论文标题
一个具有概率解释的平滑分段线性模型的家族
A family of smooth piecewise-linear models with probabilistic interpretations
论文作者
论文摘要
如今，平滑的分段线性模型涵盖了广泛的应用。基本上，其中有两类：模型根据相位转换区域的行为是过渡或双曲线。这项研究探索了三种不同的方法来构建平滑的分段线性模型，我们通过统一的建模框架分析了它们的相互关系。我们认为平滑的相位转换区是发生混合过程的域，这确保了根据随机阈值对双曲线和过渡模型的概率解释。文献中发现的许多流行模型都是我们方法论的特殊情况。此外，这项研究将新颖的回归模型作为替代品引入，例如Epanechnikov，正常和偏斜的正常弯曲仪。
The smooth piecewise-linear models cover a wide range of applications nowadays. Basically, there are two classes of them: models are transitional or hyperbolic according to their behaviour at the phase-transition zones. This study explored three different approaches to build smooth piecewise-linear models, and we analysed their inter-relationships by a unifying modelling framework. We conceived the smoothed phase-transition zones as domains where a mixture process takes place, which ensured probabilistic interpretations for both hyperbolic and transitional models in the light of random thresholds. Many popular models found in the literature are special cases of our methodology. Furthermore, this study introduces novel regression models as alternatives, such as the Epanechnikov, Normal and Skewed-Normal Bent-Cables.
