Effect of class_weight and sample_weight in Keras

Question

Can someone tell me mathematically how sample_weight and class_weight are used in Keras in the calculation of loss function and metrics? A simple mathematical express will be great.

Answer 1

It is a simple multiplication. The loss contributed by the sample is magnified by its sample weight. Assuming i = 1 to n samples, a weight vector of sample weights w of length n, and that the loss for sample i is denoted L_i:

In Keras in particular, the product of each sample's loss with its weight is divided by the fraction of weights that are not 0 such that the loss per batch is proportional to the number of weight > 0 samples. Let p be the proportion of non-zero weights.

Here's the relevant snippet of code from the Keras repo:

score_array = loss_fn(y_true, y_pred)

if weights is not None:
    score_array *= weights
    score_array /= K.mean(K.cast(K.not_equal(weights, 0), K.floatx()))

return K.mean(score_array)

class_weight is used in the same way as sample_weight; it is just provided as a convenience to specify certain weights across entire classes.

The sample weights are currently not applied to metrics, only loss.