Innovation is a key factor driving economic growth in countries worldwide. However, innovation is hard to define and, therefore, even harder to measure. To help policy makers and business leaders better understand how to foster innovation, we need robust ways to quantify innovation at local and global scales. In this work, we use a data-driven, machine-learning approach for measuring innovation. Analyzing a large number of country-level metrics, we aim to automatically discover actionable 'levers' of innovation. Using unsupervised learning methods, we determine groups of related world development indicators among a collection compiled by the World Bank. We then train a Group Lasso predictive model using data from the World Economic Forum (WEF) that captures the perceived level of innovation in 150 countries. Aside from providing high predictive accuracy, the Group Lasso also provides a model that is easily interpretable. The result is the Open Innovation Index (OII), an automatic global model for measuring innovation using machine learning algorithms and open data. We predict the OII scores for countries that only have World Development Indicators data and no existing WEF innovation scores. Furthermore, we also present case studies for which the innovation levers of a few representative countries are uncovered automatically by the proposed model.