[Hans Blom, 970521d]
(Bill Powers (970521.0556 MDT))
So it's all a matter of levels. Even the "master program", the
sequencer, needs to consult the expert who knows when the game is
finished in order to decide whether it can stop. Encoding that
knowledge into the master program itself could trivially be done,
of course. Incorporating _all_ knowledge into the master program
can be done as well. But "clean" program development usually
proceeds in a modular fashion. That is what computer science
teaches, anyway.
It's also been the basic concept behind HPCT, starting before 1960.
I wonder why MCT didn't pick up this idea.
Because MCT, at least the modeling part of it, is basically a bottom-
up approach. Given the raw (input and output) data, a model is
constructed of how those data hang together. If that is in a modular
way, that will be discovered: some of the cross-correlation
coefficients will turn out to be zero. It is only after the model has
been constructed that it can be modularized, much like in a neural
net after training, where links that have zero weight can be cut with
impunity. Or not, that does not matter: because they are zero, it
does not matter in the net's behavior whether they are there or not.
PCT, on the other hand, is a top-down approach. You choose/design a
certain network topology a priori and hope that it works. If you
choose well, you probably have used additional information, which an
MCT model does not have a priori -- only a posteriori.
Any progress, by the way, on working out a hierarchical/modular
version of MCT?
In fact, I have already -- long time ago -- presented an MCT
controller with an extra layer on top of it. The basic model part
(the basic correlator) requires certain assumptions, e.g. the noise
variances, in order to be able to work. If these are unknown but are
given some start-up value, model building does not proceed optimally
and will most likely be either too slow or oscillatory. Those initial
assumptions can, however, be corroberated by comparing them to
"reality" -- in fact, the average prediction error gives the
information of whether the choice was too conservative (resulting in
too slow convergence) or too "liberal" (resulting in unwarranted
parameter value variations/oscillations).
Both "top-down" and "bottom-up" approaches exist in humans, I would
say, where the top-down approach would attempt to work with what is
fixed in our anatomy and physiology, whereas the bottom-up approach
would use the raw perceptual data to create/maintain a "neural net"
in the associative cortex. But that applies mostly to the higher
levels, as you propose, and in higher organisms -- the ones with a
neocortex, I guess.
So, MCT models can become modular of their own -- if the data warrant
it. It can become hierarchical -- but in a way very different from
the PCT model -- by adding layers which put the initial assumptions
in question and adjust initial guesses in such a direction that the
model's consistency with its assumptions improves.
So don't expect too much of a "development" of MCT into the direction
of PCT :-).
Greetings,
Hans