
#1




BiasVariance Analysis

#2




Re: BiasVariance Analysis
It is not necessarily the best approximation of the target function, but it is often close. If we have one, infinitesize training set, and we have infinite computational power that goes with it, we can arrive at the best approximation. In the biasvariance analysis, we are given an infinite number of finite training sets, and we are restricted to using one of these finite training sets at a time, then averaging the resulting hypotheses. This restriction can take us away from the absolute optimal, but usually not by much.
__________________
Where everyone thinks alike, no one thinks very much 
#3




Re: BiasVariance Analysis
Thank you very much for your answer Prof. Yaser. It clarified my doubt.
My kind regards, Andrea 
#4




Re: BiasVariance Analysis
Hi,
I have a doubt regarding g bar. I tried to calculate the bias for the second learner, i.e. h(x) = ax + b. So this is how did it:
Now I have two questions: 1. Please let me know whether I am proceeding in the right direction or not. 2. When I am trying to repeat this process with a polynomial model instead of linear model, my calculated bias for the polynomial model varies in great margin, even if the sample data points doesn't change. For polynomial as well, I took the mean of the coefficients, but still my answer (both g bar and bias) varies greatly with each run. What I am missing here? 
#5




Re: BiasVariance Analysis
Quote:
2. Not sure if this is the reason, but if you are still using a 2point training set, a polynomial model will have too many parameters, leading to nonunique solutions that could vary wildly.
__________________
Where everyone thinks alike, no one thinks very much 
#6




Re: BiasVariance Analysis
Thank You Prof. Yaser for your reply.
I am using a 10 point dataset for the polynomial model. However, the problem I am referring to defines y = f(x) + noise = x + noise. Previously by mistake I was assuming f(x) as y rather than only x. Later I noticed that all the calculation of bias and variance concentrate purely on f(x). Hence later I ignored the noise and now I am getting stable bias and variance for polynomial model for each run. 
#7




Re: BiasVariance Analysis
I am confused in trying to get from the first line to the second line for the first set of equations on page 63: ... ED[Ex[(g... on the first line to ...Ex[ED[( on the second line.
I sort of see the first line: expected value with respect to data set x (a subset of D I assume) is averaged over all possible data set x's in D. On the second line we have what might be the average of the argument over all of D inside the outer brackets. I don't know how to interpret Ex outside the outer brackets. In short, I certainly don't understand what exactly is meant by the 2nd line, and I may well not understand the first line. Any further explanation possible? 
Thread Tools  
Display Modes  

