Approximate Confidence and Prediction Intervals for Least Squares Support Vector Regression

TLDR

The paper proposes bias‑corrected approximate 100(1‑α)% confidence and prediction intervals for least squares support vector machines. The authors develop a bias‑correction method that avoids higher‑order derivatives, a variance estimator for both homoscedastic and heteroscedastic data, and apply Šidák and upcrossing‑based corrections to construct simultaneous intervals, benchmarking them against a bootstrap approach. Simulations demonstrate that the proposed intervals are comparable to bootstrap intervals while being computationally cheaper.

Abstract

Bias-corrected approximate 100(1-α)% pointwise and simultaneous confidence and prediction intervals for least squares support vector machines are proposed. A simple way of determining the bias without estimating higher order derivatives is formulated. A variance estimator is developed that works well in the homoscedastic and heteroscedastic case. In order to produce simultaneous confidence intervals, a simple Šidák correction and a more involved correction (based on upcrossing theory) are used. The obtained confidence intervals are compared to a state-of-the-art bootstrap-based method. Simulations show that the proposed method obtains similar intervals compared to the bootstrap at a lower computational cost.