The events of recent years have highlighted the importance of telemedicine solutions which could potentially allow remote treatment and diagnosis. Relatedly, Computational Paralinguistics, a unique subfield of Speech Processing, aims to extract information about the speaker and form an important part of telemedicine applications. In this work, we focus on two paralinguistic problems: mask detection and breathing state prediction. Solutions developed for these tasks could be invaluable and have the potential to help monitor and limit the spread of a virus like COVID-19. The current state-of-the-art methods proposed for these tasks are ensembles based on deep neural networks like ResNets in conjunction with feature engineering. Although these ensembles can achieve high accuracy, they also have a large footprint and require substantial computational power reducing portability to devices with limited resources. These drawbacks also mean that the previously proposed solutions are infeasible to be used in a telemedicine system due to their size and speed. On the other hand, employing lighter feature-engineered systems can be laborious and add further complexity making them difficult to create a deployable system quickly. This work proposes an ensemble-based automatic feature selection method to enable the development of fast and memory-efficient systems. In particular, we propose an output-gradient-based method to discover essential features using large, well-performing ensembles before training a smaller one. In our experiments, we observed considerable (25-32%) reductions in inference times using neural network ensembles based on output-gradient-based features. Our method offers a simple way to increase the speed of the system and enable real-time usage while maintaining competitive results with larger-footprint ensemble using all spectral features.