<p>u r right. That method only takes the data uncertainty into account (assuming u don't fit the neural net while applying the noise). As a side note, alternatively when fitting the data using a neural net u may also apply mixture density networks (see one of the many tutorials). </p>

<p>More importantly, in order to account for model uncertainty u should apply bayesian neural nets. U could could start e.g. with Monte-Carlo dropout. Also very interesting should be this work on performing sampling-free inference when using Monte-Carlo dropout</p>

<p><a href="https://arxiv.org/abs/1908.00598" rel="nofollow noreferrer">https://arxiv.org/abs/1908.00598</a></p>

<p>This work explicitly uses error propagation through neural networks and should be very interesting for u!</p>

<p>Best</p>
How to propagate uncertainty into the prediction of a neural network?
<p>I have inputs <code>x_1, ..., x_n</code> that have known 1-sigma uncertainties <code>e_1, ..., e_n</code>. I am using them to predict outputs <code>y_1, ..., y_m</code> on a trained neural network. How can I obtain 1-sigma uncertainties on my predictions? </p>

<p>My idea is to randomly perturb each input <code>x_i</code> with normal noise having mean 0 and standard deviation <code>e_i</code> a large number of times (say, 10000), and then take the median and standard deviation of each prediction <code>y_i</code>. Does this work? </p>

<p>I fear that this only takes into account the "random" error (from the measurements) and not the "systematic" error (from the network), i.e., each prediction inherently has some error to it that is not being considered in this approach. How can I properly obtain 1-sigma error bars on my predictions?</p>