Support Vector Machines and Kernel Methods for Co-Reference Resolution 2007 Summer Workshop on Human Language Technology Center for Language and Speech Processing John Hopkins University Baltimore, Agust 22, 2007 Alessandro Moschitti and Xiaofeng Yang
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Support Vector Machines and Kernel Methods for Co-Reference Resolution
Support Vector Machines and Kernel Methods for Co-Reference Resolution. Alessandro Moschitti and Xiaofeng Yang. 2007 Summer Workshop on Human Language Technology Center for Language and Speech Processing John Hopkins University Baltimore, Agust 22, 2007. Outline. Motivations - PowerPoint PPT Presentation
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Support Vector Machines and Kernel Methods for Co-Reference ResolutionSupport Vector Machines and Kernel Methods for Co-Reference Resolution
2007 Summer Workshop on Human Language TechnologyCenter for Language and Speech Processing
John Hopkins UniversityBaltimore, Agust 22, 2007
Alessandro Moschitti and Xiaofeng Yang
OutlineOutline
MotivationsSupport Vector MachinesKernel Methods
Polynomial Kernel
Sequence KernelsTree kernels
Kernels for Co-reference problemAn effective syntactic structureMention context via word sequences
ExperimentsConclusions
MotivationsMotivations
Intra/Cross document coreference resolution require the definition of complex features, i.e.
syntactic/semantic structures
For pronoun resolutionPreference factors: Subject, Object, First-Mention, Definite NP
Constraint factors: C-commanding,…
For non-pronoun Predicative Structure, Appositive Structure
Motivations (2)Motivations (2)
How to represent such structures in the learning
algorithm?
How to combine different features ?
How to select the relevant ones?
Kernel methods allows us torepresent structures in terms of substructures (high dimensional feature spaces)
define implicit and abstract feature spaces
Support Vector Machines “select” the relevant
featuresAutomatic Feature engineering side-effect
Support Vector MachinesSupport Vector Machines
Var1
Var2kbxw
kbxw
0 bxw
kk
w
The margin is equal to2 k
w
We need to solve
negative is if ,
positive is if ,
||||
2max
xkbxw
xkbxw
w
k
SVM Classification Function and the Kernel TrickSVM Classification Function and the Kernel Trick
From the primal form
)sgn()( bwxxf
SVM Classification Function and the Kernel TrickSVM Classification Function and the Kernel Trick
From the primal form
To the dual form
where l is the number of training examples
)sgn()( bwxxf
bxxyxfi
iii
..1
sgn)(
SVM Classification Function and the Kernel TrickSVM Classification Function and the Kernel Trick
From the primal form
To the dual form
where l is the number of training examples
)sgn()( bwxxf
bxxyxfi
iii
..1
sgn)(
bookybooyi
iiii
iii ),(sgn)()(sgn.1.1 ..
Flat features (Linear Kernel)Flat features (Linear Kernel)