Paper:
Examples are not Enough, Learn to Criticize! Criticism for Interpretability
Example-based explanations are widely used in the effort to improve the interpretability of highly complex distributions. However, prototypes alone are rarely sufficient to represent the gist of the complexity. In order for users to construct better mental models and understand complex data distributions, we also need criticism to explain what are not captured by prototypes. Motivated by the Bayesian model criticism framework, we develop MMD-critic which efficiently learns prototypes and criticism, designed to aid human interpretability. A human subject pilot study shows that the MMD-critic selects prototypes and criticism that are useful to facilitate human understanding and reasoning. We also evaluate the prototypes selected by MMD-critic via a nearest prototype classifier, showing competitive performance compared to baselines.

Review:
The authors give a presentation of the mmd-critic algorithm, which selects prototypes and criticism for human interpretable machine learning by optimizing a statistic called the maximum mean discrepancy. This is a novel application of a method that was previously applied to model comparison and comparing models to input data. They describe the model and show a proof for submodularity that ensures the method is scalable. They tested the method against other prototype-based machine learning baseline methods from Bien and Tibshirani (2011) for different numbers of prototypes on the USPS handwritten digit database. The local version of MMD-critic showed superior performance to the baselines, mainly for less than 1000 prototypes. A qualitative test was done on images of dogs. Finally, they ran a pilot study to collect measures of interpretability for MMD-critic. They concluded that people performed best when given both prototypes and criticisms.
The authors explore the compelling question of how to develop interpretable machine learning methods using prototypes and criticisms. The paper was well written and clear, even for a non-expert in the field like myself. The mathematical results appear to be sound.  It is hard for me to assess the originality of the work in the field of machine learning, but I imagine that there is work on training with both positive and negative examples. At the very least, within the human category learning literature the issue of learning a concept through examples of the concept and non-examples has been explored. Given that the authors are interested in human interpretable machine learning methods, they should investigate this work in psychology.  Relatedly, the methods they compare mmd-criticism to do not have criticisms (negative examples), which makes direct comparison between the algorithms difficult to assess. This is also the case for the human experiments: participants may have done well if they were simply given randomly chosen criticisms and not those chosen by mmd-criticism. In short, the authors have certainly shown that computer and human performance is better given prototypes and criticisms rather than only prototypes. It would have been interesting to see how mmd-critic performs against other algorithms that also provide both types of data.  Smaller points: - Eq 4 seems to be missing "k(" - In figure 1, does the value on the x axis include both prototypes and criticisms for the mmd-critic model?