As we have seen from my previous post. The probability vector of a deterministic network cannot consistently capture the uncertainty of its prediction. And we have also seen that if we use the entropy of the probablity vector as a proxy to uncertainty, the performance of active learning is pretty bad. In this post, I want to discuss some basics of Bayesian statistics and using it to study the model uncertainty. Then we will use this uncertainty to design an active learning query strategy.

Given a list of positive integers $(x_0,…,x_n)$ and a positive integer $m$, how many non-negative integer tuples $(v_0,…,v_n)$ are there so that

$$\sum v_i x_i = m$$

A homo sapien learns its environment by investigating objects that it is uncertain about. More successful homo sapiens are generally those who push themselves outside their comfort zone and navigate through unfamiliar circumstances. Suppose deep learning models do in some sense mimic how human brain works, then can we use the success story of those donquixotic apes to train our models? In this post, let’s study the notion of model’s uncertainty and use it in our training process