MIX-QUANTITIES: Quantities from log files relating to mixture models.
The quantities below relating the mixture models can be obtained from
log files (eg, for use in mix-plt). The generic quantities documented
in quantities.doc are also available. The Markov chain quantities
documented in mc-quantities.doc are defined as well, but at present
most of them are not meaningful for mixture models, since the standard
Markov chain operations are not supported.
The quantities specific to mixture models are as follows (if "n" is
present after the letter, it represents a numeric modifier):
tn Array of n'th target values for training cases.
u An array containing the mean offset for each target value.
un An array containing the offset parameters for component n,
numbered (starting at 1) in order of decreasing frequency
in the training set. If n is greater than the number of
components currently represented in the training set, the
value of un is the same as the mean offset (quantity u).
V As an array, the variances of offsets for each target value.
As a scalar, the top-level variance hyperparameter that
controls these variances.
v Same as for V, but expressed in terms of standard deviations
rather than variances.
N As an array, the hyperparameters controlling the variances
for each of the (real) target values in the components of the
mixture. As a scalar, the top-level variance hyperparameter
that controls these variances. Valid only when the targets
are real-valued.
n Same as for N, but expressed in terms of standard deviations
rather than variances.
Nn Array of noise variances for the n'th component, or array of
noise-variance hyperparameters if n is greater than the number
of components currently active in the training set.
nn As for Nn, but in terms of standard deviations.
Cn The fraction of training cases that are associated with the
first n mixture components. The components are ordered according
to the number of training cases with which they are associated
(most frequent first).
cn The frequency of the n'th most common mixture component among the
training cases. The components are ordered according to the number
of training cases with which they are associated (most frequent
first). The value is zero if there are fewer than n active
components at present.
a[n] The number of components needed to account for all but n% of the
training cases. The default is n=0 - ie, just "a" is the total
number of currently active components.
on Array giving for each training case (numbered from 0) the offset
parameter for the n'th target value for the component associated
with this training case.
h Array giving for each training case (numbered from 0) the number
of training cases currently associated with the component associated
with this training case (counting this case itself, so the minimum
value is 1, and the maximum is the number of training cases).
Copyright (c) 1997, 1998 by Radford M. Neal