A training strategy for hybrid models to break the curse of dimensionality

Abstract

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. By the integration of first principles into a data-driven approach, hybrid modeling promises a feasible data demand alongside extrapolation. In this work, we introduce a learning strategy for tree-structured hybrid models to perform a binary classification task. 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. Our strategy employs graph-theoretic methods to analyze the data and deduce a function that maps input features to output labels. 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 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. 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. 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. 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.