  Radiomics analysis has achieved great success in recent years. However,
conventional Radiomics analysis suffers from insufficiently expressive
hand-crafted features. Recently, emerging deep learning techniques, e.g.,
convolutional neural networks (CNNs), dominate recent research in
Computer-Aided Diagnosis (CADx). Unfortunately, as black-box predictors, we
argue that CNNs are "diagnosing" voxels (or pixels), rather than lesions; in
other words, visual saliency from a trained CNN is not necessarily concentrated
on the lesions. On the other hand, classification in clinical applications
suffers from inherent ambiguities: radiologists may produce diverse diagnosis
on challenging cases. To this end, we propose a controllable and explainable
{\em Probabilistic Radiomics} framework, by combining the Radiomics analysis
and probabilistic deep learning. In our framework, 3D CNN feature is extracted
upon lesion region only, then encoded into lesion representation, by a
controllable Non-local Shape Analysis Module (NSAM) based on self-attention.
Inspired from variational auto-encoders (VAEs), an Ambiguity PriorNet is used
to approximate the ambiguity distribution over human experts. The final
diagnosis is obtained by combining the ambiguity prior sample and lesion
representation, and the whole network named $DenseSharp^{+}$ is end-to-end
trainable. We apply the proposed method on lung nodule diagnosis on LIDC-IDRI
database to validate its effectiveness.
