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Mixture ratio modeling of dynamic systems
International Journal of Adaptive Control and Signal Processing ( IF 3.1 ) Pub Date : 2021-02-09 , DOI: 10.1002/acs.3219
Miroslav Kárný 1 , Marko Ruman 1
Affiliation  

Any knowledge extraction relies (possibly implicitly) on a hypothesis about the modelled‐data dependence. The extracted knowledge ultimately serves to a decision‐making (DM). DM always faces uncertainty and this makes probabilistic modelling adequate. The inspected black‐box modeling deals with “universal” approximators of the relevant probabilistic model. Finite mixtures with components in the exponential family are often exploited. Their attractiveness stems from their flexibility, the cluster interpretability of components and the existence of algorithms for processing high‐dimensional data streams. They are even used in dynamic cases with mutually dependent data records while regression and auto‐regression mixture components serve to the dependence modeling. These dynamic models, however, mostly assume data‐independent component weights, that is, memoryless transitions between dynamic mixture components. Such mixtures are not universal approximators of dynamic probabilistic models. Formally, this follows from the fact that the set of finite probabilistic mixtures is not closed with respect to the conditioning, which is the key estimation and predictive operation. The paper overcomes this drawback by using ratios of finite mixtures as universally approximating dynamic parametric models. The paper motivates them, elaborates their approximate Bayesian recursive estimation and reveals their application potential.

中文翻译:

动态系统的混合比建模

任何知识提取都依赖于(可能是隐式的)关于建模数据依赖的假设。提取的知识最终可用于决策(DM)。DM总是面临不确定性,这使得概率建模足够了。经检查的黑盒模型处理相关概率模型的“通用”近似值。经常使用具有指数族成分的有限混合物。它们的吸引力源于它们的灵活性,组件的集群可解释性以及用于处理高维数据流的算法的存在。它们甚至在具有相互依赖的数据记录的动态情况下使用,而回归和自回归混合组件则用于依赖关系建模。但是,这些动态模型大多采用与数据无关的组件权重,也就是说,动态混合成分之间的无记忆过渡。这样的混合不是动态概率模型的通用近似器。形式上,这是由于以下事实:有限概率混合的集合相对于条件而言是不封闭的,这是关键的估计和预测操作。本文通过使用有限混合比作为通用逼近动态参数模型来克服此缺点。本文激励了他们,阐述了它们的近似贝叶斯递归估计,并揭示了它们的应用潜力。
更新日期:2021-02-09
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