Hyperspectral target detection algorithms rely on knowing the desired target signature in advance. However, obtaining an effective target signature can be difficult; signatures obtained from laboratory measurements or hand-spectrometers in the field may not transfer to airborne imagery effectively. One approach to dealing with this difficulty is to learn an effective target signature from training data. An approach for learning target signatures from training data is presented. The proposed approach addresses uncertainty and imprecision in groundtruth in the training data using a multiple instance learning, diverse density (DD) based objective function. After learning the target signature given data with uncertain and imprecise groundtruth, target detection can be applied on test data. Results are shown on simulated and real data.