bayespy.nodes.GaussianMarkovChain¶

class bayespy.nodes.GaussianMarkovChain(mu, Lambda, A, nu, n=None, inputs=None, **kwargs)[source]¶

Node for Gaussian Markov chain random variables.

In a simple case, the graphical model can be presented as:

where $\boldsymbol{\mu}$ and $\mathbf{\Lambda}$ are the mean and the precision matrix of the initial state, $\mathbf{A}$ is the state dynamics matrix and $\boldsymbol{\nu}$ is the precision of the innovation noise. It is possible that $\mathbf{A}$ and/or $\boldsymbol{\nu}$ are different for each transition instead of being constant.

The probability distribution is

$p(\mathbf{x}_0, \ldots, \mathbf{x}_{N-1}) = p(\mathbf{x}_0) \prod^{N-1}_{n=1} p(\mathbf{x}_n | \mathbf{x}_{n-1})$

where

$p(\mathbf{x}_0) &= \mathcal{N}(\mathbf{x}_0 | \boldsymbol{\mu}, \mathbf{\Lambda}) \\ p(\mathbf{x}_n|\mathbf{x}_{n-1}) &= \mathcal{N}(\mathbf{x}_n | \mathbf{A}_{n-1}\mathbf{x}_{n-1}, \mathrm{diag}(\boldsymbol{\nu}_{n-1})).$

Parameters:

mu (Gaussian-like node or (...,D)-array) – $\boldsymbol{\mu}$ , mean of $x_0$ , $D$ -dimensional with plates (…)
Lambda (Wishart-like node or (...,D,D)-array) – $\mathbf{\Lambda}$ , precision matrix of $x_0$ , $D\times D$ -dimensional with plates (…)
A (Gaussian-like node or (D,D)-array or (...,1,D,D)-array or (...,N-1,D,D)-array) – $\mathbf{A}$ , state dynamics matrix, $D$ -dimensional with plates (D,) or (…,1,D) or (…,N-1,D)
nu (gamma-like node or (D,)-array or (...,1,D)-array or (...,N-1,D)-array) – $\boldsymbol{\nu}$ , diagonal elements of the precision of the innovation process, plates (D,) or (…,1,D) or (…,N-1,D)
n (int, optional) – $N$ , the length of the chain. Must be given if $\mathbf{A}$ and $\boldsymbol{\nu}$ are constant over time.

__init__(mu, Lambda, A, nu, n=None, inputs=None, **kwargs)[source]¶: Create GaussianMarkovChain node.

Methods

`__init__`(mu, Lambda, A, nu[, n, inputs])	Create GaussianMarkovChain node.
`add_plate_axis`(to_plate)
`broadcasting_multiplier`(plates, *args)
`delete`()	Delete this node and the children
`get_gradient`(rg)	Computes gradient with respect to the natural parameters.
`get_mask`()
`get_moments`()
`get_parameters`()	Return parameters of the VB distribution.
`get_pdf_nodes`()
`get_riemannian_gradient`()	Computes the Riemannian/natural gradient.
`get_shape`(ind)
`has_plotter`()	Return True if the node has a plotter
`initialize_from_parameters`(*args)
`initialize_from_prior`()
`initialize_from_random`()	Set the variable to a random sample from the current distribution.
`initialize_from_value`(x, *args)
`load`(filename)
`logpdf`(X[, mask])	Compute the log probability density function Q(X) of this node.
`lower_bound_contribution`([gradient, ...])	Compute E[ log p(X\|parents) - log q(X) ]
`lowerbound`()
`move_plates`(from_plate, to_plate)
`observe`(x, *args[, mask])	Fix moments, compute f and propagate mask.
`pdf`(X[, mask])	Compute the probability density function of this node.
`plot`([fig])	Plot the node distribution using the plotter of the node
`random`(*phi[, plates])	Draw a random sample from the distribution.
`rotate`(R[, inv, logdet])
`save`(filename)
`set_parameters`(x)	Set the parameters of the VB distribution.
`set_plotter`(plotter)
`show`()	Print the distribution using standard parameterization.
`unobserve`()
`update`([annealing])

Attributes

`dims`
`plates`
`plates_multiplier`	Plate multiplier is applied to messages to parents

bayespy.nodes.GaussianMarkovChain¶

BayesPy

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