bias -variance graph

[Katie C.]

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]

Originally Posted by Katie C.

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 (square root to match the scale of other elements in the graph). To calculate , 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 at random, evaluating the part inside the expectation for each , then averaging these quantities over a large number of 's.

[Katie C.]

As I understand it, the 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]

Originally Posted by Katie C.

As I understand it, the 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 at random, it's statistically certain that it will be different from the two points you used for training.