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Allow me to clarify my current understanding:

Interpreting a binary classification prediction made by a deterministic neural network

On one hand, point estimates fall on a sigmoid curve (between 0-1, where 0.5 is the classification threshold). So they already have a pseudo probability/ strength associated with them given how far away the estimate is from 0.5 (e.g. a prediction of 0.85 is much more certain than a prediction of 0.54)

Interpreting a binary classification prediction made by a bayesian (probabilistic) neural network

On the other hand, a BNN not only provides a point estimate (mean, also on a sigmoid curve) but also provides confidence intervals. So could I say something like, "here we see a sigmoid value of 0.6, AND we are X% certain that it is above 0.5?"

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Is my understanding correct/ missing anything important?

cross post: https://stackoverflow.com/questions/75848574/how-to-interpret-a-bayesian-neural-network-prediction-for-binary-classification?noredirect=1#comment133789503_75848574

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Bayesian neural networks do not provide confidence intervals, confidence intervals are a frequentist statistic.

Bayesian neural networks often estimate a distribution of parameter values for each parameter, whereas traditional neural networks estimate a point estimate for each parameter.

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  • $\begingroup$ If each weight has a distribution, wouldn’t that mean the final output has a distribution? $\endgroup$
    – Kermit
    Mar 30, 2023 at 16:41
  • $\begingroup$ You are correct. $\endgroup$ Mar 30, 2023 at 18:19
  • $\begingroup$ Using that output distribution, could I draw conclusions like "95% of the distribution lies between _ and _" and "_% of the distribution is above 0.5"? $\endgroup$
    – Kermit
    Mar 31, 2023 at 19:17

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