Hi, The question related to the the expectation. The topic related to data mining, but problem is about statistic calculating.
The article link is from http://www.inf.ed.ac.uk/teaching ... e4/BiasVariance.pdf
My problem is about i am trying to caculate the bias and variance to get the answer using following examples
Assume that, the training set , x={1,2,3} with t={7,8,9} ，Assume that f(x) is the function to approximate t value for data x. let assume that my function f(x)=y={5,6,7} after predicting data x
According to the formular from article, MSE = [(7-5)2+ （8-6)2 + （9-7)2] /3 =4
[FONT=Tahoma, Helvetica, SimSun, sans-serif]Next it is required to calculate E(MSE]. From the article link, they infer that E(MSE) = bias + variance[/FONT]
E{(fi -yi)2} = E{(fi-E(yi)2} + E{(E{yi) - yi)2} = bias + variance
Thus, for my example
E(yi) (5+6+7)/3= 6;
(fi-E(yi)2 => (7-6)2+(8-6)2+(9-6)2 = 1+4+9=14; So, E(fi-E(yi)2) = 14/3;
(E{yi) - yi)2 => (6-5)2+(6-6)2+(7-6)2 = 1+0+1=2；So, E(E(yi)-yi)2) = 2/3;
[FONT=Tahoma, Helvetica, SimSun, sans-serif]But, E(MSE)= 4/3 not equal 14/3+2/3, I think the Expectation step is wrong. Plz help me to correct it. Thank you very much[/FONT]
The article link is from http://www.inf.ed.ac.uk/teaching ... e4/BiasVariance.pdf
My problem is about i am trying to caculate the bias and variance to get the answer using following examples
Assume that, the training set , x={1,2,3} with t={7,8,9} ，Assume that f(x) is the function to approximate t value for data x. let assume that my function f(x)=y={5,6,7} after predicting data x
According to the formular from article, MSE = [(7-5)2+ （8-6)2 + （9-7)2] /3 =4
[FONT=Tahoma, Helvetica, SimSun, sans-serif]Next it is required to calculate E(MSE]. From the article link, they infer that E(MSE) = bias + variance[/FONT]
E{(fi -yi)2} = E{(fi-E(yi)2} + E{(E{yi) - yi)2} = bias + variance
Thus, for my example
E(yi) (5+6+7)/3= 6;
(fi-E(yi)2 => (7-6)2+(8-6)2+(9-6)2 = 1+4+9=14; So, E(fi-E(yi)2) = 14/3;
(E{yi) - yi)2 => (6-5)2+(6-6)2+(7-6)2 = 1+0+1=2；So, E(E(yi)-yi)2) = 2/3;
[FONT=Tahoma, Helvetica, SimSun, sans-serif]But, E(MSE)= 4/3 not equal 14/3+2/3, I think the Expectation step is wrong. Plz help me to correct it. Thank you very much[/FONT]