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Support Vector Machines: Hype or Hallelujah?. Kristin Bennett Math Sciences Dept Rensselaer Polytechnic Inst. http://www.rpi.edu/~bennek. Outline. Support Vector Machines for Classification Linear Discrimination Nonlinear Discrimination Extensions Application in Drug Design Hallelujah

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support vector machines hype or hallelujah

Support Vector Machines:Hype or Hallelujah?

Kristin Bennett

Math Sciences Dept

Rensselaer Polytechnic Inst.

http://www.rpi.edu/~bennek

M2000

outline
Outline
  • Support Vector Machines for Classification
    • Linear Discrimination
    • Nonlinear Discrimination
  • Extensions
  • Application in Drug Design
  • Hallelujah
  • Hype

M2000

support vector machines svm
Support Vector Machines (SVM)

Key Ideas:

  • “Maximize Margins”
  • “Do the Dual”
  • “Construct Kernels”

A methodology for inference based on Vapnik’s

Statistical Learning Theory.

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find using quadratic program
Find using quadratic program

Many existing and new solvers.

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best linear separator supporting plane method
Best Linear Separator:Supporting Plane Method

Maximize distance

Between two parallel

supporting planes

Distance

= “Margin”

=

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dual of closest points method is support plane method
Dual of Closest Points Method is Support Plane Method

Solution only depends on support vectors:

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statistical learning theory
Statistical Learning Theory
  • Misclassification error and the function complexity bound generalization error.
  • Maximizing margins minimizes complexity.
  • “Eliminates” overfitting.
  • Solution depends only on Support Vectors not number of attributes.

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margins and complexity
Margins and Complexity

Skinny margin

is more flexible

thus more complex.

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margins and complexity17
Margins and Complexity

Fat margin

is less complex.

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linearly inseparable case
Linearly Inseparable Case

Convex Hulls Intersect!

Same argument

won’t work.

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reduced convex hulls don t intersect
Reduced Convex Hulls Don’t Intersect

Reduce by adding

upper bound D

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find closest points then bisect
Find Closest Points Then Bisect

No change except for D.

D determines number of Support Vectors.

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linearly inseparable case supporting plane method
Linearly Inseparable Case:Supporting Plane Method

Just add non-negative error

vector z.

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dual of closest points method is support plane method22
Dual of Closest Points Method is Support Plane Method

Solution only depends on support vectors:

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nonlinear classification map to higher dimensional space
Nonlinear Classification: Map to higher dimensional space

IDEA: Map each point to higher dimensional feature space and

construct linear discriminant in the higher dimensional space.

Dual SVM becomes:

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generalized inner product
Generalized Inner Product

By Hilbert-Schmidt Kernels (Courant and Hilbert 1953)

for certain  and K, e.g.

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final classification via kernels
Final Classification via Kernels

The Dual SVM becomes:

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final svm algorithm
Final SVM Algorithm
  • Solve Dual SVM QP
  • Recover primal variable b
  • Classify new x

Solution only depends on support vectors:

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support vector machines svm29
Support Vector Machines (SVM)
  • Key Formulation Ideas:
    • “Maximize Margins”
    • “Do the Dual”
    • “Construct Kernels”
  • Generalization Error Bounds
  • Practical Algorithms

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svm extensions
SVM Extensions
  • Regression
  • Variable Selection
  • Boosting
  • Density Estimation
  • Unsupervised Learning
    • Novelty/Outlier Detection
    • Feature Detection
    • Clustering

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example in drug design
Example in Drug Design
  • Goal to predict bio-reactivity of molecules to decrease drug development time.
  • Target is to predict the logarithm of inhibition concentration for site "A" on the Cholecystokinin (CCK) molecule.
  • Constructs quantitative structure activity relationship (QSAR) model.

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lccka problem
LCCKA Problem
  • Training data – 66 molecules
  • 323 original attributes are wavelet coefficients of TAE Descriptors.
  • 39 subset of attributes selected by linear 1-norm SVM (with no kernels).
  • For details see DDASSL project link off of http://www.rpi.edu/~bennek.
  • Testing set results reported.

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lcck prediction
LCCK Prediction

Q2=.25

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many other applications
Many Other Applications
  • Speech Recognition
  • Data Base Marketing
  • Quark Flavors in High Energy Physics
  • Dynamic Object Recognition
  • Knock Detection in Engines
  • Protein Sequence Problem
  • Text Categorization
  • Breast Cancer Diagnosis
  • See: http://www.clopinet.com/isabelle/Projects/

SVM/applist.html

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hallelujah
Hallelujah!
  • Generalization theory and practice meet
  • General methodology for many types of problems
  • Same Program + New Kernel = New method
  • No problems with local minima
  • Few model parameters. Selects capacity.
  • Robust optimization methods.
  • Successful Applications

BUT…

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slide38
HYPE?
  • Will SVMs beat my best hand-tuned method Z for X?
  • Do SVM scale to massive datasets?
  • How to chose C and Kernel?
  • What is the effect of attribute scaling?
  • How to handle categorical variables?
  • How to incorporate domain knowledge?
  • How to interpret results?

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support vector machine resources
Support Vector Machine Resources
  • http://www.support-vector.net/
  • http://www.kernel-machines.org/
  • Links off my web page:

http://www.rpi.edu/~bennek

M2000

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