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Machine Learning: Difference between revisions
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A hypothesis class <math>H</math> has uniform convergence if there exists <math>m^{UC}(\epsilon, \delta)</math> such that for every <math>\epsilon, \delta</math>, if we draw a sample <math>S</math> then with probability <math>1-\delta</math>, <math>S</math> is <math>\epsilon</math>-representative. | A hypothesis class <math>H</math> has uniform convergence if there exists <math>m^{UC}(\epsilon, \delta)</math> such that for every <math>\epsilon, \delta</math>, if we draw a sample <math>S</math> then with probability <math>1-\delta</math>, <math>S</math> is <math>\epsilon</math>-representative. | ||
===VC dimension=== | |||
[https://en.wikipedia.org/wiki/Vapnik%E2%80%93Chervonenkis_dimension Wikipedia Page] | |||
====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. | |||
====Definition==== | |||
Stolen from wikipedia:<br> | |||
The VC dimension of a model <math>f</math> is the maximum number of points that can be arranged so that <math>f</math> shatters them. | |||
More formally, it is the maximum cardinal <math>D</math> such that some data point set of cardinality <math>D</math> can be shattered by <math>f</math>. | |||