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Ph.D. Defense: Iain Carmichael

March 29, 2019 @ 10:00 am - 12:00 pm

Ph.D. Thesis Defense

Public Presentation
Friday, March 29th, 2019

125 Hanes Hall
10:00 AM

Iain Carmichael

 

 

Geometric Insights into Support Vector Machine Behavior

using the KKT Conditions

The support vector machine (SVM) is a powerful and widely used classification algorithm. We use the Karush-Kuhn-Tucker conditions to provide rigorous mathematical proof for new insights into the behavior of SVM. These insights provide perhaps unexpected relationships between SVM and two other linear classifiers: the mean difference and the maximal data piling direction. For example, we show that in many cases SVM can be viewed as a cropped version of these classifiers. By carefully exploring these connections we show how SVM tuning behavior is affected by characteristics including: balanced vs. unbalanced classes, low vs. high dimension, separable vs. non-separable data. These results provide further insights into tuning SVM via cross-validation by explaining observed pathological behavior and motivating improved cross-validation methodology. Finally, we also provide new results on the geometry of complete data piling directions in high dimensional space.

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Details

Date:
March 29, 2019
Time:
10:00 am - 12:00 pm
Event Category:

Venue

125 Hanes Hall
Hanes Hall
Chapel Hill, NC 27599 United States