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Machine Learning: Difference between revisions
→Shattering
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[https://www.stat.berkeley.edu/~bartlett/courses/2013spring-stat210b/notes/10notes.pdf Some slides] | [https://www.stat.berkeley.edu/~bartlett/courses/2013spring-stat210b/notes/10notes.pdf Some slides] | ||
====Shattering==== | ====Shattering==== | ||
A model <math>f</math> parameterized by <math>\theta</math> is said to shatter a set of points <math>\{x_1, ..., x_n\}</math> if there exists <math>\theta</math> such that <math>f</math> makes no errors. | A model <math>f</math> parameterized by <math>\theta</math> is said to shatter a set of points <math>\{x_1, ..., x_n\}</math> if for every possible set of binary labellings <math>\{y_1,...,y_n\}</math> there exists <math>\theta</math> such that <math>f</math> makes no errors. | ||
====Definition==== | ====Definition==== | ||
Intuitively, the VC dimension of a hypothesis set is how complex of a model it is.<br> | Intuitively, the VC dimension of a hypothesis set is how complex of a model it is.<br> | ||