Computational Learning Theory

Mondrain Composition
https://www.khanacademy.org/humanities/ap-art-history/later-europe-and-americas/modernity-ap/a/mondrian-composition
Colored Vornoi Diagram

support vector machines SVMs perceptron
Nearest neighbor 1-NN
decision trees

-defining learning problems
-showing specific algorithms work
-show these problems are fundamentally hard

Theory of computing analyzes how use resources: time, space, o(nlogn), o(n^2)

Inductive learning
1.probability of successful training
2.number of examples to train on
3.complexity of hypothesis class
4.accuracy to which target concept is approximated
5.manner in which training examples presented
6.manner in which training examples selected

computational complexing
– how much computational effort is needed for a learner to coverage?
sample complexing -batch
– how many training examples are needed for a learner to create a successful hypothesis
mistake bounds – online
– how many misclassfications can a learner make over an infinite run

true hypothesis: ceH Training set:s<=X candidate hypothesis: heH consistent learner: produce c(x)=h(x) far xeS version space: VS(s) = {h s.t. heH consistent wants} hypotheses consistent with examples errord(h) = Prx~d[c(x)=h(x)]