Matt,
You asked "What would be a good test for understanding an algorithm?"
Thanks for posing this question. It has been a good exercise. Assuming
that the key word here is "understanding" rather than algorithm, I submit -
A test of understanding is if one can give a correct *explanation* for
any and all of the possible outputs that it (the thing to understand)
produces.
I see this as having merit in explaining "understanding" because it
shows that one grasps the transformations that occur in the system. If
one is given a set of inputs and states, then one could state what the
output would be by stepping through the transformations that take place.
This differs slightly from prediction because prediction demands that
you be able to instrument every state and input for a given moment. This
creates a distinction between it being "hard" or "extremely hard" or in
practice "impossible" to predict vs. not so hard to "understand" what is
going on.
Stan
Jim Bromer wrote:
----- Original Message ----
From: Matt Mahoney <[EMAIL PROTECTED]>
--- Jim Bromer <[EMAIL PROTECTED] <mailto:[EMAIL PROTECTED]>> wrote:
> I don't want to get into a quibble fest, but understanding is not
> necessarily constrained to prediction.
What would be a good test for understanding an algorithm?
-- Matt Mahoney, [EMAIL PROTECTED] <mailto:[EMAIL PROTECTED]>
------------------------------------------------------
I don't have a ready answer for this. First of all, (maybe I do have a
ready answer to this), understanding has to be understood in the context
of partial understanding. I can understand something about a subject
without being an expert in the subject, and I am Skeptical of anyone who
claims that total understanding is feasible, (except for a bounded
discussion of a bounded concept in which case I would only be skeptical
with a small s.)
So to start with, I could say that understanding an algorithm could be
defined by various kinds of partial knowledge of it. What kinds of
input does it react to, and what kinds of internal actions does it
take? What kind of output does it produce. Can generalizations of the
input it takes, its internal actions and its output be made. What was
it designed to do? Can relations between specific examples or derived
generalizations of its input, its internal actions and its output be made.
While some of this kind of knowledge would require some kind of
intelligence, others could be expressed in simpler data-concepts.
Harnad's categorical grounding comes to mind. An experimental AI
program would be capable of deriving data from the operation of an
algorithm if its program was created around this paradigm of examining
an algorithm. It could then create its own kind of analyses of the
algorithm, and even though it might not be the same as an analysis that
we might create, it still might be usable to produce something that
would border on understanding.
The capacity of prediction is significant in the kind of derived
generalizations and categorical exemplars that I am thinking of, but the
concept of understanding must go beyond simple prediction.
Jim Bromer
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