type FANode

Perform Factor Analysis.

The current implementation should be most efficient for long
data sets: the sufficient statistics are collected in the
training phase, and all EM-cycles are performed at
its end.

The 'execute' function returns the Maximum A Posteriori estimate
of the latent variables. The 'generate_input' function generates
observations from the prior distribution.

tol -- tolerance (minimum change in log-likelihood before exiting
       the EM algorithm)
max_cycles -- maximum number of EM cycles
verbose -- if True, print log-likelihood during the EM-cycles

Internal variables of interest:
self.mu -- Mean of the input data (available after training)
self.A -- Generating weights (available after training)
self.E_y_mtx -- Weights for Maximum A Posteriori inference
self.sigma -- Vector of estimated variance of the noise
              for all input components

More information about Factor Analysis can be found in
Max Welling's classnotes:
http://www.ics.uci.edu/~welling/classnotes/classnotes.html ,
in the chapter 'Linear Models'.

Overrides: Node.__init__

Generate data from the prior distribution.

If the training phase has not been completed yet, call stop_training.

Input arguments:
len_or_y -- If integer, it specified the number of observation
            to generate. If array, it is used as a set of samples
            of the latent variables
noise -- if True, generation includes the estimated noise

Return True if the node can be inverted, False otherwise.

Overrides: Node.is_invertible

(inherited documentation)