With the advent of automated machine learning, automated hyperparameter optimization methods are by now routinely used. However, this progress is not yet matched by equal progress on automatic analyses that yield information beyond performance-optimizing hyperparameter settings. In this work, we aim to answer the following two questions: Given an algorithm, what are generally its most important hyperparameters, and what are good priors over their hyperparameters' ranges to draw values from?
We present methodology and a framework to answer these questions based on meta-learning across many datasets. We apply this methodology using the experimental meta-data available on OpenML to determine the most important hyperparameters of support vector machines, random forests and Adaboost, and to infer priors for all their hyperparameters. Our results, obtained fully automatically, provide a quantitative basis to focus efforts in both manual algorithm design and in automated hyperparameter optimization. Our experiments confirm that the selected hyperparameters are indeed the most important ones and that our obtained priors also lead to improvements in hyperparameter optimization.