论文标题
横截面种群数据的随机动力系统的推断
Inference of Stochastic Dynamical Systems from Cross-Sectional Population Data
论文作者
论文摘要
从人群或时间表数据中推断动态系统的驾驶方程在几个科学领域，例如生物化学，流行病学，金融数学等。尽管存在从轨迹测量中学习动力学的算法，但很少有尝试直接从人群数据中推断动态系统。在这项工作中，我们根据随机微分方程描述了人口概率密度的演变，从而推断然后计算估计fokker-Planck方程。然后，按照USDL方法，我们将Fokker-Planck方程投影到适当的测试功能，将其转换为线性方程式。最后，我们应用稀疏的推理方法来求解后一个系统，从而诱导动力学系统的驱动力。我们的方法在合成数据和实际数据中都进行了说明，包括非线性，多模式随机微分方程，生化反应网络以及质量细胞仪生物学测量值。
Inferring the driving equations of a dynamical system from population or time-course data is important in several scientific fields such as biochemistry, epidemiology, financial mathematics and many others. Despite the existence of algorithms that learn the dynamics from trajectorial measurements there are few attempts to infer the dynamical system straight from population data. In this work, we deduce and then computationally estimate the Fokker-Planck equation which describes the evolution of the population's probability density, based on stochastic differential equations. Then, following the USDL approach, we project the Fokker-Planck equation to a proper set of test functions, transforming it into a linear system of equations. Finally, we apply sparse inference methods to solve the latter system and thus induce the driving forces of the dynamical system. Our approach is illustrated in both synthetic and real data including non-linear, multimodal stochastic differential equations, biochemical reaction networks as well as mass cytometry biological measurements.
