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https://www.selleckchem.com/MEK.html Incorporating constraints is a major concern in probabilistic machine learning. A wide variety of problems require predictions to be integrated with reasoning about constraints, from modeling routes on maps to approving loan predictions. In the former, we may require the prediction model to respect the presence of physical paths between the nodes on the map, and in the latter, we may require that the prediction model respect fairness constraints that ensure that outcomes are not subject to bias. Broadly speaking, constraints may be probabilistic, logical or causal, but the overarching challenge is to determine if and how a model can be learnt that handles a declared constraint. To the best of our knowledge, treating this in a general way is largely an open problem. In this paper, we investigate how the learning of sum-product networks, a newly introduced and increasingly popular class of tractable probabilistic models, is possible with declared constraints. We obtain correctness results about the training of these models, by establishing a relationship between probabilistic constraints and the model's parameters.Osteoradionecrosis (ORN) is a major side-effect of radiation therapy in oropharyngeal cancer (OPC) patients. In this study, we demonstrate that early prediction of ORN is possible by analyzing the temporal evolution of mandibular subvolumes receiving radiation. For our analysis, we use computed tomography (CT) scans from 21 OPC patients treated with Intensity Modulated Radiation Therapy (IMRT) with subsequent radiographically-proven ≥ grade II ORN, at three different time points pre-IMRT, 2-months, and 6-months post-IMRT. For each patient, radiomic features were extracted from a mandibular subvolume that developed ORN and a control subvolume that received the same dose but did not develop ORN. We used a Multivariate Functional Principal Component Analysis (MFPCA) approach to characterize the temporal trajectories of these

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