金融数据贝叶斯决策树分类不确定性的估计
Estimating Classification Uncertainty of Bayesian Decision Tree Technique on Financial Data
摘要：
贝叶斯平均分类模型允许评估分类结果的不确定性，这对于在必须估计风险的金融等应用中做出可靠的决策至关重要。分类的不确定性由可用于训练的数据量、分类器集成的多样性和所需性能之间的权衡来确定。分类模型的可解释性还可以为负责进行可靠分类的专家提供有用的信息。因此，决策树（DT）似乎是有吸引力的分类模型。DT集合的所需多样性可以通过使用平均所有可能DT的贝叶斯模型来实现。在实践中，贝叶斯方法可以基于从后验分布随机抽样的马尔可夫链蒙特卡罗（MCMC）技术来实现。对于大的离散时间点的采样，MCMC方法被扩展为可逆跳跃技术，允许在给定的先验条件下诱导离散时间点。对于DT大小的先验信息不可用的情况，定义先验的扫描技术隐含地揭示了更好的性能。在本章中，我们将探讨贝叶斯MCMC技术在StatLog Repository和真实金融数据的一些数据集上的分类不确定性。分类的不确定性进行比较内的不确定性包络技术处理类后验分布和给定的置信概率。这种技术提供了对分类不确定性的现实估计，可以很容易地用统计术语解释，以进行风险评估。
英文摘要：
Bayesian averaging over classification models allows the uncertainty of classification outcomes to be evaluated, which is of crucial importance for making reliable decisions in applications such as financial in which risks have to be estimated. The uncertainty of classification is determined by a trade-off between the amount of data available for training, the diversity of a classifier ensemble and the required performance. The interpretability of classification models can also give useful information for experts responsible for making reliable classifications. For this reason Decision Trees (DTs) seem to be attractive classification models. The required diversity of the DT ensemble can be achieved by using the Bayesian model averaging all possible DTs. In practice, the Bayesian approach can be implemented on the base of a Markov Chain Monte Carlo (MCMC) technique of random sampling from the posterior distribution. For sampling large DTs, the MCMC method is extended by Reversible Jump technique which allows inducing DTs under given priors. For the case when the prior information on the DT size is unavailable, the sweeping technique defining the prior implicitly reveals a better performance. Within this Chapter we explore the classification uncertainty of the Bayesian MCMC techniques on some datasets from the StatLog Repository and real financial data. The classification uncertainty is compared within an Uncertainty Envelope technique dealing with the class posterior distribution and a given confidence probability. This technique provides realistic estimates of the classification uncertainty which can be easily interpreted in statistical terms with the aim of risk evaluation.
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