论文标题
部分可观测时空混沌系统的无模型预测
Bayesian Repulsive Mixture Modeling with Matérn Point Processes
论文作者
论文摘要
混合模型是统计分析的标准工具，广泛用于密度建模和基于模型的聚类。当前方法通常将混合组件的参数建模为自变量。当群集数量或混合物组件的形式被弄清楚时，这可能会导致重叠或分离不良的簇。这种模型错误指定会破坏这些混合模型的解释性和简单性。为了解决这个问题，我们提出了一个贝叶斯混合模型，并在混合物组件之间排斥。排斥是由通用的Matérn类型III排斥点过程模型，该过程通过主要泊松点过程上的依赖顺序稀薄方案获得。我们为后推断提供了一种新颖而有效的Gibbs采样器，并在许多合成和现实世界问题上演示了所提出方法的实用性。
Mixture models are a standard tool in statistical analysis, widely used for density modeling and model-based clustering. Current approaches typically model the parameters of the mixture components as independent variables. This can result in overlapping or poorly separated clusters when either the number of clusters or the form of the mixture components is misspecified. Such model misspecification can undermine the interpretability and simplicity of these mixture models. To address this problem, we propose a Bayesian mixture model with repulsion between mixture components. The repulsion is induced by a generalized Matérn type-III repulsive point process model, obtained through a dependent sequential thinning scheme on a primary Poisson point process. We derive a novel and efficient Gibbs sampler for posterior inference, and demonstrate the utility of the proposed method on a number of synthetic and real-world problems.
