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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.

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  • $\begingroup$ What do you mean by "merging" them? What do you want to merge? Why? $\endgroup$
    – Tim
    Jul 16, 2020 at 7:12
  • $\begingroup$ Update beliefs about unknown class due to new information $\endgroup$
    – Oleg Dats
    Jul 16, 2020 at 7:19
  • $\begingroup$ Could you give us more details and maybe give example? Your description is not very clear, so it'd be hard to answer. $\endgroup$
    – Tim
    Jul 16, 2020 at 7:23
  • $\begingroup$ @Tim I have added an example. Please let me know if this improved description. $\endgroup$
    – Oleg Dats
    Jul 16, 2020 at 7:41
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    $\begingroup$ 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? $\endgroup$
    – Tim
    Jul 16, 2020 at 7:50

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