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Old 04-24-2013, 05:31 PM
Katie C. Katie C. is offline
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Default bias -variance graph

How is the gray zone of the bias-variance plot (slide 15/22 in Lecture 8) drawn? I am trying to understand how to compute bias(x) and var(x). Are these quantities illustrated in the graphs?
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Old 04-24-2013, 06:00 PM
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yaser yaser is offline
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Default Re: bias -variance graph

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Originally Posted by Katie C. View Post
How is the gray zone of the bias-variance plot (slide 15/22 in Lecture 8) drawn? I am trying to understand how to compute bias(x) and var(x). Are these quantities illustrated in the graphs?
The grey zones' height is the square root of the {\bf var}(x) (square root to match the scale of other elements in the graph). To calculate {\bf var}(x), evaluate the formula in slide 8 of that lecture. You can do that analytically by evaluating the expected value, or you can do that using Monte Carlo method; generating data sets {\cal D} at random, evaluating the part inside the expectation for each {\cal D}, then averaging these quantities over a large number of {\cal D}'s.
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Old 04-25-2013, 06:36 PM
Katie C. Katie C. is offline
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Default Re: bias -variance graph

As I understand it, the g{\cal D}(x) is a function that was learned from a training data set and is now being evaluated on a new set of x values, is that correct? In fact, I think that all the red xs on slide 8 are from new data that was not used during training. Is that correct?
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Old 04-25-2013, 06:39 PM
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Default Re: bias -variance graph

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Originally Posted by Katie C. View Post
As I understand it, the g{\cal D}(x) is a function that was learned from a training data set and is now being evaluated on a new set of x values, is that correct? In fact, I think that all the red xs on slide 8 are from new data that was not used during training. Is that correct?
You are correct on both counts. If you pick the test point x at random, it's statistically certain that it will be different from the two points you used for training.
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