Uncertainty Quantification in Extreme Learning Machine: Analytical Developments, Variance Estimates and Confidence Intervals

Uncertainty quantification is crucial to assess prediction quality of a\nmachine learning model. In the case of Extreme Learning Machines (ELM), most\nmethods proposed in the literature make strong assumptions on the data, ignore\nthe randomness of input weights or neglect the bias contribution in confidence\ninterval estimations. This paper presents novel estimations that overcome these\nconstraints and improve the understanding of ELM variability. Analytical\nderivations are provided under general assumptions, supporting the\nidentification and the interpretation of the contribution of different\nvariability sources. Under both homoskedasticity and heteroskedasticity,\nseveral variance estimates are proposed, investigated, and numerically tested,\nshowing their effectiveness in replicating the expected variance behaviours.\nFinally, the feasibility of confidence intervals estimation is discussed by\nadopting a critical approach, hence raising the awareness of ELM users\nconcerning some of their pitfalls. The paper is accompanied with a scikit-learn\ncompatible Python library enabling efficient computation of all estimates\ndiscussed herein.\n