How to do serverless machine learning with scikit-learn on Google Cloud ML Engine

On Google Cloud Platform, Cloud ML Engine provides serverless machine learning, for training, hyperparameter optimization and predictions. Until recently, that was only for TensorFlow. Recently, though, the team has implemented all three capabilities for scikit-learn. In this article, I will take it for a spin. The problem is to predict the weight of a baby given some information about the pregnancy.