We propose a robust filtering approach based on semi-supervised and multiple instance learning (MIL). We assume that the posterior density would be unimodal if not for the effect of outliers that we do not wish to explicitly model. Therefore, we seek for a point estimate at the outset, rather than a generic approximation of the entire posterior. Our approach can be thought of as a combination of standard finite-dimensional filtering (Extended Kalman Filter, or Unscented Filter) with multiple instance learning, whereby the initial condition comes with a putative set of inlier measurements. We show how both the state (regression) and the inlier set (classification) can be estimated iteratively and causally by processing only the current measurement. We illustrate our approach on visual tracking problems whereby the object of interest (target) moves and evolves as a result of occlusions and deformations, and partial knowledge of the target is given in the form of a bounding box (training set).