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The fact that machine learning models, despite their advancements, are still trained on randomly gathered data is proof that a lasting solution to the problem of optimal data gathering has not yet been found. In this paper, we investigate whether a Bayesian approach to the classification problem can provide assumptions under which one is guaranteed to perform at least as good as random sampling. For a logistic regression model, we show that maximal expected information gain on model parameters is a promising criterion for selecting samples, assuming that our classification model is well-matched to the data. Our derived criterion is closely related to the maximum model change. We experiment with data sets which satisfy this assumption to varying degrees to see how sensitive our performance is to the violation of our assumption in practice.

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Motivated by the challenging segmentation task of pancreatic tubular networks, this paper tackles two commonly encountered problems in biomedical imaging: Topological consistency of the segmentation, and expensive or difficult annotation. Our contributions are the following: a) We propose a topological score which measures both topological and geometric consistency between the predicted and ground truth segmentations, applied to model selection and validation. b) We provide a full deep-learning methodology for this difficult noisy task on time-series image data. In our method, we first use a semisupervised U-net architecture, applicable to generic segmentation tasks, which jointly trains an autoencoder and a segmentation network. We then use tracking of loops over time to further improve the predicted topology. This semi-supervised approach allows us to utilize unannotated data to learn feature representations that generalize to test data with high variability, in spite of our annotated training data having very limited variation. Our contributions are validated on a challenging segmentation task, locating tubular structures in the fetal pancreas from noisy live imaging confocal microscopy. We show that our semi-supervised model outperforms not only fully supervised and pre-trained models but also an approach which takes topological consistency into account during training. Further, our approach achieves a mean loop score of 0.808 for detecting loops in the fetal pancreas, compared to a U-net trained with clDice with mean loop score 0.762.