隐马尔可夫模型预测下一次观测 [英] Hidden Markov Model predicting next observation

问题描述

我有500次观察鸟类运动的序列.我想预测这只鸟的第501次移动.我在网上搜索，我猜这可以通过使用HMM来完成，但是我对该主题没有任何经验.谁能解释用于解决此问题的算法的步骤?

I have a sequence of 500 observations of the movements of a bird. I want to predict what the 501st movement of the bird would be. I searched the web and I guess this can be done by using HMM, however I do not have any experience on that subject. Can anyone explain the steps of an algorithm used to solve this problem?

推荐答案

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

以上称为前向后向算法( http://en.wikipedia.org/wiki/Forward- Backward_algorithm )，并且是这种特殊树(简单的链上悬挂着节点的链)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.您可以忽略后退"步骤，因为您只关心最后一个状态，因此不需要它.

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.

如果您的HMM中的转换概率未知，则您必须:

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

• 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数据上的跃迁并计算频率来计算给定先前状态的跃迁事件的频率)

这篇关于隐马尔可夫模型预测下一次观测的文章就介绍到这了，希望我们推荐的答案对大家有所帮助，也希望大家多多支持IT屋！