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What loss function to use when labels are probabilities?
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What loss function is most appropriate when training a model with target values that are probabilities? For example, I have a 3-output model with x=[some features] and y=[0.2, 0.3, 0.5].
It seems like something like cross-entropy doesn't make sense here since it assumes that a single target is the correct label.
Would something like MSE (after applying softmax) make sense, or is there a better loss function?
neural-networks loss-functions probability-distribution
asked 6 hours ago
Thomas JohnsonThomas Johnson
1083
New contributor
Thomas Johnson is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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add a comment |
$begingroup$
What loss function is most appropriate when training a model with target values that are probabilities? For example, I have a 3-output model with x=[some features] and y=[0.2, 0.3, 0.5].
It seems like something like cross-entropy doesn't make sense here since it assumes that a single target is the correct label.
Would something like MSE (after applying softmax) make sense, or is there a better loss function?
neural-networks loss-functions probability-distribution
asked 6 hours ago
Thomas JohnsonThomas Johnson
1083
New contributor
Thomas Johnson is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment |
$begingroup$
What loss function is most appropriate when training a model with target values that are probabilities? For example, I have a 3-output model with x=[some features] and y=[0.2, 0.3, 0.5].
It seems like something like cross-entropy doesn't make sense here since it assumes that a single target is the correct label.
Would something like MSE (after applying softmax) make sense, or is there a better loss function?
neural-networks loss-functions probability-distribution
asked 6 hours ago
Thomas JohnsonThomas Johnson
1083
New contributor
Thomas Johnson is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
What loss function is most appropriate when training a model with target values that are probabilities? For example, I have a 3-output model with x=[some features] and y=[0.2, 0.3, 0.5].
It seems like something like cross-entropy doesn't make sense here since it assumes that a single target is the correct label.
Would something like MSE (after applying softmax) make sense, or is there a better loss function?
neural-networks loss-functions probability-distribution
neural-networks loss-functions probability-distribution
asked 6 hours ago
Thomas JohnsonThomas Johnson
1083
New contributor
Thomas Johnson is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 6 hours ago
Thomas JohnsonThomas Johnson
1083
New contributor
Thomas Johnson is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 6 hours ago
Thomas JohnsonThomas Johnson
1083
New contributor
Thomas Johnson is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 6 hours ago
Thomas JohnsonThomas Johnson
1083
asked 6 hours ago
Thomas JohnsonThomas Johnson
1083
1083
New contributor
Thomas Johnson is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Thomas Johnson is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Thomas Johnson is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
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1 Answer
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$begingroup$
Actually, the cross-entropy loss function would be appropriate here, since it measures the "distance" between a distribution $q$ and the "true" distribution $p$.
You are right, though, that using a loss function called "cross_entropy" in many APIs would be a mistake. This is because these functions, as you said, assume a one-hot label. You would need to use the general cross-entropy function,
$$H(p,q)=-sum_xin X p(x) log q(x).$$
$ $
Note that one-hot labels would mean that
$$
p(x) =
begincases
1 & textif x text is the true label\
0 & textotherwise
endcases$$
which causes the cross-entropy $H(p,q)$ to reduce to the form you're familiar with:
$$H(p,q) = -log q(x_label)$$
answered 5 hours ago
Philip RaeisghasemPhilip Raeisghasem
963119
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1 Answer
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1 Answer
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$begingroup$
Actually, the cross-entropy loss function would be appropriate here, since it measures the "distance" between a distribution $q$ and the "true" distribution $p$.
You are right, though, that using a loss function called "cross_entropy" in many APIs would be a mistake. This is because these functions, as you said, assume a one-hot label. You would need to use the general cross-entropy function,
$$H(p,q)=-sum_xin X p(x) log q(x).$$
$ $
Note that one-hot labels would mean that
$$
p(x) =
begincases
1 & textif x text is the true label\
0 & textotherwise
endcases$$
which causes the cross-entropy $H(p,q)$ to reduce to the form you're familiar with:
$$H(p,q) = -log q(x_label)$$
answered 5 hours ago
Philip RaeisghasemPhilip Raeisghasem
963119
$endgroup$
add a comment |
$begingroup$
Actually, the cross-entropy loss function would be appropriate here, since it measures the "distance" between a distribution $q$ and the "true" distribution $p$.
You are right, though, that using a loss function called "cross_entropy" in many APIs would be a mistake. This is because these functions, as you said, assume a one-hot label. You would need to use the general cross-entropy function,
$$H(p,q)=-sum_xin X p(x) log q(x).$$
$ $
Note that one-hot labels would mean that
$$
p(x) =
begincases
1 & textif x text is the true label\
0 & textotherwise
endcases$$
which causes the cross-entropy $H(p,q)$ to reduce to the form you're familiar with:
$$H(p,q) = -log q(x_label)$$
answered 5 hours ago
Philip RaeisghasemPhilip Raeisghasem
963119
$endgroup$
add a comment |
$begingroup$
Actually, the cross-entropy loss function would be appropriate here, since it measures the "distance" between a distribution $q$ and the "true" distribution $p$.
You are right, though, that using a loss function called "cross_entropy" in many APIs would be a mistake. This is because these functions, as you said, assume a one-hot label. You would need to use the general cross-entropy function,
$$H(p,q)=-sum_xin X p(x) log q(x).$$
$ $
Note that one-hot labels would mean that
$$
p(x) =
begincases
1 & textif x text is the true label\
0 & textotherwise
endcases$$
which causes the cross-entropy $H(p,q)$ to reduce to the form you're familiar with:
$$H(p,q) = -log q(x_label)$$
answered 5 hours ago
Philip RaeisghasemPhilip Raeisghasem
963119
$endgroup$
Actually, the cross-entropy loss function would be appropriate here, since it measures the "distance" between a distribution $q$ and the "true" distribution $p$.
You are right, though, that using a loss function called "cross_entropy" in many APIs would be a mistake. This is because these functions, as you said, assume a one-hot label. You would need to use the general cross-entropy function,
$$H(p,q)=-sum_xin X p(x) log q(x).$$
$ $
Note that one-hot labels would mean that
$$
p(x) =
begincases
1 & textif x text is the true label\
0 & textotherwise
endcases$$
which causes the cross-entropy $H(p,q)$ to reduce to the form you're familiar with:
$$H(p,q) = -log q(x_label)$$
answered 5 hours ago
Philip RaeisghasemPhilip Raeisghasem
963119
answered 5 hours ago
Philip RaeisghasemPhilip Raeisghasem
963119
answered 5 hours ago
Philip RaeisghasemPhilip Raeisghasem
963119
answered 5 hours ago
Philip RaeisghasemPhilip Raeisghasem
963119
963119
add a comment |
add a comment |
Thomas Johnson is a new contributor. Be nice, and check out our Code of Conduct.
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