Per-sample prediction intervals for extreme learning machines

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

Research output: Contribution to journalArticleScientificpeer-review


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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