Robotic manipulation tasks often require the control of forces and torques exerted on external objects. This paper presents a machine learning approach for estimating forces when no force sensors are present on the robot platform. In the training phase, the robot executes the desired manipulation tasks under controlled conditions with systematically varied parameter sets. All internal sensor data, in the presented case from more than 100 sensors, as well as the force exerted by the robot are recorded. Using Transfer Entropy, a statistical model is learned that identifies the subset of sensors relevant for torque estimation in the given task. At runtime, the model is used to accurately estimate the torques exerted during manipulations of the demonstrated kind. The feasibility of the approach is shown in a setting where a robotic manipulator operates a torque wrench to fasten a screw nut. Torque estimates with an accuracy of well below ±1Nm are achieved. A strength of the presented model is that no prior knowledge of the robot's kinematics, mass distribution or sensor instrumentation is required.