Density estimation is a versatile technique underlying many data mining tasks and techniques,ranging from exploration and presentation of static data, to probabilistic classification, or identifying changes or irregularities in streaming data. With the pervasiveness of embedded systems and digitisation, this latter type of streaming and evolving data becomes more important. Nevertheless, research in density estimation has so far focused on stationary data, leaving the task of of extrapolating and predicting density at time points outside a training window an open problem. For this task, Temporal Density Extrapolation (TDX) is proposed. This novel method models and predicts gradual monotonous changes in a distribution. It is based on the expansion of basis functions, whose weights are modelled as functions of compositional data over time by using an isometric log-ratio transformation. Extrapolated density estimates are then obtained by extrapolating the weights to the requested time point, and querying the density from the basis functions with back-transformed weights. Our approach aims for broad applicability by neither being restricted to a specific parametric distribution, nor relying on cluster structure in the data.It requires only two additional extrapolation-specific parameters, for which reasonable defaults exist. Experimental evaluation on various data streams, synthetic as well as from the real-world domains of credit scoring and environmental health, shows that the model manages to capture monotonous drift patterns accurately and better than existing methods. Thereby, it requires not more than 1.5-times the run time of a corresponding static density estimation approach.

该论文提出了一种称为 TDX 的方法，用于模拟和预测分布中逐渐单调变化的模式的密度，该方法基于扩展基础函数的权重，并使用等距对数比变换将其建模为随时间变化的组合数据的函数。通过对这些权重进行外推，可以获得外推密度估计。实验表明该方法对于捕捉单调漂移模式比现有方法更准确，并且只需要不超过相应静态密度估计方法1.5倍的运行时间。

动态基方法的时间密度外推