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Katie C. 04-24-2013 06:31 PM

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?

yaser 04-24-2013 07:00 PM

Re: bias -variance graph
 
Quote:

Originally Posted by Katie C. (Post 10587)
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.

Katie C. 04-25-2013 07:36 PM

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?

yaser 04-25-2013 07:39 PM

Re: bias -variance graph
 
Quote:

Originally Posted by Katie C. (Post 10602)
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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