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In Basic PAC(Probably approximately correct) learning model, How do we find the error and probability of the hypothesis obtained from a learning algorithm. As in basic PAC model, we have hypothesis space as set of f:X->{0,1} if we random example , x1 whose actual output value is 1. But our hypothesis fn predicts it as 0, then error = 1 > epsilon. epsilon can take values as 0.1,0.2,0.3 anything b/n 0 and 1. then how does probability changes. suppose we have 10 test samples, How to find error and probability?? |
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It's assumed that there's a probability distribution on X, and a correct hypothesis h. Suppose you guess hypothesis f. Then the generalization error is Pr[f(x) != h(x)]. If you are learning this idea, and want to visualize it, think of X as the plane (R^2), and then maybe visualize f and h as rectangles. Then the parts where the rectangles of f and h differ are the points x where f(x) != h(x), and the error of your hypothesis is the probability of picking a random point in that difference (set-wise it's called the symmetric difference). If you have 10 test samples, then you're just empirically approximating the true error rate. If you have a million sample points, you would get a better approximation. |
