How to calculate prediction uncertainty using Keras? - machine-learning

Question

I would like to calculate NN model certainty/confidence (see What my deep model doesn't know) - when NN tells me an image represents "8", I would like to know how certain it is. Is my model 99% certain it is "8" or is it 51% it is "8", but it could also be "6"? Some digits are quite ambiguous and I would like to know for which images the model is just "flipping a coin".
I have found some theoretical writings about this but I have trouble putting this in code. If I understand correctly, I should evaluate a testing image multiple times while "killing off" different neurons (using dropout) and then...?
Working on MNIST dataset, I am running the following model:
from keras.models import Sequential
from keras.layers import Dense, Activation, Conv2D, Flatten, Dropout
model = Sequential()
model.add(Conv2D(128, kernel_size=(7, 7),
activation='relu',
input_shape=(28, 28, 1,)))
model.add(Dropout(0.20))
model.add(Conv2D(64, (3, 3), activation='relu'))
model.add(Dropout(0.20))
model.add(Flatten())
model.add(Dense(units=64, activation='relu'))
model.add(Dropout(0.25))
model.add(Dense(units=10, activation='softmax'))
model.summary()
model.compile(loss='categorical_crossentropy',
optimizer='sgd',
metrics=['accuracy'])
model.fit(train_data, train_labels, batch_size=100, epochs=30, validation_data=(test_data, test_labels,))
How should I predict with this model so that I get its certainty about predictions too? I would appreciate some practical examples (preferably in Keras, but any will do).
To clarify, I am looking for an example of how to get certainty using the method outlined by Yurin Gal (or an explanation of why some other method yields better results).

Answer 1

If you want to implement dropout approach to measure uncertainty you should do the following:
Implement function which applies dropout also during the test time:
import keras.backend as K
f = K.function([model.layers[0].input, K.learning_phase()],
[model.layers[-1].output])
Use this function as uncertainty predictor e.g. in a following manner:
def predict_with_uncertainty(f, x, n_iter=10):
result = numpy.zeros((n_iter,) + x.shape)
for iter in range(n_iter):
result[iter] = f(x, 1)
prediction = result.mean(axis=0)
uncertainty = result.var(axis=0)
return prediction, uncertainty
Of course you may use any different function to compute uncertainty.

Answer 2

Made a few changes to the top voted answer. Now it works for me.
It's a way to estimate model uncertainty. For other source of uncertainty, I found https://eng.uber.com/neural-networks-uncertainty-estimation/ helpful.
f = K.function([model.layers[0].input, K.learning_phase()],
[model.layers[-1].output])
def predict_with_uncertainty(f, x, n_iter=10):
result = []
for i in range(n_iter):
result.append(f([x, 1]))
result = np.array(result)
prediction = result.mean(axis=0)
uncertainty = result.var(axis=0)
return prediction, uncertainty

Answer 3

Your model uses a softmax activation, so the simplest way to obtain some kind of uncertainty measure is to look at the output softmax probabilities:
probs = model.predict(some input data)[0]
The probs array will then be a 10-element vector of numbers in the [0, 1] range that sum to 1.0, so they can be interpreted as probabilities. For example the probability for digit 7 is just probs[7].
Then with this information you can do some post-processing, typically the predicted class is the one with highest probability, but you can also look at the class with second highest probability, etc.

Answer 4

A simpler way is to set training=True on any dropout layers you want to run during inference as well (essentially tells the layer to operate as if it's always in training mode - so it is always present for both training and inference).
import keras
inputs = keras.Input(shape=(10,))
x = keras.layers.Dense(3)(inputs)
outputs = keras.layers.Dropout(0.5)(x, training=True)
model = keras.Model(inputs, outputs)
Code above is from this issue.