Inferring properties about time-evolving populations is a widespread problem, yet a non-standard machine learning task. Most existing machine learning models can either handle a static snapshot of a population or a single trajectory. In this talk I will present a generic framework, based on the expected signature which enables to compactly summarize a cloud of time series and make decisions on it. I will discuss an application in agricultural monitoring, where a key challenge is to predict the yield before harvest using a collection of time series acquired by satellite-sensors.