Goertzel [EMAIL PROTECTED]
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Subject:RE: [agi] A probabilistic/algorithmic puzzle...
Date sent: Thu, 20 Feb 2003 14:25:54 -0500
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OK... life lesson #567: When a mathematical explanation confuses
Ben Goertzel wrote:
Suppose you have a large set of people, say, all the people on Earth
Then you have a bunch of categories you're interested in, say:
...
The problem at hand is, you're given some absolute and
some conditional probabilities regarding the concepts
at hand, and you want to
The problem at hand is, you're given some absolute and
some conditional probabilities regarding the concepts
at hand, and you want to infer a bunch of others.
Hmm. The think I find interesting here is that humans don't have a good
solution to this problem. Give a typical human a set of
1) Humans use special-case algorithms to solve these problem, a different
algorithm for each domain
2) Humans have a generalized mental tool for solving these problems, but
this tool can only be invoked when complemented by some domain-specific
knowledge
My intuitive inclination is
Hi Ben,
Thanks for the brain teaser! As a sometimes believer in Occam's Razor, I
think it makes sense to assume that Xi and Xj are indepenent, unless we know
otherwise. This simplifies things, and is the rational thing to do (for
some definition of rational ;-). So why not construct a bayes
Hi Ben,
Thanks for the brain teaser! As a sometimes believer in Occam's Razor, I
think it makes sense to assume that Xi and Xj are indepenent, unless we know
otherwise. This simplifies things, and is the rational thing to do (for
some definition of rational ;-). So why not construct a
Lakoff and Nunez
(http://perso.unifr.ch/rafael.nunez/reviews.html) have a theory
that we compare lengths in our head to do arithmetic, when we're
not using school-learned rules. Our innate mathematical ability
is based on visuo-spatial comparisons in their view.
This would basically be
This is also an example of how weird the brain can be from an algorithmic
perspective. In designing an AI system, one tends to abstract cognitive
processes and create specific processes based on these abstractions. (And
this is true in NN type AI architectures, not just logicist ones.) But
Brad wrote:
I think this is a core principle of AGI design and that a system that
only makes inferences it *knows* are correct would be fairly
uninteresting and incapable of performing in the real world. The fact
that the information in the P(xi|xj) list is very incomplete is what
Brad said, responding to Moshe:
We have insufficient knowledge, so we need to make some assumptions to
approximate P(Xi|Xj). I argue that under these circumstances, the best
assumption to make is that Xi and Xj are independent, (ie,
P(Xi|Xj)=P(Xi)).
Does this clarify things?
You are
Let X_i, i=1,...,n, denote a set of discrete
random variables
X_i is the set of all integers
between i and n, initial value for i is 1?
or is i any member of the set
X?
or does i function only as a lower
bound to set X?
hi me again. if forgot to ask: is
Thursday, February 20, 2003, 10:58:57 AM, Ben Goertzel wrote:
BG OK... I can see that I formulated the problem too formally for a lot of
BG people
BG I will now rephrase it in the context of a specific test problem.
snip
BG I don't know if this test problem will clarify things or confuse them
BG I don't know if this test problem will clarify things or
confuse them ;-)
For me, it's confused them. I thought I was following it before,
sorta...
OK, well I'm pressed for time today, so I'll write a nonmathematical version
of the problem late tonight or tomorrow or over the weekend.
PROTECTED]Subject: Re: [agi] A probabilistic/algorithmic
puzzle...
Isn't this problem made more complex when we
consider that things belong to various categories.
For instance, if we know that
-40% of americans are fat
-americans are "people"
-a person can be male or fem
If P1 and P2 are contradictory, compare the truth values of the
assertions. If they are very similar, do nothing, because it's
impossible to know which is correct. If they vary
significantly(and at least one of them is above a certain
threshold), alter the probabilities towards one
But anyway, using the weighted-averaging rule dynamically and iteratively
can lead to problems in some cases. Maybe the mechanism you suggest -- a
nonlinear average of some sort -- would have better behavior, I'll think
about it.
The part of the idea that guaranteed an eventual equilibrium
Thursday, February 20, 2003, 2:25:54 PM, Ben Goertzel wrote:
BG The basic situation can be thought of as follows.
snip
Thanks, this does clarify things a lot. Your first statement of the
problem did leave some things out though...but, perhaps
unsurprisingly, I'm still a bit puzzled.
I don't
, February 20, 2003 3:26 PM
To: [EMAIL PROTECTED]
Subject: Re: [agi] A probabilistic/algorithmic puzzle...
But anyway, using the weighted-averaging rule dynamically and
iteratively
can lead to problems in some cases. Maybe the mechanism you
suggest -- a
nonlinear average of some sort -- would
Hi Cliff,
BG One thing that complicates the problem is that ,in some
cases, as well as
BG inferring probabilities one hasn't been given, one may want to make
BG corrections to probabilities one HAS been given. For
instance, sometimes
BG one may be given inconsistent information, and one
Thursday, February 20, 2003, 8:11:48 PM, Ben Goertzel wrote:
CS Somehow I see this ending up as finding a set a bell curves (i.e.
CS their height, spread and optimum) for each estimate. That is to say I
CS don't see *just* the probability as relevant but the probability
CS distribution...if I
Isn't there some way, if a full curve is too computationally
exensive, some way of expressing, say, 2 sigmas (standard deviations)
or whatever? E.g. 74% will fall within 1 standard dev. of optimum X?
We tried that, but generally, after a few inference iterations, the
confidence intervals
Hi Cliff and others,
As I came up with this kind of a test perhaps I should
say a few things about its motivation...
The problem was that the Webmind system had a number of
proposed reasoning systems and it wasn't clear which was
the best. Essentially the reasoning systems took as input
a
Hi,
This one is for the more mathematically/algorithmically inclined people on
the list.
I'm going to present a mathematical problem that's come up in the Novamente
development process. We have two different solutions for it, each with
strengths and weaknesses. I'm curious if, perhaps,
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