A big part of intelligence is not acting when one is uncertain. I wanted to explore this direction by building an MNIST classifier which can express un certainty of the input image being a particular digit.
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Such a classifier will have a high accuracy when you show it digits but refuse to classify when you throw unrelated images at it. You can access the code here and may want to follow the Jupyter notebook contained in the repo along with this tutorial.
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The key idea is pretty simple: in the Bayesian worldview, everything has a probability distribution attached to it , including model parameters weights and biases in NNs. In programming languages, we have variables that can take a specific value and every-time you access the variable, you get the same value.
In contrast to that, in the bayesian world, we have similar entities that are called random variables that give a different value every time you access it. This process of getting a new value from a random variable is called sampling. The wider the probability distribution associated with a random variable, the more uncertainty there is regarding its value because it could then take any value as per the wide probability distribution.
In a traditional neural networks you have fixed weights and biases that determine how an input is transformed into an output. In a bayesian neural network, all weights and biases have a probability distribution attached to them.
To classify an image, you do multiple runs forward passes of the network, each time with a new set of sampled weights and biases. Instead of a single set of output values what you get is multiple sets, one for each of the multiple runs. The set of output values represent a probability distribution on output values and hence you can find out confidence and uncertainty in each of the outputs.
The code assumes familiarity with basic ideas of probabilistic programming and PyTorch. PyTorch has a companion library called Pyro that gives the functionality to do probabilistic programming on neural networks written in PyTorch. Inference is the most difficult step of the entire process. The key idea of the Bayes theorem which you should remember is that we want to use data to find out the updated distributions of weights and biases P A B posterior.
Just like using initially randomly assigned weights and biases of a network, the initial distributions of parameters priors will give us wrong results.
Only after using data to get updated distributions of parameters can we use the network to classify images. I know that the paragraph above may make strict Bayesians cry in horror. I know the definitions are imprecise. This tutorial is about practical implementation of a Bayesian neural network. I scratched my head for days diving into Pyro tutorials and trying to convert one of their examples into a classifier.
After importing PyTorch, Pyro and other standard libraries like matplotlib and numpy , we define a standard feedforward neural network of one hidden layer of units. In Pyro, the model function defines how the output data is generated. Within model , the function pyro. Finally, through pyro.
Take a look at the Bayes equation again:. The P B A part of the equation is represented by the neural network because given the parameters weights and biases , we can do multiple runs on image, label pairs and find out the corresponding probability distribution of training data. All sales final.
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