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生成运动坐标中的变分滤波
Variational filtering in generated coordinates of motion |
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| 课程网址: |
http://videolectures.net/aispds08_friston_vfgc/
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| 主讲教师: |
Karl Friston
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| 开课单位: |
伦敦大学学院
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| 开课时间: |
2008-09-09
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| 课程语种: |
英语
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| 中文简介: |
本文回顾了动态模型的变分处理，该变分处理提供了系统状态的路径或轨迹上的时变条件密度及其参数的时变密度。这些方法是在关于它们的形式的固定形式假设下，通过使相对于条件密度的变分作用最大化而得到的。自由能的作用或路径积分表示模型对数证据或模型选择和平均所需的边际可能性的下界。该方法建立在运动广义坐标优化的基础上。该方法可用于非线性动态因果模型的在线贝叶斯反演，并优于现有的卡尔曼和粒子滤波方法。此外，它还使用完全相同的原理对系统的状态、参数和超参数进行了对偶和三重推断。该方案的自由形式(变分滤波)和固定形式(动态期望最大化)变体将使用模拟(鸟鸣)和真实数据(来自神经影像学研究中的血流动力学系统)进行演示。
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| 课程简介: |
This presentation reviews a variational treatment of dynamic models that furnishes time-dependent conditional densities on the path or trajectory of a system's states and the time-independent densities of its parameters. These obtain by maximizing a variational action with respect to conditional densities, under a fixed-form assumption about their form. The action or path-integral of free-energy represents a lower-bound on the model’s log-evidence or marginal likelihood required for model selection and averaging. This approach rests on formulating the optimization in generalized co-ordinates of motion. The resulting scheme can be used for on-line Bayesian inversion of nonlinear dynamic causal models and is shown to outperform existing approaches, such as Kalman and particle filtering. Furthermore, it provides for dual and triple inference on a system’s states, parameters and hyperparameters using exactly the same principles. Free-form (Variational filtering) and fixed form (Dynamic Expectation Maximization) variants of the scheme will be demonstrated using simulated (bird-song) and real data (from hemodynamic systems studied in neuroimaging).
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| 关 键 词: |
运动坐标; 变分滤波
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| 课程来源: |
视频讲座网
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| 最后编审: |
2021-02-04：nkq
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| 阅读次数: |
37
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