Conditional Markov Models: MaxEnt Tagging and MEMMs

William W. Cohen

CALD

Announcements

• Confused about what to write up?– Mon 2/9: Ratnaparki & Frietag et al– Wed 2/11: Borthwick et al & Mikheev– Mon 2/16: no class (President’s day)– Wed 2/18: Sha & Pereira, Lafferty et al– Mon 2/23: Klein & Manning, Toutanova et al– Wed 2/25: no writeup due– Mon 3/1: no writeup due– Wed 3/3: project proposal due: personnel + 1-2 page – Spring break week, no class

Review of review

• Multinomial HMMs are sequential version of naïve Bayes.

• One way to drop independence assumption: use a maxent instead of NB, and a conditional model

From NB to Maxent

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From NB to Maxent

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From NB to Maxent

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Learning: set alpha parameters to maximize this: the ML model of the data, given we’re using the same functional form as NB.

Turns out this is the same as maximizing entropy of p(y|x) over all distributions.

MaxEnt Comments

• Functional form same as Naïve Bayes (loglinear model)

• Numerical issues & smoothing important

• All methods are iterative

• Classification performance can be competitive with state-of-art

• optimizes Pr(y|x), not error rate

What is a symbol?

Ideally we would like to use many, arbitrary, overlapping features of words.

St -1

St

Ot

St+1

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identity of wordends in “-ski”is capitalizedis part of a noun phraseis in a list of city namesis under node X in WordNetis in bold fontis indentedis in hyperlink anchor…

…

…part of

noun phrase

is “Wisniewski”

ends in “-ski”

What is a symbol?

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identity of wordends in “-ski”is capitalizedis part of a noun phraseis in a list of city namesis under node X in WordNetis in bold fontis indentedis in hyperlink anchor…

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…part of

noun phrase

is “Wisniewski”

ends in “-ski”

Idea: replace generative model in HMM with a maxent model, where state depends on observations

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What is a symbol?

St -1

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identity of wordends in “-ski”is capitalizedis part of a noun phraseis in a list of city namesis under node X in WordNetis in bold fontis indentedis in hyperlink anchor…

…

…part of

noun phrase

is “Wisniewski”

ends in “-ski”

Idea: replace generative model in HMM with a maxent model, where state depends on observations and previous state

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What is a symbol?

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identity of wordends in “-ski”is capitalizedis part of a noun phraseis in a list of city namesis under node X in WordNetis in bold fontis indentedis in hyperlink anchor…

…

…part of

noun phrase

is “Wisniewski”

ends in “-ski”

Idea: replace generative model in HMM with a maxent model, where state depends on observations and previous state history

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Ratnaparkhi’s MXPOST

• Sequential learning problem: predict POS tags of words.

• Uses MaxEnt model described above.

• Rich feature set.

• To smooth, discard features occurring < 10 times.

MXPOST

MXPOST: learning & inference

GISFeature

selection

MXPost inference

Adwait: consider only

extensions suggested by a

dictionary

MXPost results

• State of art accuracy (for 1996)

• Same approach used successfully for several other sequential classification steps of a stochastic parser (also state of art).

• Same approach used for NER by Borthwick, Malouf, Collins, Manning, and others.

Alternative inference

Finding the most probable path: the Viterbi algorithm (for HMMs)

• define to be the probability of the most probable path accounting for the first i characters of x and ending in state k (ending in with tag k)

)(ivk

• we want to compute , the probability of the most probable path accounting for all of the sequence and ending in the end state

• can define recursively• can use dynamic programming to find efficiently

)(LvN

)(LvN

Finding the most probable path: the Viterbi algorithm for HMMs

• initialization:

1)0(0 v

k statesother for ,0)0( kv

The Viterbi algorithm for HMMs

• recursion for emitting states (i =1…L):

klkk

ill aivxbiv )1(max)()(

The Viterbi algorithm for HMMs and Maxent Taggers

• recursion for emitting states (i =1…L):

klkilk

l aivxbiv )1()(max)(

)1(),|Pr(max)( ivvxviv kkilk

l

Previous tag k i-th token

MEMMs (Frietag & McCallum)

• Basic difference from ME tagging:– ME tagging: previous state is feature of MaxEnt

classifier– MEMM: build a separate MaxEnt classifier for each

state.• Can build any HMM architecture you want; eg parallel nested

HMM’s, etc.• Data is fragmented: examples where previous tag is “proper

noun” give no information about learning tags when previous tag is “noun”

– Mostly a difference in viewpoint – easier to see parallels to HMMs

MEMM task: FAQ parsing

MEMM features

MEMMs

Borthwick et al: MENE system

• Much like MXPost, with some tricks for NER:– 4 tags/field: x_start, x_continue, x_end, x_unique– Features:

• Section features• Tokens in window• Lexical features of tokens in window• Dictionary features of tokens (is token a firstName?)• External system of tokens (is this a NetOwl_company_start?

proteus_person_unique?)• Smooth by discarding low-count features

– No history: viterbi search used to find best consistent tag sequence (e.g. no continue w/o start)

Dictionaries in MENE

MENE results (dry run)

MENE learning curves

96.393.392.2

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Short names

Longer names

LTG system

• Another MUC-7 competitor• Handcoded rules for “easy” cases (amounts, etc)• Process of repeated tagging and “matching” for hard cases

– Sure-fire (high precision) rules for names where type is clear (“Phillip Morris, Inc – The Walt Disney Company”)

– Partial matches to sure-fire rule are filtered maxent classifier (candidate filtering) using contextual information, etc

– Higher-recall rules, avoiding conflicts with partial-match output “Phillip Morris announced today…. - “Disney’s ….”

– Final partial-match & filter step on titles with different learned filter.

• Exploits discourse/context information

LTG Results

LTG

Identifinder

MENE+Proteus

Manitoba(NB filtered names)

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