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Pancreatic ductal adenocarcinoma (PDAC) is the third most common cause of cancer death in the United States. Predicting tumors like PDACs (including both classification and segmentation) from medical images by deep learning is becoming a growing trend, but usually a large number of annotated data are required for training, which is very labor-intensive and time-consuming. In this paper, we consider a partially supervised setting, where cheap image-level annotations are provided for all the training data, and the costly per-voxel annotations are only available for a subset of them. We propose an Inductive Attention Guidance Network (IAG-Net) to jointly learn a global image-level classifier for normal/PDAC classification and a local voxel-level classifier for semi-supervised PDAC segmentation. We instantiate both the global and the local classifiers by multiple instance learning (MIL), where the attention guidance, indicating roughly where the PDAC regions are, is the key to bridging them: For global MIL based normal/PDAC classification, attention serves as a weight for each instance (voxel) during MIL pooling, which eliminates the distraction from the background; For local MIL based semi-supervised PDAC segmentation, the attention guidance is inductive, which not only provides bag-level pseudo-labels to training data without per-voxel annotations for MIL training, but also acts as a proxy of an instance-level classifier. Experimental results show that our IAG-Net boosts PDAC segmentation accuracy by more than 5% compared with the state-of-the-arts. [ABSTRACT FROM AUTHOR]