# Shapley Values as a Strategy for Ensemble Weights Estimation
## 6 Conclusions  
The proposed weighting strategy for ensemble learning used the reciprocal of binary cross-entropy as a model performance metric and the Shapley value estimation to enhance performance weighting with a more global ensembling aspect: how useful the model in question is, if we test all possible ensemble combinations both including and excluding it, under the assumption of equal weights. Two variations of this strategy (posShape and maxShap) were implemented and empirically compared with the monolith model and other weighting strategies using two large banking-related datasets. A decision tree and logistic regression were used as our base learners for constructing homogenous and heterogeneous ensembles. The highest performance gains over the monolith model in homogeneous ensembles were observed for the posShape strategy, with the largest ensemble size of 13 members: 4.8% and 1.9% for the BNG_credit-a and Bank Marketing datasets, respectively. If compared to traditional performance-based weighting (Perf), our approach improved the performance by 0.7%. The posShape was ranked as the best strategy, except for the case of the Python decision tree classifier using the Bank Marketing dataset. Similarly, the posShape weighting strategy in heterogeneous ensembles achieved the best performance with the largest ensemble size of 16 members, achieving a performance gain of 1.4% over the monolith approach using the BNG-credit-a dataset. Using the Bank Marketing dataset, posShape featured a 0.4% gain, but the winner there was equal weighting with a 0.6% gain over the monolith model. From the two variants tested only posShape was successful, whereas maxShap was outperformed by all other weighting strategies, implicating that efforts to correct model outputs could not improve the performance of a resulting ensemble and simply eliminating such models from the ensemble works better. While the performance of posShape differs with respect to the dataset and the base learner used, the experiments demonstrate that it performs better or at least similarly when compared to other weighting strategies, including the most similar Shapley vote-based strategy (Roz). [PERSON]; [PERSON] A streaming ensemble algorithm (SEA) for large-scale classification. In Proceedings of the Seventh ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, San Francisco, CA, USA, 26 August 2001. * [PERSON] et al. (2003) [PERSON]; [PERSON]; [PERSON]; [PERSON] Mining concept-drifting data streams using ensemble classifiers. In Proceedings of the Ninth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, Washington, DC, USA, 24 August 2003. * [PERSON] and [PERSON] (2007) [PERSON]; [PERSON] Dynamic weighted majority: An ensemble method for drifting concepts. _[PERSON]. [PERSON]. Learn. Res._**2007**, \(8\), 2755-2790. * [PERSON] et al. (2014) [PERSON]; [PERSON] [PERSON]; [PERSON] [PERSON]; [PERSON] [PERSON]; [PERSON] Sharing Data While Protecting Privacy in Citizen Science. _Interactions_**2014**, _21_, 70-73. [CrossRef]
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