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