Class 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'.

If the input dimension and the output dimension are
unspecified, they will be set when the 'train' or 'execute'
method is called for the first time.
If dtype is unspecified, it will be inherited from the data
it receives at the first call of 'train' or 'execute'.

Every subclass must take care of up- or down-casting the internal
structures to match this argument (use _refcast private
method when possible).

Return the list of dtypes supported by this node.

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.