verification of Circuits and Programs Natural Language Processing Robotics Vision Computer Security.

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CS498-EA Reasoning in AI Lecture #2

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Cs498 ea reasoning in ai lecture 2

CS498-EAReasoning in AILecture #2

Professor: Eyal Amir

Fall Semester 2009


Today

Today

  • Applications of reasoning in AI

    • Econometrics

    • Social Networks

    • Verification of Circuits and Programs

    • Natural Language Processing

    • Robotics

    • Vision

    • Computer Security


Econometrics example a recession model of a country

Econometrics Example: A Recession Model of a country

  • 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)


Experiments

Experiments


Experiments1

Experiments


Social networks

Social Networks

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)


Cs498 ea reasoning in ai lecture 2

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Scaling up computing pr f x y

Scaling-Up: Computing Pr(f(x,y))

Figure 5: Computation time for


Application hardware verification

Application: Hardware Verification

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


Application hardware verification1

Application: Hardware Verification

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


Hardware verification

Hardware Verification

  • 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


Natural language processing

Natural-Language Processing

  • Logical semantics

  • Probabilistic choice between meanings

  • Inference over time


Robotics

Robotics

  • Videos


Vision

Vision

  • Videos


Computer security

Computer Security

  • Shortest paths


Finding the best path between two points

Finding the “best” path between two points

  • 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


Stochastic setting

Stochastic setting

  • 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...


Stochastic setting1

Stochastic setting

  • 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


Stochastic setting2

Stochastic setting

  • 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


Stochastic setting3

Stochastic setting

  • 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


Many applications

Many applications

  • 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...


Many applications1

Many applications

  • 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)


Many applications2

Many applications

  • Just to name a few:

    • Network QoS routing

    • Parsing w/ weighted FSAs

    • Robot navigation

e.g., DARPA Grand Challenge


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