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#4
02-01-2013, 11:11 AM
 yaser Caltech Join Date: Aug 2009 Location: Pasadena, California, USA Posts: 1,477
Re: Calculating Average Hypothesis

Quote:
 Originally Posted by ripande 1. I calculated the value of "a" for which the which minimizes the least square for two points ( x, sin(pi*x) ), x being between -1 and 1. 2. Repeated the above for 100 times and hence got 100 values of "a"
These steps are correct (with instead of in step 1) in calculating the final hypothesis for 100 different sets .

Quote:
 3. Then I chose a fresh point x3 between [-1, 1] and calculated the value of y3 = a*x3 for all 100 points
This step evaluates for each in the 100 runs. If is fixed for all 100 runs, this step can be used to evaluate the bias and variance at the point (namely and ).

Quote:
 4. Calculated average value of y3 for 100 points, say y_avg.
If the 100 points are the same with different , then the average approximates . If the points are different, I am not sure about the utility of this quantity for the calculation of bias and variance.

Quote:
 5. Calculated "a" for avg hypothesis as : y_avg/x3
You already have the different values of for different data sets (these are the values of that you used to calculated from ). Because the formula for the hypothesis is linear in , you can directly calculate of the average hypothesis by averaging all the 's. What you are suggesting is equivalent in this case.
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