# Bayes Theorem and Neural networks

For example, I have MNIST dataset and a trained neural network: input image and the output is a probability distribution over 10 classes.

I show image and prediction is: 5% for each class and 55% for the number 2. I choose another image from the same class as the first one and get the same prediction: 5% for each class and 55% for number 2.

Can you please suggest how to update beliefs about the unknown class due to new information? Should the confidence about the number 2 increase (from 55%) after the second observation? Can we use Bayes Theorem for this problem?

Example:

1. Select 2 images of the same class from the dataset. For example 2 images of number 2
2. NN(image_1) -> probability distribution {5%,55%,5%,5%...,5%} over {1,2,3,...9}
3. NN(image_2) -> probability distribution {5%,55%,5%,5%...,5%} over {1,2,3,...9}
4. What is the final distribution over the 10 classes?

In other words: There is a hidden class from a set {1,2...9}. You sequentially get 2 observations (images) of this class and sequentially update your beliefs about what is in a black box.

• What do you mean by "merging" them? What do you want to merge? Why?
– Tim
Jul 16, 2020 at 7:12
• Update beliefs about unknown class due to new information Jul 16, 2020 at 7:19
• Could you give us more details and maybe give example? Your description is not very clear, so it'd be hard to answer.
– Tim
Jul 16, 2020 at 7:23
• @Tim I have added an example. Please let me know if this improved description. Jul 16, 2020 at 7:41
• I'm afraid that I still don't get it. What is the "same class"? Could you give a practical example? If you have digits classifier (say, trained on MNIST) and make predictions for images with digit "2" then what do you mean by "final distribution"? I mean, either the classifier correctly classifies them as "2" or not, or I'm missing something?
– Tim
Jul 16, 2020 at 7:50