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This paper presents an open-source Python toolbox called Ensemble Feature Importance (EFI) to provide machine learning (ML) researchers, domain experts, and decision makers with robust and accurate feature importance quantification and more reliable mechanistic interpretation of feature importance for prediction problems using fuzzy sets. The toolkit was developed to address uncertainties in feature importance quantification and lack of trustworthy feature importance interpretation due to the diverse availability of machine learning algorithms, feature importance calculation methods, and dataset dependencies. EFI merges results from multiple machine learning models with different feature importance calculation approaches using data bootstrapping and decision fusion techniques, such as mean, majority voting and fuzzy logic. The main attributes of the EFI toolbox are: (i) automatic optimisation of ML algorithms, (ii) automatic computation of a set of feature importance coefficients from optimised ML algorithms and feature importance calculation techniques, (iii) automatic aggregation of importance coefficients using multiple decision fusion techniques, and (iv) fuzzy membership functions that show the importance of each feature to the prediction task. The key modules and functions of the toolbox are described, and a simple example of their application is presented using the popular Iris dataset., Comment: 16 pages, 5 tables, 9 figures

With the widespread use of machine learning to support decision-making, it is increasingly important to verify and understand the reasons why a particular output is produced. Although post-training feature importance approaches assist this interpretation, there is an overall lack of consensus regarding how feature importance should be quantified, making explanations of model predictions unreliable. In addition, many of these explanations depend on the specific machine learning approach employed and on the subset of data used when calculating feature importance. A possible solution to improve the reliability of explanations is to combine results from multiple feature importance quantifiers from different machine learning approaches coupled with re-sampling. Current state-of-the-art ensemble feature importance fusion uses crisp techniques to fuse results from different approaches. There is, however, significant loss of information as these approaches are not context-aware and reduce several quantifiers to a single crisp output. More importantly, their representation of 'importance' as coefficients is misleading and incomprehensible to end-users and decision makers. Here we show how the use of fuzzy data fusion methods can overcome some of the important limitations of crisp fusion methods., Comment: 12 pages, 11 figures, 8 tables

Turbulent winds and gusts fluctuate on a wide range of timescales from milliseconds to minutes and longer, a range that overlaps the timescales of avian flight behavior, yet the importance of turbulence to avian behavior is unclear. By combining wind speed data with the measured accelerations of a golden eagle (Aquila chrysaetos) flying in the wild, we show that the eagle's accelerations can be explained by a linear interaction with turbulence for timescales between about 1/2 and 10 s. These timescales are comparable to those of typical eagle behaviors, corresponding to between about 1 and 25 wingbeats, and to those of turbulent gusts both larger than the eagle's wingspan and smaller than large-scale atmospheric phenomena such as convection cells. The eagle's accelerations exhibit power spectra and intermittent activity characteristic of turbulence, and increase in proportion to the turbulence intensity. Intermittency results in accelerations that are occasionally several times stronger than gravity, and much larger than the ones we experience while driving, for instance. These imprints of turbulence on the bird's movements need to be further explored to understand the energetics of birds and other volant lifeforms, to improve our own methods of flying through ceaselessly turbulent environments, and to engage airborne wildlife as distributed probes of the changing conditions in the atmosphere., Comment: 21 pages, 4 figures