Loss Function for Probability Regression
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I'm trying to predict a probability with a neural network, but having trouble figuring out which loss function is best. Cross entropy was my first thought, but other resources always talk about it in the context of a binary classification problem where the labels are {0, 1}, but in my case I have an actual probability as the target. Is one of these options clearly best, or maybe are they all valid with just minor differences around the extreme 0/1 regions?
Assuming x is the output of the final layer of my model.
Cross Entropy:
target * -log(sigmoid(x)) + (1 - target) * -log(1 - sigmoid(x))
Mean Squared Error with Sigmoid:
(sigmoid(x) - target)^2
Mean Squared Error with Clamp:
(x - target)^2
When I use the output I clamp the values between [0, 1].
neural-network regression logistic-regression loss-function probability
asked 4 hours ago
ahbutforeahbutfore
1
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add a comment |
$begingroup$
I'm trying to predict a probability with a neural network, but having trouble figuring out which loss function is best. Cross entropy was my first thought, but other resources always talk about it in the context of a binary classification problem where the labels are {0, 1}, but in my case I have an actual probability as the target. Is one of these options clearly best, or maybe are they all valid with just minor differences around the extreme 0/1 regions?
Assuming x is the output of the final layer of my model.
Cross Entropy:
target * -log(sigmoid(x)) + (1 - target) * -log(1 - sigmoid(x))
Mean Squared Error with Sigmoid:
(sigmoid(x) - target)^2
Mean Squared Error with Clamp:
(x - target)^2
When I use the output I clamp the values between [0, 1].
neural-network regression logistic-regression loss-function probability
asked 4 hours ago
ahbutforeahbutfore
1
$endgroup$
add a comment |
$begingroup$
I'm trying to predict a probability with a neural network, but having trouble figuring out which loss function is best. Cross entropy was my first thought, but other resources always talk about it in the context of a binary classification problem where the labels are {0, 1}, but in my case I have an actual probability as the target. Is one of these options clearly best, or maybe are they all valid with just minor differences around the extreme 0/1 regions?
Assuming x is the output of the final layer of my model.
Cross Entropy:
target * -log(sigmoid(x)) + (1 - target) * -log(1 - sigmoid(x))
Mean Squared Error with Sigmoid:
(sigmoid(x) - target)^2
Mean Squared Error with Clamp:
(x - target)^2
When I use the output I clamp the values between [0, 1].
neural-network regression logistic-regression loss-function probability
asked 4 hours ago
ahbutforeahbutfore
1
$endgroup$
I'm trying to predict a probability with a neural network, but having trouble figuring out which loss function is best. Cross entropy was my first thought, but other resources always talk about it in the context of a binary classification problem where the labels are {0, 1}, but in my case I have an actual probability as the target. Is one of these options clearly best, or maybe are they all valid with just minor differences around the extreme 0/1 regions?
Assuming x is the output of the final layer of my model.
Cross Entropy:
target * -log(sigmoid(x)) + (1 - target) * -log(1 - sigmoid(x))
Mean Squared Error with Sigmoid:
(sigmoid(x) - target)^2
Mean Squared Error with Clamp:
(x - target)^2
When I use the output I clamp the values between [0, 1].
neural-network regression logistic-regression loss-function probability
neural-network regression logistic-regression loss-function probability
asked 4 hours ago
ahbutforeahbutfore
1
asked 4 hours ago
ahbutforeahbutfore
1
asked 4 hours ago
ahbutforeahbutfore
1
asked 4 hours ago
ahbutforeahbutfore
1
asked 4 hours ago
ahbutforeahbutfore
1
1
add a comment |
add a comment |
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