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Machine learning has the potential to revolutionize healthcare and disease detection. One big problem however is that single organisations like hospitals often do not have enough data on their own to train strong well generalising models. This could be solved by hospitals for example sharing their data with each other, but this would violate the patients privacy. Federated learning offers a solution. Here, a model is trained based upon a larger variation of data, while no actual raw data needs to be shared. When data is iid, federated learning using simple aggregation algorithms like FedAvg works well. Definitely in a healthcare setting however, this is not realistic and data across institutions is often extremely heterogeneous. Multiple other federated algorithms have been proposed and claimed to solve this issue. In this thesis, several of those algorithms and others will be tested and compared to each other to see which ones really address the issue and to what extent. This will be done by using the extremely heterogeneous Fed-Heart-Disease dataset with natural splits from the Flamby dataset suite. Performances will be compared to local and pooled settings. It was found that with a complex enough model, the pooled setting will generally outperform all other settings. On the other hand, most federated algorithms do perform better than the local settings, proving the usefulness of federated learning. Furthermore, classical federated averaging was found to underperform on the hospitals with less data. On the other hand, all algorithms claiming to solve the non-iid issue, did in fact result in more stable improvement and convergence and less domination of the bigger client hospitals compared to FedAvg. FedNova and FedAdagrad performed the best, even obtaining scores reaching closely to the ones obtained in a pooled setting. Finally, the influence of used model on federated learning performance was shortly tested. It was found that the performance of certain federated algorithms does differ when a different model is used. On top of this, the relationship between the pooled, local and federated setting also changes, with multiple federated methods even outperforming the pooled setting when a simpler model is used. There are however also some common trends.

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Score matching generative models have recently received a lot of attention due to their state-of-the-art performance on estimating high dimensional data distributions for image generation and audio synthesis applications. This thesis develops a connection between various classes of generative modeling techniques and proposes a novel framework for handling irregular time series for causal discovery of healthcare data.