Technological advancements enable collecting vast data, i. e., Big Data, in science and industry including biomedical field. Increased computational power allows expedient analysis of collected data using statistical and machine-learning approaches. Historical data incompleteness problem and curse of dimensionality diminish practical value of pure data-driven approaches, especially in biomedicine. Advancements in deep learning (DL) frameworks based on deep neural networks (DNN) improved accuracy in image recognition, natural language processing, and other applications yet severe data limitations and/or absence of transferlearning-relevant problems drastically reduce advantages of DNN-based DL. Our earlier works demonstrate that hierarchical data representation can be alternatively implemented without NN, using boosting-like algorithms for utilization of existing domain knowledge, tolerating significant data incompleteness, and boosting accuracy of low-complexity models within the classifier ensemble, as illustrated in physiological-data analysis. Beyond obvious use in initial-factor selection, existing simplified models are effectively employed for generation of realistic synthetic data for later DNN pre-training. We review existing machine learning approaches, focusing on limitations caused by trainingdata incompleteness. We outline our hybrid framework that leverages existing domain-expert models/knowledge, boosting-like model combination, DNN-based DL and other machine learning algorithms for drastic reduction of training-data requirements. Applying this framework is illustrated in context of analyzing physiological data.