Vector valued regression for iron overload estimation

In this work we present and discuss in detail a novel vector-valued regression technique: our approach allows for an all-at-once estimation, as opposed to solve a number of scalar-valued regression tasks. Despite its general purpose nature, the method has been designed to solve a delicate medical issue: a reliable and non-invasive assessment of body-iron overload. The Magnetic Iron Detector (MID) measures the magnetic track of a person, which depends on the anthropometric characteristics and the body-iron burden. We aim to provide an estimate of this signal in absence of iron overload. We show how this question can be formulated as the estimation of a vector-valued function which encompasses the prior knowledge on the shape of the magnetic track. This is accomplished by designing an appropriate vector-valued feature map. We successfully applied the method on a dataset of 84 volunteers.