[PPT] - Prob obab abil ilit ity y an and d Tim Time: Ma Marko kov PowerPoint Presentation

SLIDE 1

CPSC322 Summer 2017 Slide 1

Prob

bab

abil ilit ity y an and d Tim Time: Ma Marko kov v Mo Mode dels ls

Com

mputer Science c

cpsc sc322, Lecture 3 31 (Te Text xtboo

ok

k Chpt 6.5.1)

June, 2 20, 2 2017

6/21/2017

SLIDE 2

CPSC322 Summer 2017 Slide 2

Lectu ture re Ov Overv rvie iew

Recap

p

Te

Tempo poral l Prob

babi

bilistic ic Mo Mode dels ls

Start Markov Models
Markov Chain
Markov Chains in Natural Language

Processing

6/21/2017

SLIDE 3

CPSC322 Summer 2017 Slide 3

Bi Big g Pi Pict ctur ure: e: R&R &R sy syst stem ems

Environ

nment

Prob

blem

Qu Query Planning Dete terministi tic Sto tochas asti tic Se Sear arch Arc Consiste tency Sear arch Sear arch Val alue Ite terat ation Var

ar. Eliminat

ation Constr trai aint t Sat atisfac acti tion Logics STRIPS Belief N Nets ts Var ars + Constr trai aints ts Decision Nets ts Mar arkov Pr v Processes Var

ar. Eliminat

ation Sta tati tic Se Sequenti tial al Representa tati tion Reas asoning Technique SLS

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SLIDE 4

CPSC322 Summer 2017 Slide 4

Answerin ing Query u y unde der Un Uncertai ainty

Sta tati tic B Belief Netw twork

& V Variab able le Elimi mina nation ion Dynamic mic Bayesia ian n Network rk Probab abil ility ity Theory ry Hidden n Markov

v Models

Email il spam m filters rs Diagno nosti stic c Sy Systems ms (e.g., ., medici cine ne) Natural al Language age Processin ssing St Student t Tracing ng in tutorin ing g Sy Systems ms Monitori

ring

ng (e.g credit t cards) BioInforma rmati tics cs Markov

v Chains

6/21/2017

SLIDE 5

CPSC322 Summer 2017 Slide 5

Lectu ture re Ov Overv rvie iew

Recap

p

Te

Tempo poral l Prob

babi

bilistic ic Mo Mode dels ls

Start Markov Models
Markov Chain
Markov Chains in Natural Language

Processing

6/21/2017

SLIDE 6

Mod

dell

llin ing g st stat atic ic Envi viro ronme ments ts

So far we have used Bnets to perform inference in st static environ

nments

s

For instance, the system keeps collecting evidence to

diagnose the cause of a fault in a system (e.g., a car).

The environment (values of the evidence, the true cause)

does not change as I gather new evidence

What does change?

The system’s beliefs over possible causes

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SLIDE 7

Mode deli ling Ev Evolv lvin ing E Envir ironments

Often we need to make inferences about evolving

environments.

Represent the state of the world at each specific point

in time via a series of snapshots, or time sl slices, Tu Tutor

ring

g sy syst stem tracing student knowledge and morale

Knows-Subtrac action t-1 Moral ale t-1 Moral ale t Solve veProblem t-1 Solve veProblemt Knows-Subtrac action t

t

6/21/2017 CPSC322 Summer 2017 Slide 7

SLIDE 8

CPSC322 Summer 2017 Slide 8

Lectu ture re Ov Overv rvie iew

Recap

p

Te

Tempo poral l Prob

babi

bilistic ic Mo Mode dels ls

Start Markov Models
Mar

arko kov v Ch Chai ain

Markov Chains in Natural Language

Processing

6/21/2017

SLIDE 9

CPSC322 Summer 2017 Slide 9

Si Simp mple lest st Pos

ssi

sible le DBN BN

Thus
Intuitively St conveys all of the information about the history

that can affect the future states.

“The future is independent of the past given the present.”
On

One ran andom va variab able for each time slice: let’s assume St represents the state at time t. with domain {v1 …vn }

Eac

ach ran andom va variab able depends only o y on th the previ vious one

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SLIDE 10

Simplest Possible DBN (cont’)

Stationary process assumption: the mechanism

that regulates how state variables change overtime is st station

nary, that is it can be described by a single

transition model

P(St|St-1)
How many CPTs do we need to specify?
B. 4

A.

A. 1

C . . 2 D.

D. 3

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SLIDE 11

Stat atio ionar ary Ma y Markov Ch v Chai ain ( (SMC MC)

A stationary Markov Chain : for all t >0

P (St+1| S0,…,St) = P (St+1|St) and
P (St +1|St) is the same

We only need to specify and

Simple Model, easy to specify
Often the natural model
The network can extend indefinitely
Var

ariat ations of SMC ar are at at th the c core o

f man

any y Nat atural al L Lan anguag age Processing (NLP) ap applicat ations!

6/21/2017 CPSC322 Summer 2017 Slide 1 1

SLIDE 12

Stat atio ionar ary Ma y Markov Ch v Chai ain ( (SMC MC)

A stationary Markov Chain : for all t >0

P (St+1| S0,…,St) = P (St+1|St) and
P (St +1|St) is the same
B. P (S0)

A.

A. P (St +1 |St) and P (S0)

C . . P (St +1|St) D.

D. P (St |St+1 )

So we only need to specify?

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SLIDE 13

Sta Stati tion

nar

ary y Mar arko kov-Ch Chai ain: Exa xamp mple le

Probability of initial state

t t q p q p .3 .4 .6 1 a h e .4 1 a h e .3 .4 .6 1

1  t

S

t

S

Domain of variable Si is {t , q, p, a, h, e}

t q .6 .4 p a h e

Stochastic Transition Matrix

P (S0) P (St+1|St)

t t q p q p 1 1 .3 1 a h e a h e 1 1 .2 1

1  t

S

t

S

B. Right one only

A. A.Left one only C . . Both D.

D. None

Which of these two is a possible STM?

6/21/2017 CPSC322 Summer 2017 Slide 13

SLIDE 14

CPSC322 Summer 2017 Slide 14

Sta Stati tion

nar

ary y Mar arko kov-Ch Chai ain: Exa xamp mple le

Probability of initial state

t t q p q p .3 .4 .6 1 a h e .4 1 a h e .3 .4 .6 1

1  t

S

t

S

Domain of variable Si is {t , q, p, a, h, e} We only need to specify…

t q .6 .4 p a h e

Stochastic Transition Matrix

P (S0) P (St+1|St)

6/21/2017

SLIDE 15

CPSC322 Summer 2017 Slide 15

Mark rkov

v-Chai

ain: Infe fere rence

Probability of a sequence of states S0 … ST

) ,..., (

T

S S P  ) , , ( p q t P

Exa xample:

t q .6 .4 p a h e t t q p q p 0 .3 .4 0 .6 1 a h e .4 1 a h e .3 .4 .6 0 1

P (S0) P (St+1|St)

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SLIDE 16

CPSC322 Summer 2017 Slide 16

Lectu ture re Ov Overv rvie iew

Recap

p

Te

Tempo poral l Prob

babi

bilistic ic Mo Mode dels ls

Marko

kov Mod

dels

ls

Mar

arko kov v Ch Chai ain

Markov Chains in Natural Language

Processing

6/21/2017

SLIDE 17

6/21/2017 CPSC322 Summer 2017 17

Ke Key pro roble lems s in in NLP

Assign a probability to a sentence

Part-of-speech tagging
Word-sense disambiguation,
Probabilistic Parsing

Predict the next word

Speech recognition
Hand-writing recognition
Augmentative communication for the disabled

? ) ,.., (

1 n

w w P

Impo possib ible le t to estim imat ate 

? ) ,.., (

1 n

w w P

“Book me a room near UBC”

Summariza zation

n, Machine

Translation….....

SLIDE 18

6/21/2017 CPSC322 Summer 2017 18

Impo possib ible le t to e estim imat ate!

Assuming 105 words and average sentence contains 10 words …….

Go Google le la languag age re repo posit itory y (22 Sept. 2006)

contained “only”: 95,119,665,584 sentences

? ) ,.., (

1 n

w w P

Mos

st se

sentences w s will not

t appear or
r appear on
nly on
nce 

SLIDE 19

6/21/2017 CPSC322 Summer 2017 19

What at can an w we do?

?

Make a strong simplifying assumption! Sentences are generated by a Markov Chain P(Th The b big g red dog

g barks

ks)= P(Th The|<S>) * * ) | ( ) | ( ) ,.., (

1 2 1 1  



  

k k n k n

w w P S w P w w P

SLIDE 20

6/21/2017 CPSC322 Summer 2017 20

Est stim imat ates es fo for r Bi Bigr gram ams

    ) ( ) , ( ) ( ) , ( ) ( ) , ( ) | ( big C red big C N big C N red big C big P red big P big red P

words pairs

Silly language repositories with on

nly two
se

sentences: “<S>The big red dog barks against the big pink dog” “<S>The big pink dog is much smaller”

SLIDE 21

Bigrams in practice…

) | (

1  i i w

w P

If you have 105 words in your dictionary will contain this many numbers.. ?? C. . 5 * 105 A. A.2 *105 B.

B. 1010

D. D.2 *1010

6/21/2017 CPSC322 Summer 2017 Slide 21

SLIDE 22

CPSC322 Summer 2017 Slide 22

Learning Goals for today’s class

Yo You c can an:

Specify a Markov Chain and compute the

probability of a sequence of states

Justify and apply Markov Chains to compute

the probability of a Natural Language sentence

6/21/2017

SLIDE 23

CPSC322 Summer 2017 Slide 23

Mar arko kov v Mod

del

els

Markov Chains Hidden Markov Model Markov Decision Processes (MDPs) Simplest Possible Dynamic Bnet We cannot observe directly what we care about Add Actions and Values (Rewards)

6/21/2017

SLIDE 24

CPSC322 Summer 2017 Slide 24

Ne Next xt Cl Clas ass

Fin

inis ish P Proba babi bili lity y an and d Ti Time: : Hidden Markov Models (HMM) (TextBook 6.5.2)

Star

art D Decis isio ion n networks (TextBook chpt 9)

As

Assi sign gnment 4 is s available on

n Con
nnect. Due Su

Sunday, June 2 25th @ @ 11:5 :59 pm. . Late su submiss ssion

ns

s will not

t be

accepted, a and late days s may not

t be use
sed. Th

This s is s due t to

next

xt week k being e g exa xam week, k, and we w want to

be ab

able to

release

se the so solution

ns

s immediately.

Co Cour urse se Ele leme ment nts

6/21/2017