Colorectal polyps are critical indicators of colorectal cancer (CRC). Blue Laser Imaging and Linked Color Imaging are two modalities that allow improved visualization of the colon. In conjunction with the Blue Laser Imaging (BLI) Adenoma Serrated International Classification (BASIC) classification, endoscopists are capable of distinguishing benign and pre-malignant polyps. Despite these advancements, this classification still prevails a high misclassification rate for pre-malignant colorectal polyps. This work proposes a computer aided diagnosis (CADx) system that exploits the additional information contained in two novel imaging modalities, enabling more informative decision-making during colonoscopy. We train and benchmark six commonly used CNN architectures and compare the results with 19 endoscopists that employed the standard clinical classification model (BASIC). The proposed CADx system for classifying colorectal polyps achieves an area under the curve (AUC) of 0.97. Furthermore, we incorporate visual explanatory information together with a probability score, jointly computed from White Light, Blue Laser Imaging, and Linked Color Imaging. Our CADx system for automatic polyp malignancy classification facilitates future advances towards patient safety and may reduce time-consuming and costly histology assessment.