This paper considers the problem of controlling an autonomous vehicle that must share the road with human-driven cars.We present proactive collision avoidance algorithms that take into account the expressed intent of human driven cars and minimize the need for sudden braking or other purely reactive sudden actions. The presented algorithm utilizes multi-stage Gaussian Processes (GPs) in order to learn the transition model for each vehicle given the intention of the vehicle's driver. It further updates the trajectory predictions on-line to provide an intention-based trajectory prediction and collision avoidance adapted to various driving manners and road/weather conditions. The effectiveness of this concept is demonstrated by a variety of simulations utilizing real human driving data in various scenarios including an intersection and a highway. The experiments are done in a specially developed driving simulation and a highly realistic third-party car simulator.