PAC is great in some ways because it is one of the best ways of proving things about what you can do with finite samples. But practically the bounds will mostl

PAC is great in some ways because it is one of the best ways of proving things about what you can do with finite samples. But practically the bounds will mostly be too weak for an application, and empirically measured error rates will usually be much better than the PAC bounds. There are two other good features of a PAC analysis of a problem that often get overlooked: * you need to precisely define a model for how your data is being generated. This helps you reason about the data source a little better and to quantify your expectations of what you are expecting to see. You can turn this into anomaly detection by identifying highly improbably input data to your model. * doing a PAC analysis will give you a principled method of ranking different methods for modeling the same data. Without anything else to go on, a ML algorithm with a better PAC bound is probably a better first choice than an algorithm with a weaker or no PAC bound. All of this provides a better methodology to approaching a new model than the typical one of building random deep learning architectures and then pulling the slot machine arm to see if you hit a jackpot.