Hands deserve particular attention in virtual reality (VR) applications because they represent our primary means for interacting with the environment. Although marker-based motion capture works adequately for full body tracking, it is less reliable for small body parts such as hands and fingers which are often occluded when captured optically, thus leading VR professionals to rely on additional systems (e.g. inertial trackers). We present a machine learning pipeline to track hands and fingers using solely a motion capture system based on cameras and active markers. Our finger animation is performed by a predictive model based on neural networks trained on a movements dataset acquired from several subjects with a complementary capture system. We employ a two-stage pipeline that first resolves occlusions and then recovers all joint transformations. We show that our method compares favorably to inverse kinematics by inferring automatically the constraints from the data, provides a natural reconstruction of postures, and handles occlusions better than three proposed baselines.