All Questions
4 questions
2
votes
2
answers
724
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Optimal way to estimate the irreducible error E [ V [Y | X] ]?
I was reading about conditional variance in Wikipedia and then the following property showed up
$$E[V[Y \mid X]]=E[(Y-f(X))^2]-E[(E[Y \mid X]-f(X))^2]$$
Which i interpret as an irreducible error, ...
- 113
1
vote
0
answers
44
views
When to use all 3 variables in a graph to estimate a conditional expectation of 2
The title might not be perfect. But here goes:
Suppose there are 3 variables $(A,X,Y)$. And they have the following dependencies :
$\Pr(Y,A,X)=\Pr(Y\mid A,X)\Pr(X\mid A)\Pr(A)$
$A \rightarrow (X,Y)$...
- 11
3
votes
0
answers
315
views
Average conditional variance
Related to Explanatory power of variable. Given a data for 1d variable $Y$ and multidimensional variable $X$, what is the best way to compute average conditional variance of $Y$ given $X$:
$$
\Bbb V(...
- 419
7
votes
1
answer
358
views
What's the maximum expectation of a conditional variance, $E[\operatorname{Var}(X+Z_1 \mid X+Z_2)]$?
Let $X,Z_1,Z_2$ be 3 mutually independent RV's, with $Z_1, Z_2$ assuming $N(0,1)$ distribution. $X$ is constrained to have unit 2nd moment, i.e. $E[X^2] =1$, but may take arbitrary distribution. The ...
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