However, the predictions obtained with ML methods are only reliable within the convex hull of the given training data. Here, ML has become one of the most practicable tools for building predictive models. Such challenges appear particularly in medical and biomedical contexts. There was no additional external funding received for this study.Ĭompeting interests: The authors have declared that no competing interests exist.īy learning from data, Machine Learning (ML) allows to model complex systems in which the mechanisms controlling the system are poorly understood. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Samadi’s contribution to this work was partially performed as part of the Helmholtz School for Data Science in Life, Earth and Energy (HDS-LEE, ) and received funding from the Helmholtz Association of German Research Centres ( ). Also, the schematic representation of the structure of the synthetic data is presented in the S1 Appendix.įunding: Moein E. The process of generating the synthetic data used in this study is introduced in the manuscript under the Data sources section. Then, in a bilateral process, a solution for the data exchange can be found in compliance with legal and ethical restrictions. However, researchers who are interested in the data, may send their informal request to the Department of Intensive Care Medicine (Email: of the University Hospital RWTH Aachen with a statement which research questions they aim at and which data are necessary for this purpose. Thus, according to the Health Data Protection Act North Rhine-Westphalia (Gesundheitsdatenschutzgesetz NRW) and the internal guidelines of the Data Protection Officer of the University Hospital RWTH Aachen, the raw patient data must not be made publicly available, since a total anonymisation cannot be guaranteed. k-anonymity, cannot be applied usefully without a relevant loss of information. Due to the small data set, anonymisation techniques, like e.g. Thus, there is a high risk that patients included in the data set could be re-identified. The included population is quite small and represents the first patients that were treated with COVID-19 in our hospital having a severe course of the disease. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.ĭata Availability: The data of the COVID-19 patients, which were included into this study, contain sensitive health-related information. Received: MaAccepted: AugPublished: September 15, 2022Ĭopyright: © 2022 E. Samadi M, Kiefer S, Fritsch SJ, Bickenbach J, Schuppert A (2022) A training strategy for hybrid models to break the curse of dimensionality. Our learning strategy yields the existence of patient cohorts for whom knowing the vital status enables extrapolation to the entire valid input space of the developed hybrid model.Ĭitation: E. As an application, we have fitted a tree-structured hybrid model to the vital status of a cohort of COVID-19 patients requiring intensive-care unit treatment and mechanical ventilation. An implementation of our strategy yields a notable reduction of training-data demand in a binary classification task compared with different supervised machine learning algorithms. Our strategy shows the existence of small sets of data points within given binary data for which knowing the labels allows for extrapolation to the entire valid input space. Our focus here is on data sets represented by binary features in which the label assessment of unlabeled data points is always extrapolation. Our strategy employs graph-theoretic methods to analyze the data and deduce a function that maps input features to output labels. Given a set of binary labeled data, the challenge is to use them to develop a model that accurately assesses labels of new unlabeled data.

In this work, we introduce a learning strategy for tree-structured hybrid models to perform a binary classification task. By the integration of first principles into a data-driven approach, hybrid modeling promises a feasible data demand alongside extrapolation. Mechanistic/data-driven hybrid modeling is a key approach when the mechanistic details of the processes at hand are not sufficiently well understood, but also inferring a model purely from data is too complex.

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