Margin Learning, Online Learning, and The Voted - PowerPoint Presentation

Slide1

Margin Learning, Online Learning, and The Voted Perceptron

SPLODD~= AE* – 3, 2011

* Autumnal EquinoxSlide2

Review

Computer science is full of equivalencesSQL  relational algebra

YFCL optimizing … on the training data

g

cc

–O4

foo.c



gcc

foo.c

Also full of

relationships

between

sets

:

Finding smallest error-free decision tree >> 3-SAT

DataLog

>> relational algebra

CFL >>

Det

FSMs =

RegExSlide3

Review

Bayes Nets: describe a (family of) joint distribution(s) between random variables

They are an

operational description

(a program) for how data can be

generated

They are a

declarative description

(a definition) for the joint distribution, and from this we can derive

algorithms

for doing stuff other than generation

There is a close connection between Naïve

Bayes

and

loglinear

modelsSlide4

NB vs loglinear

models

Loglinear

classif

.

NB

classif

.

Multinomial?

c

lassif

.

*

SymDir(100)

* AbsDisc(0.01)

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

* Max CL(y|x) + G(0,1.0)

*

NB-JL

NB-CL

NB-CL*Slide5

NB vs

loglinear models

Loglinear

classif

.

NB

classif

.

Multinomial?

c

lassif

.

*

SymDir(100)

*

*

*

*

*

*

*

*

* Max CL(y|x) + G(0,1.0)

*

Y

W

j

“Optimal if”Slide6

Similarly for sequences…

An HMM is a Bayes netIt implies a set of independence assumptions

ML parameter setting and

Viterbi

are optimal if these hold

A CRF is a Markov field

It implies a set of independence assumptions

These, plus the goal of maximizing Pr(

y

|x

), give us a learning algorithmYou can construct features so that any HMM can be emulated by a CRF with those featuresSlide7

In sequence space…

CRF/

l

oglinear

models

HMMs

Multinomial? models

*

SymDir

(100)

*

AbsDisc

(0.01)

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

* Max CL(

y|x

) + G(0,1.0)

*

JL

CL

CL*Slide8

Review: CRFs/Markov Random Fields

When will

prof

Cohen post the notes

Semantics of a Markov random field

Y

1

Y2

Y3

Y4

Y5

Y6

Y7

What’s independent

: Pr(

Y

i

|other

Y’s) = Pr(Y

i

|Y

i-1

,Y

i+1

)

Probability distribution: Slide9

Review: CRFs/Markov Random Fields

B

I

O

B

I

O

B

I

O

B

I

O

B

I

O

B

I

O

B

I

O

When will prof Cohen post the notes … Slide10

Review: CRFs/Markov Random Fields

When will

prof

Cohen post the notes

Y

1

Y2

Y3

Y4

Y5

Y6

Y7

What’s independent

: Pr(

Y

i

|other

Y’s) = Pr(

Y

i

|neighbors

of Y

i

)

Probability distribution:

YfSlide11

Pseudo-likelihood and dependency networks

Any Markov field defines a (family of) probability distributions DBut

not

a simple program for generation/sampling

We can use MCMC in the general case

If you have for each node

i

, P

D

(X

i|Pai), that’s a dependency netStill no simple program for generation/sampling (but can use Gibbs)

You can learn these from data using YFCLEquivalently: learning this maximizes pseudo-likelihood, just as HMM learning maximizes (real) likelihood on a sequence.

A weirdness: every MRF has an equivalent dependency net, but every dependency net (set of local conditionals) does not have an equivalent MRFSlide12

And now for …