We present an approach to learn inverse kinematics of redundant systems without prior- or expert-knowledge. The method allows for an iterative bootstrapping and refinement of the inverse kinematics estimate. The essential novelty lies in a path-based sampling approach: we generate training data along paths, which result from execution of the currently learned estimate along a desired path towards a goal. The information structure thereby induced enables an efficient detection and resolution of inconsistent samples solely from directly observable data. We derive and illustrate the exploration and learning process with a low-dimensional kinematic example that provides direct insight into the bootstrapping process. We further show that the method scales for high dimensional problems, such as the Honda humanoid robot or hyperredundant planar arms with up to 50 degrees of freedom.