Node for categorical Markov chain random variables.
The node models a Markov chain which has a discrete set of K possible states and the next state depends only on the previous state and the state transition probabilities. The graphical model is shown below:
where 
contains the probabilities for the initial
state and 
is the state transition probability matrix. It
is possible to have varying in time.
where
![p(x_0=k) &= \pi_k, \quad \text{for } k \in \{0,\ldots,K-1\},
\\
p(x_n=j|x_{n-1}=i) &= a_{ij}^{(n-1)} \quad \text{for } n=1,\ldots,N-1,\,
i\in\{1,\ldots,K-1\},\, j\in\{1,\ldots,K-1\}
\\
a_{ij}^{(n)} &= [\mathbf{A}_n]_{ij}](../../../_images/math/67c46b93565836889d4b656464d5ffc7104b0e57.svg)
This node can be used to construct hidden Markov models by using
Mixture for the emission distribution.
pi (Dirichlet-like node or (...,K)-array) – , probabilities for the first
state. 
-dimensional Dirichlet.
A (Dirichlet-like node or (K,K)-array or (...,1,K,K)-array or (...,N-1,K,K)-array) – , probabilities for state
transitions. -dimensional Dirichlet with plates (K,) or
(…,1,K) or (…,N-1,K).
states (int, optional) – 
, the length of the chain.
Methods
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Create categorical Markov chain |
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Delete this node and the children |
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Computes gradient with respect to the natural parameters. |
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Return parameters of the VB distribution. |
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Computes the Riemannian/natural gradient. |
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Return True if the node has a plotter |
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Set the variable to a random sample from the current distribution. |
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Compute the log probability density function Q(X) of this node. |
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Compute E[ log p(X|parents) - log q(X) ] |
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Fix moments, compute f and propagate mask. |
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Compute the probability density function of this node. |
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Plot the node distribution using the plotter of the node |
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Draw a random sample from the distribution. |
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Set the parameters of the VB distribution. |
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Print the distribution using standard parameterization. |
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Attributes
Plate multiplier is applied to messages to parents |