Learning Greedy Policies for the Easy-First Framework Jun Xie, Chao - - PowerPoint PPT Presentation

Learning Greedy Policies for the Easy-First Framework

Jun Xie, Chao Ma, Janardhan Rao Doppa, Prashanth Mannem, Xiaoli Fern, Tom Dietterich, Prasad Tadepalli Oregon State University

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The Easy-First Framework: Example

A 4.2 magnitude earthquake struck near eastern Sonoma County. A tremor struck in Sonoma County.

Doc 1 Doc 2

The Easy-First Framework: Example

A 4.2 magnitude earthquake struck near eastern Sonoma County. A tremor struck in Sonoma County.

Doc 1 Doc 2 A 4.2 magnitude earthquake A tremor eastern Sonoma County Sonoma County

• 1. Begin with every mention in its own cluster

The Easy-First Framework: Example

A 4.2 magnitude earthquake struck near eastern Sonoma County. A tremor struck in Sonoma County.

Doc 1 Doc 2 A 4.2 magnitude earthquake A tremor eastern Sonoma County Sonoma County

• 1. Begin with every mention in its own cluster
• 2. Evaluate all possible merges with a scoring function

and select the highest scoring merge (easiest)

The Easy-First Framework: Example

A 4.2 magnitude earthquake struck near eastern Sonoma County. A tremor struck in Sonoma County.

Doc 1 Doc 2 A 4.2 magnitude earthquake A tremor eastern Sonoma County Sonoma County

• 1. Begin with every mention in its own cluster
• 2. Evaluate all possible merges with a scoring function

and select the highest scoring merge (easiest)

• 3. Repeat until stopping condition is met

Easy First Training

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Initial State

S

…… a b c d

04 . ) (  a f

36 . ) (  b f 57 . ) (  c f 63 . ) (  d f 03 . ) (  a f 12 . ) (  b f 29 . ) (  d f 47 . ) (  c f

1

S

…… e g h i

27 . ) (  e f 39 . ) (  g f 41 . ) (  h f 52 . ) (  i f

2

S

Good Bad …… j k m n

31 . ) (  j f 38 . ) (  k f 51 . ) (  m f 68 . ) (  n f 34 . ) (  j f 36 . ) (  k f 55 . ) (  m f 62 . ) (  n f

3

S

……

T

S

Weight Update Weight Update

Learning Scoring Function

Possible goal: learn a scoring function such that:

in every state ALL good actions are ranked higher than all bad actions

A better goal: learn a scoring function such that in every state ONE good action is ranked higher than all bad actions

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Over-Constrained Goal

  



   

B b b g G g w

x w x w B ) max 1 ( 1 argmin

Proposed Objective for Update

max

𝑕∈𝐻 𝑥 ⋅ 𝑦𝑕 > 𝑥 ⋅ 𝑦𝑐 + 1

for all 𝑐 ∈ 𝐶

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• Goal: find a linear function such that it ranks
• ne good action higher than all bad actions

– This can be achieved by a set of constraints

• Our Objective:
• Use hinge loss to capture the constraints
• Regularization to avoid overly aggressive update

2 c

w w  

Optimization

• Majorization Minimization algorithm to find a

local optimal solution.

• In each MM iteration:

– Let be the current highest scoring good action – Solve following convex objective (via subgradient descent)

  



   

B b b g G g w

x w x w B ) max 1 ( 1 argmin

2 c

w w  

* g

x w

Contrast with Existing Methods

Good Bad Average-Good Average-Bad

• Average-good vs. average-bad (AGAB)
• Best-good vs. best-bad (BGBB)

Best-good Best-bad

• Proposed method: Best-good vs. violated-bad (BGVB)

Best-good Violated-bad

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10 20 30 40 50 60 70 80 MUC B-CUBE CEAF_e CoNLL

Results on EECB corpus (Lee et al., 2012)

BGBB R-BGBB BGVB R-BGVB Lee et al.

Experiment I: cross-document entity and event coref

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Experiment II: within-doc Coref

10 20 30 40 50 60 70 80 MUC B-CUBE CEAF_e CoNLL

Results on OntoNotes

BGBB R-BGBB BGVB R-BGVB

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Approach Total Steps Mistakes Recoveries Percentage Accuracy RBGVB 50195 16228 4255 0.262 0.87

Diagnostics

• Some training statistics on ACE 2004 corpus:

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Approach Total Steps Mistakes Recoveries Percentage Accuracy RBGVB 50195 16228 4255 0.262 0.87 BGBB 50195 11625 4075 0.351 0.82

BGBB corrects errors more aggressively than RBGVB. This is a strong evidence that overfitting does happen with BGBB.

Diagnostics

• Some training statistics on ACE 2004 corpus:

Contributions

• We precisely represent the learning goal for

Easy First as an optimization problem

• We develop an efficient Majorization

Minimization algorithm to optimize the proposed objective

• Achieve highly competitive results against

state-of-the-art for both within- and cross- document coref

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