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  "body": "\n## Summary\n\nStatistical learning theory is the mathematical theory of learning a prediction rule from examples.\nIt models the data as independent draws from an unknown distribution and measures a rule by its expected [[loss|3BTG6VVCGZ]] on new data, its risk.\nIts central results bound the gap between the error on the training data and the true risk.\nThe bounds depend on the size of the class of rules, measured for example by its [[VC dimension|KCFXR9K3GD]].\nIt was developed by Vladimir Vapnik and Alexey Chervonenkis among others, and it underlies [[empirical risk minimization|56NVR0SS61]] and support vector machines.\n\n## Explanations\n\n### L1 human\n\nA spam filter is trained on a few thousand labelled emails and must then work on emails it has never seen.\nStatistical learning theory asks when doing well on the training emails guarantees doing well on new ones.\nThe answer depends on how many examples there are and on how flexible the family of possible filters is.\nA very flexible family can memorise the training data and still fail on new data; this is overfitting.\nThe theory gives precise bounds that balance these two effects.\n",
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