There are many examples of 'wisdom of the crowd' effects in which the large number of participants imparts confidence in the collective judgment of the crowd. But how do we form an aggregated judgment when the size of the crowd is limited? Whose judgments do we include, and whose do we accord the most weight? This paper considers this problem in the context of geopolitical event forecasting, where volunteer analysts are queried to give their expertise, confidence, and predictions about the outcome of an event. We develop a forecast aggregation model that integrates topical information about a question, meta-data about a pair of forecasters, and their predictions in a deep siamese neural network that decides which forecasters' predictions are more likely to be close to the correct response. A ranking of the forecasters is induced from a tournament of pair-wise forecaster comparisons, with the ranking used to create an aggregate forecast. Preliminary results find the aggregate prediction of the best forecasters ranked by our deep siamese network model consistently beats typical aggregation techniques by Brier score.
With respect to forecast aggregation, recent work has focused on integrating forecaster features and past performance. Budescu @cite_16 proposes a method for measuring a single judge's (e.g., a single forecaster's) contribution to the crowd's performance and uses positive contributors to build a weighting model for aggregating forecasts. Forlines @cite_17 shows how heuristic rules based on the qualities of each forecaster can significantly improve aggregated predictions. Hosen @cite_10 applies a neural network to forecast a range of likely outcomes based on a weighted average aggregation of forecaster predictions. Further work by Ramos @cite_6 uses a particular nonparametric density estimation technique called L2E, which aims at making the aggregation robust to clusters of opinions and dramatic changes. The Good Judgement project by Tetlock @cite_14 introduces an approach based on a novel cognitive-debiasing training design. Atanasov @cite_26 shows that team prediction polls outperform prediction markets once forecasts are statistically aggregated using various techniques such as temporal decay, differential weighting based on past performance, and recalibration.
@cite_14 @cite_26 @cite_6 @cite_16 @cite_10 @cite_17
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Statistical aggregation is often used to combine multiple opinions within a group. Such aggregates outperform individuals, including experts, in various prediction and estimation tasks. This result is attributed to the “wisdom of crowds.” We seek to improve the quality of such aggregates by eliminating poorly performing individuals from the crowd. We propose a new measure of contribution to assess the judges' performance relative to the group and use positive contributors to build a weighting model for aggregating forecasts. In Study 1, we analyze 1,233 judges forecasting almost 200 current events to illustrate the superiority of our model over unweighted models and models weighted by measures of absolute performance. In Study 2, we replicate our findings by using economic forecasts from the European Central Bank and show how the method can be used to identify smaller crowds of the top positive contributors. We show that the model derives its power from identifying experts who consistently outperform the crowd. Data, as supplemental material, are available at http: dx.doi.org 10.1287 mnsc.2014.1909 . This paper was accepted by James Smith, decision analysis. The aggregate prediction from a group of forecasters often outperformsthe individual forecasts from experts. In this paper, wepresent an improvement on the traditional “Wisdom of Crowds” aggregation technique that uses extra information elicited fromforecasters along with their prediction. An analysis of 64 forecastingquestions answered by a group of 1000+ novice predictorsshows that applying heuristic weighting rules to forecasts resultsin a 28 improvement in the accuracy of the group’s predictions. This paper begins by presenting a simple model of the way in which experts estimate probabilities. The model is then used to construct a likelihood-based aggregation formula for combining multiple probability forecasts. The resulting aggregator has a simple analytical form that depends on a single, easily-interpretable parameter. This makes it computationally simple, attractive for further development, and robust against overfitting. Based on a large-scale dataset in which over 1300 experts tried to predict 69 geopolitical events, our aggregator is found to be superior to several widely-used aggregation algorithms. Background: This paper describes an analysis that was conducted on newly collected repository with 92 versions of 38 proprietary, open-source and academic projects. A preliminary study perfomed before showed the need for a further in-depth analysis in order to identify project clusters. Aims: The goal of this research is to perform clustering on software projects in order to identify groups of software projects with similar characteristic from the defect prediction point of view. One defect prediction model should work well for all projects that belong to such group. The existence of those groups was investigated with statistical tests and by comparing the mean value of prediction efficiency. Method: Hierarchical and k-means clustering, as well as Kohonen's neural network was used to find groups of similar projects. The obtained clusters were investigated with the discriminant analysis. For each of the identified group a statistical analysis has been conducted in order to distinguish whether this group really exists. Two defect prediction models were created for each of the identified groups. The first one was based on the projects that belong to a given group, and the second one - on all the projects. Then, both models were applied to all versions of projects from the investigated group. If the predictions from the model based on projects that belong to the identified group are significantly better than the all-projects model (the mean values were compared and statistical tests were used), we conclude that the group really exists. Results: Six different clusters were identified and the existence of two of them was statistically proven: 1) cluster proprietary B -- T=19, p=0.035, r=0.40; 2) cluster proprietary open - t(17)=3.18, p=0.05, r=0.59. The obtained effect sizes (r) represent large effects according to Cohen's benchmark, which is a substantial finding. Conclusions: The two identified clusters were described and compared with results obtained by other researchers. The results of this work makes next step towards defining formal methods of reuse defect prediction models by identifying groups of projects within which the same defect prediction model may be used. Furthermore, a method of clustering was suggested and applied.