[FIXED] setting bias for multiclass classification python tensorflow keras

Issue

Attached model shows how to add bias in case of the unbalanced classification problem initial_bias = np.log([pos/neg]). Is there a way to add bias if you have multi-class classification with unbalanced data, Say 5 classes where classes are have distribution (0.4,0.3,0.2.0.08 and 0.02)

2) also how to calculate and use class weights in such case?

update 1

I found a way to apply weights, still not sure how to use bias

#####adding weights 20 Feb
weight_for_0 = ( 1/ 370)*(370+ 977+ 795)/3
weight_for_1 = ( 1/ 977)*(370+ 977+ 795)/3
weight_for_2 = (1 / 795)*(370+ 977+ 795)/3

#array([0, 1, 2]), array([370, 977, 795])

class_weights_dict = {0: weight_for_0, 1: weight_for_1, 2:weight_for_2}
class_weights_dict
Dcnn.fit(train_dataset,
         epochs=NB_EPOCHS,
         callbacks=[MyCustomCallback()],verbose=2,validation_data=test_dataset, class_weight=class_weights_dict)

Solution

Considering that you're using 'softmax':

softmax = exp(neurons) / sum(exp(neurons))

And that you want the results of the classes to be:

frequency = [0.4 , 0.3 , 0.2 , 0.08 , 0.02]

Biases should be given by the equation (elementwise):

frequency = exp(biases) / sum(exp(biases))

This forms a system of equations:

• f1 = e^b1 / (e^b1 + e^b2 + ... + e^b5)
• f2 = e^b2 / (e^b1 + e^b2 + ... + e^b5)
• ...
• f5 = e^b5 / (e^b1 + e^b2 + ... + e^b5)

If you can solve this system of equations, you get the biases you want.

I used excel and test-error method to determine that for the frequencies you wanted, your biases should be respectively:

[1.1 , 0.81 , 0.4 , -0.51 , -1.9] 

I don't really know how to solve that system easily, but you can keep experimenting with excel or another thing until you reach the solution.

---

Adding the biases to the layer - method 1.

Use a name when defining the layer, like:

self.last_dense = layers.Dense(units=3, activation="softmax", name='last_layer')

You may need to build the model first, so:

dummy_predictions = model.predict(np.zeros((1,) + input_shape))

Then you get the weights:

weights_and_biases = model.get_layer('last_layer').get_weights()
w, b = weights_and_biases
new_biases = np.array([-0.45752, 0.51344, 0.30730])
model.get_layer('last_layer').set_weights([w, new_biases])

Method 2

def bias_init(bias_shape):
    return K.variable([-0.45752, 0.51344, 0.30730])

self.last_dense = layers.Dense(units=3, activation="softmax", bias_initializer=bias_init)

Answered By - Daniel Möller