Adding reliability to ELM forecasts by confidence intervals

Anton Akusok, Andrey Gritsenko, Yoan Miche, Kaj-Mikael Björk, Rui Nian, Paula Lauren, Amaury Lendasse

Research output: Contribution to journalArticleScientificpeer-review

5 Citations (Scopus)


This paper proposes a way of providing transparent and interpretable results for ELM models by adding confidence intervals to the predicted outputs. In supervised learning, outputs are often random variables because they may depend on information that is unavailable, due to the presence of noise, or the projection function itself may be stochastic. Probability distribution of outputs is input dependent, and the observed output values are samples from that distribution. However, ELM predicts deterministic outputs. The proposed method addresses that problem by estimating predictive Confidence Intervals (CIs) at a confidence level α, such that random output values fall between these intervals with probability α.

Assuming that the outputs are normally distributed, only a standard deviation is needed to compute CIs of a predicted output (the predicted output itself is a mean). Our method provides CIs for ELM predictions by estimating standard deviation of a random output for a particular input sample. It shows good results on both toy and real skin segmentation datasets, and compares well with the existing Confidence-weighted ELM methods. On a toy dataset, the predicted CIs accurately represent the variable variance of outputs. On a real dataset, CIs improve the precision of a classification task at a cost of recall.
Original languageEnglish
Peer-reviewed scientific journalNeurocomputing
Issue numberJanuary
Pages (from-to)232-241
Number of pages10
Publication statusPublished - 2017
MoE publication typeA1 Journal article - refereed


  • 512 Business and Management
  • Extreme learning machines
  • Confidence
  • Confidence interval
  • Regression
  • Skin segmentation
  • Big data


Dive into the research topics of 'Adding reliability to ELM forecasts by confidence intervals'. Together they form a unique fingerprint.

Cite this