Functional network topology learning and sensitivity analysis based on ANOVA decomposition. (English) Zbl 1120.68086
Summary: A new methodology for learning the topology of a functional network from data, based on the ANOVA decomposition technique, is presented. The method determines sensitivity (importance) indices that allow a decision to be made as to which set of interactions among variables is relevant and which is irrelevant to the problem under study. This immediately suggests the network topology to be used in a given problem. Moreover, local sensitivities to small changes in the data can be easily calculated. In this way, the dual optimization problem gives the local sensitivities. The methods are illustrated by their application to artificial and real examples.
MSC:
| 68T05 | Learning and adaptive systems in artificial intelligence |
References:
| [1] | DOI: 10.1103/PhysRev.4.345 · doi:10.1103/PhysRev.4.345 |
| [2] | Buckingham E., Trans. ASME 37 pp 263– (1915) |
| [3] | DOI: 10.1023/A:1009656525752 · doi:10.1023/A:1009656525752 |
| [4] | DOI: 10.1016/S0307-904X(98)10074-4 · Zbl 0944.65136 · doi:10.1016/S0307-904X(98)10074-4 |
| [5] | DOI: 10.1111/0885-9507.00205 · doi:10.1111/0885-9507.00205 |
| [6] | DOI: 10.1016/S0375-9601(98)00312-0 · doi:10.1016/S0375-9601(98)00312-0 |
| [7] | DOI: 10.1109/3468.594909 · doi:10.1109/3468.594909 |
| [8] | DOI: 10.1080/01621459.1991.10475138 · doi:10.1080/01621459.1991.10475138 |
| [9] | DOI: 10.1214/aos/1176345462 · Zbl 0481.62035 · doi:10.1214/aos/1176345462 |
| [10] | Fisher R., Transactions of the Royal Society 52 pp 399– (1918) |
| [11] | Goda Y., Coastal Engineering 15 pp 81– (1972) |
| [12] | DOI: 10.1162/153244303322753616 · Zbl 1102.68556 · doi:10.1162/153244303322753616 |
| [13] | DOI: 10.1214/aoms/1177730196 · Zbl 0032.04101 · doi:10.1214/aoms/1177730196 |
| [14] | DOI: 10.1016/S0378-4754(02)00253-7 · Zbl 1019.65005 · doi:10.1016/S0378-4754(02)00253-7 |
| [15] | DOI: 10.1016/S0004-3702(97)00043-X · Zbl 0904.68143 · doi:10.1016/S0004-3702(97)00043-X |
| [16] | Levenberg K., Quartely Journal of Applied Mathematics 2 (2) pp 164– (1944) |
| [17] | DOI: 10.1137/0111030 · Zbl 0112.10505 · doi:10.1137/0111030 |
| [18] | DOI: 10.1214/ss/1177012413 · Zbl 0955.62619 · doi:10.1214/ss/1177012413 |
| [19] | DOI: 10.1016/S0378-4754(00)00270-6 · Zbl 1005.65004 · doi:10.1016/S0378-4754(00)00270-6 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
