How to calculate prediction uncertainty using Keras?

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 ambigious 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 a 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,))

Question: how should I predict with this model so that I get its certainty about predictions too? I would appreciate some practical example (preferably in Keras, but any will do).

EDIT: to clarify, I am looking for example how to get certainty using the method outlined by Yurin Gal (or an explanation why some other method yields better results).

Answer 1

If you want to implement dropout approach to measure uncertainty you should do the following:

1. 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])
   

2. 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

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 3

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 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.