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连续时间马尔可夫过程的近似推理

Approximate inference for continuous time Markov processes
课程网址: http://videolectures.net/aispds08_opper_aict/  
主讲教师: Manfred Opper
开课单位: 柏林工业大学
开课时间: 2008-09-17
课程语种: 英语
中文简介:
连续时间马尔可夫过程(如跳跃过程和扩散)在许多科学领域的动力系统建模中发挥着重要作用。在许多应用中,系统作为时间函数的随机状态是不能直接观测到的。一个人只能在一组离散的时间里获得一组无聊的观察结果。问题是尽可能最好地推断未知状态路径。此外,模型参数(如扩散常数或过渡速率)也可能是未知的,必须从数据中估计。虽然给出这些估计问题的理论解是相当直接的,但是用偏微分方程或蒙特卡罗抽样的实际解可能非常耗时,而且需要寻找有效的近似。我将讨论这个问题的近似解,如路径上概率测度的变分近似和弱噪声展开。
课程简介: Continuous time Markov processes (such as jump processes and diffusions) play an important role in the modelling of dynamical systems in many scientific areas. In a variety of applications, the stochastic state of the system as a function of time is not directly observed. One has only access to a set of nolsy observations taken at a discrete set of times. The problem is then to infer the unknown state path as best as possible. In addition, model parameters (like diffusion constants or transition rates) may also be unknown and have to be estimated from the data. While it is fairly straightforward to present a theoretical solution to these estimation problems, a practical solution in terms of PDEs or by Monte Carlo sampling can be very time consuming and one is looking for efficient approximations. I will discuss approximate solutions to this problem such as variational approximations to the probability measure over paths and weak noise expansions.
关 键 词: 连续时间; 马尔可夫; 近似推理
课程来源: 视频讲座网
最后编审: 2019-11-05:lxf
阅读次数: 29