  We propose a method to estimate the uncertainty of the outcome of an image
classifier on a given input datum. Deep neural networks commonly used for image
classification are deterministic maps from an input image to an output class.
As such, their outcome on a given datum involves no uncertainty, so we must
specify what variability we are referring to when defining, measuring and
interpreting uncertainty, and attributing "confidence" to the outcome. To this
end, we introduce the Wellington Posterior, which is the distribution of
outcomes that would have been obtained in response to data that could have been
generated by the same scene that produced the given image. Since there are
infinitely many scenes that could have generated any given image, the
Wellington Posterior involves inductive transfer from scenes other than the one
portrayed. We explore the use of data augmentation, dropout, ensembling,
single-view reconstruction, and model linearization to compute a Wellington
Posterior. Additional methods include the use of conditional generative models
such as generative adversarial networks, neural radiance fields, and
conditional prior networks. We test these methods against the empirical
posterior obtained by performing inference on multiple images of the same
underlying scene. These developments are only a small step towards assessing
the reliability of deep network classifiers in a manner that is compatible with
safety-critical applications and human interpretation.
