Why can the test error be written in terms of the training error in this way?
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In the below picture encircled in red:
If $L_D(h) = E_{z text{~} D}[l(h, z)]$,
Then how is $L_D(h) = E_{S' text{~} D^m}[L_{S'}(h)] $?
I see that $$large L_D(h) = E_{z in Z}[l(h, z)] = sum_{z in Z} l(h,z)D(z)$$ where $D$ is the distribution on $Z$ the set of samples. The first equation should be defined as:
$$large E_{S' text{~} D^m}[L_{S'}(h)] = sum_{S'}[frac{1}{m}sum_{z_i in S'}l(h,z_i)]D^m(S')$$
But how are these two qual?
proof-explanation machine-learning
asked Jan 17 at 17:32
Oliver GOliver G
1,4841531
$endgroup$
add a comment |
$begingroup$
In the below picture encircled in red:
If $L_D(h) = E_{z text{~} D}[l(h, z)]$,
Then how is $L_D(h) = E_{S' text{~} D^m}[L_{S'}(h)] $?
I see that $$large L_D(h) = E_{z in Z}[l(h, z)] = sum_{z in Z} l(h,z)D(z)$$ where $D$ is the distribution on $Z$ the set of samples. The first equation should be defined as:
$$large E_{S' text{~} D^m}[L_{S'}(h)] = sum_{S'}[frac{1}{m}sum_{z_i in S'}l(h,z_i)]D^m(S')$$
But how are these two qual?
proof-explanation machine-learning
asked Jan 17 at 17:32
Oliver GOliver G
1,4841531
$endgroup$
$begingroup$
Hint: If you have $m$ independent variables each with probability mass function $D,$ then pick one at random, the result has probability mass function $D.$
$endgroup$
– Dap
Jan 23 at 6:01
1
$begingroup$
If you are going to quote from a source (for example by showing an image of it), it's very poor manners not to name the source.
$endgroup$
– C Monsour
Jan 24 at 11:10
add a comment |
$begingroup$
In the below picture encircled in red:
If $L_D(h) = E_{z text{~} D}[l(h, z)]$,
Then how is $L_D(h) = E_{S' text{~} D^m}[L_{S'}(h)] $?
I see that $$large L_D(h) = E_{z in Z}[l(h, z)] = sum_{z in Z} l(h,z)D(z)$$ where $D$ is the distribution on $Z$ the set of samples. The first equation should be defined as:
$$large E_{S' text{~} D^m}[L_{S'}(h)] = sum_{S'}[frac{1}{m}sum_{z_i in S'}l(h,z_i)]D^m(S')$$
But how are these two qual?
proof-explanation machine-learning
asked Jan 17 at 17:32
Oliver GOliver G
1,4841531
$endgroup$
In the below picture encircled in red:
If $L_D(h) = E_{z text{~} D}[l(h, z)]$,
Then how is $L_D(h) = E_{S' text{~} D^m}[L_{S'}(h)] $?
I see that $$large L_D(h) = E_{z in Z}[l(h, z)] = sum_{z in Z} l(h,z)D(z)$$ where $D$ is the distribution on $Z$ the set of samples. The first equation should be defined as:
$$large E_{S' text{~} D^m}[L_{S'}(h)] = sum_{S'}[frac{1}{m}sum_{z_i in S'}l(h,z_i)]D^m(S')$$
But how are these two qual?
proof-explanation machine-learning
proof-explanation machine-learning
asked Jan 17 at 17:32
Oliver GOliver G
1,4841531
asked Jan 17 at 17:32
Oliver GOliver G
1,4841531
edited Jan 17 at 18:48
Oliver G
asked Jan 17 at 17:32
Oliver GOliver G
1,4841531
asked Jan 17 at 17:32
Oliver GOliver G
1,4841531
asked Jan 17 at 17:32
Oliver GOliver G
1,4841531
1,4841531
$begingroup$
Hint: If you have $m$ independent variables each with probability mass function $D,$ then pick one at random, the result has probability mass function $D.$
$endgroup$
– Dap
Jan 23 at 6:01
1
$begingroup$
If you are going to quote from a source (for example by showing an image of it), it's very poor manners not to name the source.
$endgroup$
– C Monsour
Jan 24 at 11:10
add a comment |
$begingroup$
Hint: If you have $m$ independent variables each with probability mass function $D,$ then pick one at random, the result has probability mass function $D.$
$endgroup$
– Dap
Jan 23 at 6:01
1
$begingroup$
If you are going to quote from a source (for example by showing an image of it), it's very poor manners not to name the source.
$endgroup$
– C Monsour
Jan 24 at 11:10
$begingroup$
Hint: If you have $m$ independent variables each with probability mass function $D,$ then pick one at random, the result has probability mass function $D.$
$endgroup$
– Dap
Jan 23 at 6:01
$begingroup$
Hint: If you have $m$ independent variables each with probability mass function $D,$ then pick one at random, the result has probability mass function $D.$
$endgroup$
– Dap
Jan 23 at 6:01
1
1
$begingroup$
If you are going to quote from a source (for example by showing an image of it), it's very poor manners not to name the source.
$endgroup$
– C Monsour
Jan 24 at 11:10
$begingroup$
If you are going to quote from a source (for example by showing an image of it), it's very poor manners not to name the source.
$endgroup$
– C Monsour
Jan 24 at 11:10
add a comment |
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$begingroup$
Hint: If you have $m$ independent variables each with probability mass function $D,$ then pick one at random, the result has probability mass function $D.$
$endgroup$
– Dap
Jan 23 at 6:01
1
$begingroup$
If you are going to quote from a source (for example by showing an image of it), it's very poor manners not to name the source.
$endgroup$
– C Monsour
Jan 24 at 11:10