Uncertainty quantification in extreme learning machine: Analytical developments, variance estimates and confidence intervals

Uncertainty quantification is crucial to assess prediction quality of a machine learning model. In the case Extreme Learning Machines (ELM), most methods proposed in literature make strong assumptions on data, ignore randomness input weights or neglect bias contribution confidence interval estimations. This paper presents novel estimations that overcome these constraints and improve understanding ELM variability. Analytical derivations are provided under general assumptions, supporting identification interpretation different variability sources. Under both homoskedasticity heteroskedasticity, several variance estimates proposed, investigated, numerically tested, showing their effectiveness replicating expected behaviours. Finally, feasibility intervals estimation discussed by adopting critical approach, hence raising awareness users concerning some pitfalls. The accompanied with scikit-learn compatible Python library enabling efficient computation all herein.