隐马尔可夫模型预测下一个观察结果

发布于 2024-12-08 03:52:45 字数 109 浏览 1 评论 0原文

我对一只鸟的运动进行了 500 次观察。我想预测鸟的第 501 次动作是什么。我在网上搜索了一下，我想这可以通过使用 HMM 来完成，但是我在这方面没有任何经验。谁能解释一下用于解决这个问题的算法的步骤？

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葬シ愛 2024-12-15 03:52:45

x1-x2-x3-x4-x5......x500-x501
|  |  |  |  |       |
y1 y2 y3 y4 y5      y500

x - actual state
y - observations

P(y_i|x_i) - how you think the observation depends on the actual state
P(x_i|x_(i-1)) - how you think the actual state evolves

for i = 1,2,3...,501:
    write down best-guess of x_i based on y_i* and x_(i-1)**
you have your solution, since you only care about the last state

* missing in step 1
** missing in step 501

上述称为前向-后向算法（ http://en.wikipedia.org/wiki/Forward-backward_algorithm ）并且是这种特定类型的树（节点悬挂的简单链）上的和积算法（在贝叶斯网络树和马尔可夫网络树上）的特例。您可以忽略“向后”步骤，因为您不需要它，因为您只关心最后一个状态。

如果 HMM 中的转移概率未知，您必须：

执行学习算法，例如 EM（在 HMM 上执行时称为 Baum-Welch）
根据领域知识进行天真的猜测（例如，如果您的隐藏状态是 DNA，则可以通过手动标记 DNA 数据上的转换并计算频率来计算给定先前状态的转换事件的频率）

x1-x2-x3-x4-x5......x500-x501
|  |  |  |  |       |
y1 y2 y3 y4 y5      y500

x - actual state
y - observations

P(y_i|x_i) - how you think the observation depends on the actual state
P(x_i|x_(i-1)) - how you think the actual state evolves

for i = 1,2,3...,501:
    write down best-guess of x_i based on y_i* and x_(i-1)**
you have your solution, since you only care about the last state

* missing in step 1
** missing in step 501

The above is known as the forward-backward algorithm ( http://en.wikipedia.org/wiki/Forward-backward_algorithm ) and is a special case of the sum-product algorithm (on Bayesian network trees and Markov network trees) on this particular kind of tree (a simple chain with nodes hanging off). You can ignore the "backwards" step because you don't need it, since you only care about the last state.

If the transition probabilities in your HMM are unknown, you must either:

perform a learning algorithm, such as EM (known as Baum-Welch when performed on HMMs)
take a naive guess based on domain knowledge (e.g. if your hidden states is DNA you can count the frequencies of transition events given the previous state by manually labeling the transitions on DNA data and computing the frequencies)

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