Galaxy Zoo is a
- They account for varying uncertainty when learning from volunteer responses.
- They predict full posteriors over the morphology of each galaxy.
How Bayesian Convolutional Neural Networks Work
There are two key steps to creating our Bayesian CNNs.1. Predict the parameters of a probability distribution, not the label itself
Training neural networks is much like any other fitting problem: you tweak the model to match the observations. If you are equally confident in all your collected labels, you can just minimise the difference (e.g. mean squared error) between your predictions and the observed values. However for Galaxy Zoo, many labels are more confident than others.
If I observe that, for some galaxy, 30% of volunteers say “bar”, my confidence in that 30% depends heavily on how many people replied – was it 4 or 40? Instead, we predict the probability that a typical volunteer will say “Bar”, and minimise how surprised we should be given the total number of volunteers who replied.
This way, our model understands that errors on galaxies where many volunteers replied are worse than errors on galaxies where few volunteers replied – letting it learn from every galaxy.
In our case, we can model our surprise with the Binomial distribution by recognising that k “Bar” responses from N volunteers is much like k successes from N independent trials.
loss = tf.reduce_mean(binomial_loss(labels, scalar_predictions))from tensorflow.keras import layers, Model
class SimpleClassifier(Model):
def __init__(self):
super(SimpleClassifier, self).__init__()
self.conv1 = layers.Conv2D(32, 3, activation='relu')
self.flatten = layers.Flatten()
self.d1 = layers.Dense(128, activation='relu')
self.dropout1 = layers.Dropout(rate=0.5)
self.d2 = layers.Dense(2, activation='softmax')
def call(self, x, training):
x = self.conv1(x)
x = self.flatten(x)
x = self.d1(x)
if training: # dropout typically applied only at train time
x = self.dropout1(x)
return self.d2(x) def call(self, x): # no ‘training’ argument required
x = self.conv1(x)
x = self.flatten(x)
x = self.d1(x)
x = self.dropout1(x) # dropout always on
return self.d2(x)| (and check out that informative galaxies are galaxies where those models confidently disagree. Why? We often hold our strongest opinions where we are least informed - and so do our CNN ( Formally, informative galaxies are galaxies where each model is confident (entropy H in the posterior from each model, p(votes|weights), is low) but the average prediction over all the models is uncertain (entropy across all averaged posteriors is high). This is only possible because we think about labels probabilistically and approximate training many models. For more, see , or |
| Our active learning system selects galaxies on the left (featured and diverse) over those on the right (smooth ‘blobs’). |
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