Classification problem with 0-1 loss
Given training data ,...,(X_n,Y_n) )
where 
under 0-1 loss.
Let  )
, Let 
denote the Bayes risk.
a) Show that  )
b) Show that equality holds above if X and Y are independent.
c) Exhibit a join distribution where X and Y are not independent but  )
Solution so far:
a) Suppose that 
is the Bayes learner, then:
![R_{Bayes} = min EL[Y_k,f(X_k)]= min \sum _{k=1}^n P[f(X_k) \neq Y_k ]](http://latex.codecogs.com/png.latex?R_{Bayes} = min EL[Y_k,f(X_k)]= min \sum _{k=1}^n P[f(X_k) \neq Y_k ] )
 = 1-P(Y=1)=1-p )
I konw that mine must be wrong because it doesn't help me with the next two problems, please help thanks!
Re: Classification problem with 0-1 loss
Hey tttcomrader.
Recall that p >= 0 so the minimum of (p,1-p) will always be less than 1 - p.
As a consideration of all possibilities let p < 1 - p this means p < 0.5. Now consider 1 - p < p This means p > 0.5.
So if 1 - p is not the minimum then p is the minimum, but this is always less than 1 - p so the inequality still holds.
