  Estimating the difficulty of a dataset typically involves comparing
state-of-the-art models to humans; the bigger the performance gap, the harder
the dataset is said to be. However, this comparison provides little
understanding of how difficult each instance in a given distribution is, or
what attributes make the dataset difficult for a given model. To address these
questions, we frame dataset difficulty -- w.r.t. a model $\mathcal{V}$ -- as
the lack of $\mathcal{V}$-$\textit{usable information}$ (Xu et al., 2019),
where a lower value indicates a more difficult dataset for $\mathcal{V}$. We
further introduce $\textit{pointwise $\mathcal{V}$-information}$ (PVI) for
measuring the difficulty of individual instances w.r.t. a given distribution.
While standard evaluation metrics typically only compare different models for
the same dataset, $\mathcal{V}$-$\textit{usable information}$ and PVI also
permit the converse: for a given model $\mathcal{V}$, we can compare different
datasets, as well as different instances/slices of the same dataset.
Furthermore, our framework allows for the interpretability of different input
attributes via transformations of the input, which we use to discover
annotation artefacts in widely-used NLP benchmarks.
