Research Article
Distributed Gaussian Granular Neural Networks Ensemble for Prediction Intervals Construction
Table 5
Statistical analysis of the comparative experiments.
| Problems | Model | PICP | MPIW | MAE | PPIM | PPISD | T(s) |
| Noisy Rossler problem | Conformal prediction in [29] | 0.9500 | 0.5758 | 0.1742 | 0.1947 | 0.0319 | 0.7623 | MVE-based NN individual | 0.8333 | 0.8917 | 2.6027 | 1.4426 | 0.22 | 0.5387 | Bayesian NN | 0.9500 | 1.0688 | 0.3243 | 1.0688 | 0.1216 | 0.7615 | NNs ensemble in [22] | 0.9833 | 1.2238 | 0.1843 | 1.2238 | 0.3881 | 50.48 | Distributed ESNs ensemble | 0.9667 | 0.6723 | 0.1506 | 0.1732 | 0.0077 | 57.44 | Distributed NNs ensemble | 0.9667 | 0.5023 | 0.1356 | 0.1509 | 0.0067 | 1474.14 |
| Noisy Mackey Glass | Conformal prediction in [29] | 0.9500 | 0.4538 | 0.1149 | 0.1162 | 0.0297 | 0.7623 | MVE-based NN individual | 0.9077 | 0.6482 | 0.4811 | 0.3417 | 0.1921 | 0.5387 | Bayesian NN | 0.9310 | 0.5084 | 0.1179 | 0.1412 | 0.0385 | 0.7615 | NNs ensemble in [22] | 0.9828 | 0.5363 | 0.1178 | 0.1388 | 0.0501 | 50.48 | Distributed ESNs ensemble | 0.9527 | 0.4323 | 0.1145 | 0.1211 | 0.0125 | 82.42 | Distributed NNs ensemble | 0.9722 | 0.4151 | 0.1129 | 0.1116 | 0.0113 | 1035.49 |
| Traffic time series | Conformal prediction in [29] | 0.9500 | 12487.00 | 4135.78 | 5394.57 | 295.1779 | 0.7623 | MVE-based NN individual | 0.9962 | 21674.00 | 30325.00 | 17267.00 | 1282.2291 | 0.5387 | Bayesian NN | 0.8958 | 12057 | 4182.77 | 5789.36 | 307.6441 | 0.7615 | NNs ensemble in [22] | 0.7615 | 6525.37 | 3694.27 | 4986.57 | 374.1657 | 50.48 | Distributed ESNs ensemble | 0.7952 | 4674.72 | 2705.11 | 2493.67 | 168.1368 | 3.54 | Distributed NNs ensemble | 0.7833 | 3046.309 | 1752.181 | 1943.746 | 129.8434 | 1108.09 |
| BFG consumption flow | Conformal prediction in [29] | 0.9500 | 7.6245 | 1.6385 | 1.7123 | 0.1265 | 0.7623 | MVE-based NN individual | 0.8077 | 5.2250 | 1.9899 | 2.1357 | 0.2401 | 0.5387 | Bayesian NN | 0.9167 | 5.0133 | 1.7477 | 1.7046 | 0.1073 | 0.7615 | NNs ensemble in [22] | 0.8563 | 4.5125 | 1.7989 | 1.9625 | 0.1758 | 50.48 | Distributed ESNs ensemble | 0.8500 | 4.3422 | 1.7285 | 1.7039 | 0.0708 | 14.31 | Distributed NNs ensemble | 0.8667 | 4.2224 | 1.6232 | 1.7032 | 0.0674 | 828.01 |
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