Switching State-Space Models
Switching State-Space Models
复制标题
切换状态空间模型
DOI：
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发表时间：
1996
期刊：
影响因子：
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通讯作者：
Geoffrey E. Hinton
中科院分区：
文献类型：
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作者：
Zoubin Ghahramani;Geoffrey E. Hinton
我们介绍了一种非线性动态时间序列数据的统计模型，该模型迭代地将数据分割成具有近似线性动态的区域，并学习每个区域的参数。该模型结合和推广了两个最广泛使用的随机时间序列模型：隐马尔可夫模型和线性动力系统模型，并与控制和计量经济学文献中广泛使用的模型有关。它也可以通过将混合专家神经网络模型(Jacobs等人，1991)扩展到其完全动态版本来推导，在该模型中，专家网络和门控网络都是循环的。推断该模型隐藏状态的后验概率在计算上是困难的，因此不能应用精确的期望最大化(EM)算法。然而，我们给出了一个变分近似，它最大化了对数似然的下界，并利用了隐马尔可夫模型的前向向后递推和线性动力系统的Kalman后向递推。
We introduce a statistical model for times series data with nonlinear dynamics which iteratively segments the data into regimes with approximately linear dynamics and learns the parameters of each of those regimes. This model combines and generalizes two of the most widely used stochastic time series models|the hidden Markov model and the linear dynamical system|and is related to models that are widely used in the control and econometrics literatures. It can also be derived by extending the mixture of experts neural network model (Jacobs et al., 1991) to its fully dynamical version, in which both expert and gating networks are recurrent. Inferring the posterior probabilities of the hidden states of this model is computationally intractable, and therefore the exact Expectation Maximization (EM) alogithm cannot be applied. However, we present a variational approximation which maximizes a lower bound on the log likelihood and makes use of both the forward{backward recursions for hidden Markov models and the Kalman lter recursions for linear dynamical systems.