loss function design to incorporate different weight for false positive and false negative

Question

I am trying to solve a semantic segmentation problem. In accordance with the real constraints, the criteria for false positive and the criteria for false negative is different. For instance, if a pixel is miscorrected as foreground is less desirable than a pixel is miscorrected as background. How to handle this kind of constraint in setting up the loss function.

Currently, I am just using binary_corrsentropy as the loss function, and I am curious to see whether it is possible to add weight for different class labels. — user297850, Feb 12 '17 at 21:17

score 7 · Accepted Answer · answered Feb 12 '17 at 21:24

7

You can use the class_weight parameter of model.fit to weight your classes and, as such, punish misclassifications differently depending on the class.

class_weight: optional dictionary mapping class indices (integers) to a weight (float) to apply to the model's loss for the samples from this class during training. This can be useful to tell the model to "pay more attention" to samples from an under-represented class.

For example:

out = Dense(2, activation='softmax')
model = Model(input=..., output=out)
model.fit(X, Y, class_weight={0: 1, 1: 0.5})

This would punish the second class less than the first.

answered Feb 12 '17 at 21:24

nemo

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Is there a way to do that element wise? Could I simply weight the output of a binary_cross entropy accordingly? What if true positives should be weighted differently than true negatives as well (and not just the positives as in your answer)? – Nickpick Feb 12 '18 at 16:16
In the end you can multiply any term you please with the output of your loss function but in order to do this you need to write your own loss function (i.e. supply a function that takes `y_pred` and `y_true`, compute your loss and multiply your weight vector). – nemo Feb 12 '18 at 21:30
But wouldn’t a binary cross entropy function always produce a loss between 0 and 1 (0.5 meaning that y_true==y_pred). Wouldn’t scaling that distort the loss function? – Nickpick Feb 13 '18 at 00:21
Can anyone gives more math behind how does class_weight works ? – Aman Dalmia Jul 23 '21 at 18:35
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@AmanDalmia basically: `weights[class[i]] * loss(y_true[i], y_pred[i])` where `class` is a mapping of sample index to respective class. and `weights` is a mapping of class to weight. therefore, the loss is re-weighted according to the class of the sample. – nemo Jul 28 '21 at 16:10

score 0 · Answer 2 · edited Sep 10 '18 at 18:42

Check out the jaccard distance (or IOU) loss function in keras-contrib:

This loss is useful when you have unbalanced numbers of pixels within an image because it gives all classes equal weight. However, it is not the defacto standard for image segmentation. For example, assume you are trying to predict if each pixel is cat, dog, or background. You have 80% background pixels, 10% dog, and 10% cat. If the model predicts 100% background should it be be 80% right (as with categorical cross entropy) or 30% (with this loss)?

Source: https://github.com/keras-team/keras-contrib/blob/master/keras_contrib/losses/jaccard.py

loss function design to incorporate different weight for false positive and false negative

2 Answers2