
#1




lecture 8: understanding bias
The VC dimension is single number that is a property of the hypothesis set.
But, what is "bias of a hypothesis set"? Bias seems to depend also on dataset size and the learning algorithm, since it depends on ; depends on the learning algorithm, and the set of datasets over which the expectation is taken depends on dataset size. Slide 4 says that bias measures "how well can approximate ". Does this mean "with a sufficiently large dataset and a perfect learning algorithm"? Is the bias of a (hypothesis set, learning algorithm) combination a single value  the asymptote of the learning curve? Or is there some notion of bias that is a property of a hypothesis set by itself? If the hypothesis set contains the target function, that does not mean the bias is zero, does it? The beginning of the lecture seems to imply otherwise, but if there is no restriction on the learning algorithm, what guarantees that the average function will in fact be close to the target function for large enough dataset size? Or is it assumed that the learning algorithm always picks a hypothesis which minimizes ? 
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Re: lecture 8: understanding bias
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#3




Re: lecture 8: understanding bias
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In HW4 #4 the average hypothesis is measurably shifted from the hypothesis set member giving the lowest mean squared error. Probably because twopoint dataset is too small, i.e. this is not representative of realistic cases? 
#4




Re: lecture 8: understanding bias
Indeed, the fewer the number of points, the more likely that the average hypothesis will differ from the best approximation. The difference tends to be small, though.
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#5




Re: lecture 8: understanding bias
Well, it is also that the two point data set is small relative to the two parameter hypotheses. If you have 100 points, and 99th degree polynomials, it would also have large variance. I will guess that minimizing bias plus variance happens with the number of fit parameters near the square root of the number of points per data set.

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Re: lecture 8: understanding bias
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On the other hand, I'm not sure how to prove that it won't be far 
#7




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