Hello -
When you get a probability from running classification model, whether it is binary or multiclass classification, what is the uncertainty associated with that probability? I can’t seem to find a digestible discussion of this, but maybe I haven’t been looking in the right places, or maybe, it just isn’t that “easy” of a topic. I am mostly interested in the uncertainty of a probability prediction when using a neural network.

Here is an example of what I mean:
If I get a probability for a classification of say 76%, then is there any kind of standard deviation, or dispersion metric that is associated with that 76% (or some other ‘thing’) that would help quantify/describe an uncertainty or confidence level? If so, how does one go about characterizing that uncertainty in a quantitative manner? Is this something that is covered in the MLS courses or some other course perhaps?

Take linear regression as an example, we train the model to get a point estimate for each of the weights. If, however, we had a probabilistic description for the weights, then we could propagate that probabilistic information to the predictions.

If y = wx where w follows the unit gaussian distribution, then the predicted y shall also follow a gaussian distribution given x, and then we can estimate the standard deviation from there.

Now we know our model formalism doesn’t accommodate probabilistic weights, and so it doesn’t give you what you are looking for. You may search for “Bayesian Neural Network” for discussions and possibly implementarions, or “Bayesian XXXX” for other Bayesian counterparts.

I hope my response has given you some ideas or leads to move on.