Many autonomous systems (e.g, driverless cars and drones) must make decisions based on predictions of the future actions of other nearby agents, whose dynamics and intentions are unknown. E.g., autonomous cars must predict the motions of surrounding vehicles, pedestrians and bicycles. Autonomous racing drones must avoid crashing into other drones on the race course. Unfortunately, only partial and noisy data on the motions of these potential hazards are available. This talk will introduce a novel method to approximate, in real-time, a predictive Koopman operator for each potential hazard from noisy data, quantify the uncertainty of the future predictions, and use the quantified predictions to provide probabilistic collision avoidance guarantees within a real-time model predictive control framework. Experiments with ground robots, a drone, and a semi-autonomous crane on an ocean going vessel will illustrate the ideas.