A common critique of deep learning is its brittleness off-distribution, combined with its tendency to give confident predictions for off-distribution inputs, as is seen in the case of adversarial examples. In response to this critique, a number of different methods have cropped up in recent years, that try to capture a model's uncertainty as well as its overall prediction. This paper tries to do a broad evaluation of uncertainty methods, and, particularly, to test how they perform on out of distribution data, including both data that is perturbed from its original values, and fully OOD data from ground-truth categories never seen during training. Ideally, we would want an uncertainty method that is less confident in its predictions as data is made more dissimilar from the distribution that the model is trained on. Some metrics the paper uses for capturing this are: 

- Brier Score (The difference between predicted score and ground truth 0/1 label, averaged over all examples)
- Negative Log Likelihood
- Expected Calibration Error (Within a given bucket, this is calculated as the difference between accuracy to ground truth labels, and the average predicted score in that bucket, capturing that you'd ideally want to have a lower predicted score in cases where you have low accuracy, and vice versa)
- Entropy - For labels that are fully out of distribution, and don't map to any of the model's categories, you can't directly calculate ground truth accuracy, but you can ideally ask for a model that has high entropy (close to uniform) probabilities over the classes it knows about when the image is drawn from an entirely different class

The authors test over image datasets small (MNIST) and large (ImageNet and CIFAR10), as well as a categorical ad-click-prediction dataset. They came up with some interesting findings. 

https://i.imgur.com/EVnjS1R.png

1. More fully principled Bayesian estimation of posteriors over parameters, in the form of Stochastic Variational Inference, works well on MNIST, but quite poorly on either categorical data or higher dimensional image datasets 

https://i.imgur.com/3emTYNP.png

2. Temperature scaling, which basically performs a second supervised calibration using a hold-out set to push your probabilities towards true probabilities, performs well in-distribution but collapses fairly quickly off-distribution (which sort of makes sense given that it too is just another supervised method that can do poorly when off-distribution) 
3. In general, ensemble methods, where you train different models on different subsets of the data and take their variance as uncertainty, perform the best across the bigger image models as well as the ad click model, likely because SVI (along with many other Bayesian methods) is too computationally intensive to get to work well on higher-dimensional data 
4. Overall, none of the methods worked particularly well, and even the best-performing ones were often confidently wrong off-distribution 

I think it's fair to say that we're far from where we wish we were when it comes to models that "know when they don't know," and this paper does a good job of highlighting that in specific fashion.