NET-APPROX:  Specify quadratic approximation to replace log likelihood.

Net-approx writes a record containing a quadratic approximation to the
log likelihood to the beginning of the log file.  This approximation
is used in place of the true likelihood in all subsequent computations.


    net-approx log-file approximation-file

A record containing the parameters of the quadratic approximation is
written to the specified log file, which must contain only
specification records (ie, records with indexes less than zero).  The
approximation of the log likelihood in terms of the network parameters
(weights, offsets, and biases, but not hyperparameters) has the form

    - a - (w - b)' V (w - b) / 2

where w is the vector of parameters and a, b, and V are the parameters
of the approximation (a is real, b is a vector, V is a matrix, usually
symmetrical).  The record written to the log file (at index -1)
contains a, b, and V, in that order, and is of type 'Q'.

The vector a and the matrix V are read from the specified file, which
should contain the numbers composing them in any of the usual decimal
formats, separated by spaces or newlines.  

This command is intended for use in setting up an approximating chain
that is coupled to the main chain, and which can be used to improve
the efficiency of estimates by exploiting correlations between the

              Copyright (c) 1995-2004 by Radford M. Neal