Markov Chain Monte Carlo (MCMC) is a computational approach to fundamental problems such as inference, integration, optimization, and simulation. The field has developed a broad spectrum of algorithms, varying in the way they are motivated, the way they are applied and how efficiently they sample. Despite all the differences, many of them share the same core principle, which we unify as the Involutive MCMC (iMCMC) framework. Building upon this, we describe a wide range of MCMC algorithms in terms of iMCMC, and formulate a number of "tricks" which one can use as design principles for developing new MCMC algorithms. Thus, iMCMC provides a unified view of many known MCMC algorithms, which facilitates the derivation of powerful extensions. We demonstrate the latter with two examples where we transform known reversible MCMC algorithms into more efficient irreversible ones.
Automatic segmentation methods based on deep learning have recently demonstrated state-of-the-art performance, outperforming the ordinary methods. Nevertheless, these methods are inapplicable for small datasets, which are very common in medical problems. To this end, we propose a knowledge transfer method between diseases via the Generative Bayesian Prior network. Our approach is compared to a pre-train approach and random initialization and obtains the best results in terms of Dice Similarity Coefficient metric for the small subsets of the Brain Tumor Segmentation 2018 database (BRATS2018).
We construct a classification model that predicts if an earthquake with the magnitude above a threshold will take place at a given location in a time range 30-180 days from a given moment of time. A common approach is to use expert forecasts based on features like Region-Time-Length (RTL) characteristics. The proposed approach uses machine learning on top of multiple RTL features to take into account effects at various scales and to improve prediction accuracy. For historical data about Japan earthquakes 1992-2005 and predictions at locations given in this database the best model has precision up to ∼ 0.95 and recall up to ∼ 0.98.
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