Per-sample prediction intervals for extreme learning machines

Anton Akusok, Yoan Miche, Kaj-Mikael Björk, Amaury Lendasse

Research output: Contribution to journalArticleScientificpeer-review

5 Citations (Scopus)


Prediction intervals in supervised machine learning bound the region where the true outputs of new samples may fall. They are necessary in the task of separating reliable predictions of a trained model from near random guesses, minimizing the rate of false positives, and other problem-specific tasks in applied machine learning. Many real problems have heteroscedastic stochastic outputs, which explains the need of input-dependent prediction intervals. This paper proposes to estimate the input-dependent prediction intervals by a separate extreme learning machine model, using variance of its predictions as a correction term accounting for the model uncertainty. The variance is estimated from the model’s linear output layer with a weighted Jackknife method. The methodology is very fast, robust to heteroscedastic outputs, and handles both extremely large datasets and insufficient amount of training data.
Original languageEnglish
Peer-reviewed scientific journalInternational Journal of Machine Learning and Cybernetics
Pages (from-to)1-11
Number of pages11
Publication statusPublished - 30.01.2018
MoE publication typeA1 Journal article - refereed


  • 512 Business and Management
  • ELM
  • Heteroscedastic
  • Prediction interval
  • Confidence interval
  • variance estimation
  • False positives
  • Coverage


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