De Brabanter Kris, De Brabanter Jos, Suykens Johan A K, De Moor Bart
Department of Electrical Engineering, Research Division SCD, Katholieke Universiteit Leuven, Leuven 3001, Belgium.
IEEE Trans Neural Netw. 2011 Jan;22(1):110-20. doi: 10.1109/TNN.2010.2087769. Epub 2010 Nov 1.
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.
提出了用于最小二乘支持向量机的偏差校正近似100(1-α)%逐点及同时置信区间和预测区间。制定了一种无需估计高阶导数来确定偏差的简单方法。开发了一种在同方差和异方差情况下均表现良好的方差估计器。为了生成同时置信区间，使用了一种简单的Šidák校正和一种更复杂的校正（基于上穿理论）。将获得的置信区间与一种基于自举法的先进方法进行比较。模拟结果表明，所提出的方法以较低的计算成本获得了与自举法相似的区间。
