一族具有概率解释的光滑分段线性模型
A family of smooth piecewise-linear models with probabilistic interpretations
摘要：
光滑分段线性模型有着广泛的应用。基本上，它们有两类：根据它们在相变区的行为，模型是过渡的或双曲线的。本研究探讨了三种不同的方法来建立光滑的分段线性模型，我们分析了它们之间的相互关系，通过一个统一的建模框架。我们设想平滑的相变区作为域的混合过程发生，这确保了概率解释双曲线和过渡模型的随机阈值。在文献中发现的许多流行的模型是我们的方法的特殊情况。此外，本研究引入了新的回归模型作为替代，如Epanechnikov，正常和斜常态弯曲电缆。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
