Jim: So, did Solomonoff's original idea involve randomizing whether the
next bit would be a 1 or a 0 in the program?
Abram: Yep.
I meant, did Solomonoff's original idea involve randomizing whether the next
bit in the program's that are originally used to produce the *prior
probabilities*
I meant:
Did Solomonoff's original idea use randomization to determine the bits of
the programs that are used to produce the *prior probabilities*? I think
that the answer to that is obviously no. The randomization of the next bit
would used in the test of the prior probabilities as done using a
: [agi] Comments On My Skepticism of Solomonoff Induction
I meant:
Did Solomonoff's original idea use randomization to determine the bits of the
programs that are used to produce the prior probabilities? I think that the
answer to that is obviously no. The randomization of the next bit would used
Mahoney, matmaho...@yahoo.com
--
*From:* Jim Bromer jimbro...@gmail.com
*To:* agi agi@v2.listbox.com
*Sent:* Fri, August 6, 2010 2:18:09 PM
*Subject:* Re: [agi] Comments On My Skepticism of Solomonoff Induction
I meant:
Did Solomonoff's original idea use
Abram,
Thanks for the explanation. I still don't get it. Your function may be
convergent but it is not a probability. You said that Solomonoff's original
construction involved flipping a coin for the next bit. What good does that
do? And how does that prove that his original idea was
Jim,
Your function may be convergent but it is not a probability.
True! All the possibilities sum to less than 1. There are ways of addressing
this (ie, multiply by a normalizing constant which must also be approximated
in a convergent manner), but for the most part adherents of Solomonoff
I guess the trans-infinite is computable, given infinite resources. It
doesn't make sense to me except that the infinite does not exist as a
number-like object, it is an active process of incrementation or something
like that. End of Count.
---
agi
I see that erasure is from an alternative definition for a Turing Machine.
I am not sure if a four state Turing Machine could be used to
make Solomonoff Induction convergent. If all programs that required working
memory greater than the length of the output string could be eliminated then
that
On Mon, Aug 2, 2010 at 7:21 AM, Jim Bromer jimbro...@gmail.com wrote:
I see that erasure is from an alternative definition for a Turing Machine.
I am not sure if a four state Turing Machine could be used to
make Solomonoff Induction convergent. If all programs that required working
memory
Jim,
Interestingly, the formalization of Solomonoff induction I'm most familiar
with uses a construction that relates the space of programs with the real
numbers just as you say. This formulation may be due to Solomonoff, or
perhaps Hutter... not sure. I re-formulated it to gloss over that in
Abram,
This is a very interesting function. I have spent a lot of time thinking
about it. However, I do not believe that does, in any way, prove or
indicate that Solomonoff Induction is convergent. I want to discuss the
function but I need to take more time to study some stuff and to work
As far as I can tell right now, my theories that Solomonoff Induction is
trans-infinite were wrong. Now that I realize that the mathematics do not
support these conjectures, I have to acknowledge that I would not be able to
prove or even offer a sketch of a proof of my theories. Although I did
Jim,
I'll argue that solomonoff probabilities are in fact like Pi, that is,
computable in the limit.
I still do not understand why you think these combinations are necessary. It
is not necessary to make some sort of ordering of the sum to get it to
converge: ordering only matters for infinite
Jim,
Fair enough.
Oh, and Matt: kudos for being better at patiently explaining details than
me.
--Abram
On Mon, Jul 26, 2010 at 4:11 PM, Jim Bromer jimbro...@gmail.com wrote:
Abram,
We all have some misconceptions about this, and about related issues. Let
me think about this more
Bromer jimbro...@gmail.com
*To:* agi agi@v2.listbox.com
*Sent:* Sat, July 24, 2010 3:59:18 PM
*Subject:* Re: [agi] Comments On My Skepticism of Solomonoff Induction
Solomonoff Induction may require a trans-infinite level of complexity just
to run each program. Suppose each program
.
-- Matt Mahoney, matmaho...@yahoo.com
--
*From:* Jim Bromer jimbro...@gmail.com
*To:* agi agi@v2.listbox.com
*Sent:* Sat, July 24, 2010 3:59:18 PM
*Subject:* Re: [agi] Comments On My Skepticism of Solomonoff Induction
Solomonoff Induction may require a trans
I got confused with the two kinds of combinations that I was thinking about.
Sorry. However, while the reordering of the partial accumulation of a
finite number of probabilities, where each probability is taken just once,
can be done with a re algorithm, there is no re algorithm that can consider
Solomonoff Induction may require a trans-infinite level of complexity just
to run each program. Suppose each program is iterated through the
enumeration of its instructions. Then, not only do the infinity of possible
programs need to be run, many combinations of the infinite programs from
each
On Sat, Jul 24, 2010 at 3:59 PM, Jim Bromer jimbro...@gmail.com wrote:
Solomonoff Induction may require a trans-infinite level of complexity just
to run each program. Suppose each program is iterated through the
enumeration of its instructions. Then, not only do the infinity of
possible
...@gmail.com
To: agi agi@v2.listbox.com
Sent: Sat, July 24, 2010 3:59:18 PM
Subject: Re: [agi] Comments On My Skepticism of Solomonoff Induction
Solomonoff Induction may require a trans-infinite level of complexity just to
run each program. Suppose each program is iterated through
jimbro...@gmail.com
*To:* agi agi@v2.listbox.com
*Sent:* Wed, July 21, 2010 3:08:13 PM
*Subject:* Re: [agi] Comments On My Skepticism of Solomonoff Induction
I should have said, It would be unwise to claim that this method could
stand as an ideal for some valid and feasible application
I have to retract my claim that the programs of Solomonoff Induction would
be trans-infinite. Each of the infinite individual programs could be
enumerated by their individual instructions so some combination of unique
individual programs would not correspond to a unique program but to the
...@yahoo.com
--
*From:* Jim Bromer jimbro...@gmail.com
*To:* agi agi@v2.listbox.com
*Sent:* Wed, July 21, 2010 3:08:13 PM
*Subject:* Re: [agi] Comments On My Skepticism of Solomonoff Induction
I should have said, It would be unwise to claim that this method could
...@gmail.com
To: agi agi@v2.listbox.com
Sent: Thu, July 22, 2010 5:06:12 PM
Subject: Re: [agi] Comments On My Skepticism of Solomonoff Induction
On Wed, Jul 21, 2010 at 8:47 PM, Matt Mahoney matmaho...@yahoo.com wrote:
The fundamental method is that the probability of a string x is proportional
.
-- Matt Mahoney, matmaho...@yahoo.com
--
*From:* Jim Bromer jimbro...@gmail.com
*To:* agi agi@v2.listbox.com
*Sent:* Thu, July 22, 2010 5:06:12 PM
*Subject:* Re: [agi] Comments On My Skepticism of Solomonoff Induction
On Wed, Jul 21, 2010 at 8:47 PM, Matt Mahoney
Jim,
Sorry for the short quip... I should have thought about how it would sound
before sending.
--Abram
On Wed, Jul 21, 2010 at 4:36 PM, Jim Bromer jimbro...@gmail.com wrote:
You claim that I have not checked how Solomonoff Induction is actually
defined, but then don't bother mentioning how
it?
-- Matt Mahoney, matmaho...@yahoo.com
--
*From:* Jim Bromer jimbro...@gmail.com
*To:* agi agi@v2.listbox.com
*Sent:* Wed, July 21, 2010 3:08:13 PM
*Subject:* Re: [agi] Comments On My Skepticism of Solomonoff Induction
I should have said, It would be unwise to claim
to the contrary.
There is a chance that I am wrong
So why don't you drop it?
-- Matt Mahoney, matmaho...@yahoo.com
From: Jim Bromer jimbro...@gmail.com
To: agi agi@v2.listbox.com
Sent: Tue, July 20, 2010 3:10:40 PM
Subject: Re: [agi] Comments On My Skepticism
--
*From:* Jim Bromer jimbro...@gmail.com
*To:* agi agi@v2.listbox.com
*Sent:* Tue, July 20, 2010 3:10:40 PM
*Subject:* Re: [agi] Comments On My Skepticism of Solomonoff Induction
The question was asked whether, given infinite resources could Solmonoff
Induction work. I made the assumption
: [agi] Comments On My Skepticism of Solomonoff Induction
The question was asked whether, given infinite resources could Solmonoff
Induction work. I made the assumption that it was computable and found that
it wouldn't work. It is not computable, even with infinite resources, for
the kind
The fundamental method of Solmonoff Induction is trans-infinite. Suppose
you iterate through all possible programs, combining different programs as
you go. Then you have an infinite number of possible programs which have a
trans-infinite number of combinations, because each tier of combinations
I should have said, It would be unwise to claim that this method could stand
as an ideal for some valid and feasible application of probability.
Jim Bromer
On Wed, Jul 21, 2010 at 2:47 PM, Jim Bromer jimbro...@gmail.com wrote:
The fundamental method of Solmonoff Induction is trans-infinite.
Jim,
This argument that you've got to consider recombinations *in addition to*
just the programs displays the lack of mathematical understanding that I am
referring to... you appear to be arguing against what you *think* solomonoff
induction is, without checking how it is actually defined...
You claim that I have not checked how Solomonoff Induction is actually
defined, but then don't bother mentioning how it is defined as if it would
be too much of an ordeal to even begin to try. It is this kind of evasive
response, along with the fact that these functions are incomputable, that
On Wed, Jul 21, 2010 at 4:01 PM, Abram Demski abramdem...@gmail.com wrote:
Jim,
This argument that you've got to consider recombinations *in addition to*
just the programs displays the lack of mathematical understanding that I am
referring to... you appear to be arguing against what you
I can't say where you are going wrong because I really have no idea.
However, my guess is that you are ignoring certain contingencies that would
be necessary to make your claims valid. I tried to use a reference to the
theory of limits to explain this but it seemed to fall on deaf ears.
If I
If someone had a profound knowledge of Solomonoff Induction and the *science
of probability* he could at the very least talk to me in a way that I knew
he knew what I was talking about and I knew he knew what he was talking
about. He might be slightly obnoxious or he might be casual or (more
From: Jim Bromer jimbro...@gmail.com
To: agi agi@v2.listbox.com
Sent: Wed, July 21, 2010 3:08:13 PM
Subject: Re: [agi] Comments On My Skepticism of Solomonoff Induction
I should have said, It would be unwise to claim that this method could stand as
an ideal for some valid and feasible
Jim,
An example reference on the theory of computability is Computability and
Logic by Boolos, Burgess and Jeffrey. For those who accept the
church-turing thesis, this mathematical theory provides a sufficient account
of the notion of computability, including the space of possible programs
(which
The question was asked whether, given infinite resources could Solmonoff
Induction work. I made the assumption that it was computable and found that
it wouldn't work. It is not computable, even with infinite resources, for
the kind of thing that was claimed it would do. (I believe that with a
I am not going in circles. I probably should not express myself in
replies. I made a lot of mistakes getting to the conclusion that I got to,
and I am a little uncertain as to whether the construction of the diagonal
set actually means that there would be uncountable sets for this
particular
Abram,
I feel a responsibility to make an effort to explain myself when someone
doesn't understand what I am saying, but once I have gone over the material
sufficiently, if the person is still arguing with me about it I will just
say that I have already explained myself in the previous messages.
I checked the term program space and found a few authors who used it, but
it seems to be an ad-hoc definition that is not widely used. It seems to be
an amalgamation of term sample space with the the set of all programs or
something like that. Of course, the simple comprehension of the idea of,
I made a remark about confusing a domain with the values that was wrong. What
I should have said is that you cannot just treat a domain of functions or of
programs as if they were a domain of numbers or values and expect them to
act in ways that are familiar from a study of numbers.
Of course
Solomonoff Induction is not well-defined because it is either incomputable
and/or absurdly irrelevant. This is where the communication breaks down. I
have no idea why you would make a remark like that. It is interesting that
you are an incremental-progress guy.
On Sat, Jul 17, 2010 at 10:59
Jim,
I think you are using a different definition of well-defined :). I am
saying Solomonoff induction is totally well-defined as a mathematical
concept. You are saying it isn't well-defined as a computational entity.
These are both essentially true.
Why you might insist that program-space is
On Sun, Jul 18, 2010 at 11:09 AM, Abram Demski abramdem...@gmail.comwrote:
Jim,
I think you are using a different definition of well-defined :). I am
saying Solomonoff induction is totally well-defined as a mathematical
concept. You are saying it isn't well-defined as a computational entity.
Abram,
I was going to drop the discussion, but then I thought I figured out why you
kept trying to paper over the difference. Of course, our personal
disagreement is trivial; it isn't that important. But the problem with
Solomonoff Induction is that not only is the output hopelessly tangled and
From: Jim Bromer jimbro...@gmail.com
To: agi agi@v2.listbox.com
Sent: Sun, July 18, 2010 9:09:36 PM
Subject: Re: [agi] Comments On My Skepticism of Solomonoff Induction
Abram,
I was going to drop the discussion, but then I thought I figured out why you
kept trying
Jim,
I'm still not sure what your point even is, which is probably why my
responses seem so strange to you. It still seems to me as if you are jumping
back and forth between different positions, like I said at the start of this
discussion.
You didn't answer why you think program space does not
Jim,
Saying that something approximates Solomonoff Induction doesn't have any
meaning since we don't know what Solomonoff Induction actually
represents. And does talk about the full program space, merit mentioning?
I'm not sure what you mean here; Solomonoff induction and the full program
On Wed, Jul 14, 2010 at 7:46 PM, Abram Demski abramdem...@gmail.com wrote:
Jim,
There is a simple proof of convergence for the sum involved in defining the
probability of a given string in the Solomonoff distribution:
At its greatest, a particular string would be output by *all* programs.
Subject: Re: [agi] Comments On My Skepticism of Solomonoff Induction
On Wed, Jul 14, 2010 at 7:46 PM, Abram Demski abramdem...@gmail.com wrote:
Jim,
There is a simple proof of convergence for the sum involved in defining the
probability of a given string in the Solomonoff distribution:
At its
I think that Solomonoff Induction includes a computational method that
produces probabilities of some sort and whenever those probabilities were
computed (in a way that would make the function computable) they would sum
up to 1. But the issue that I am pointing out is that there is no way that
Jim,
Yes this is true provable: there is no way to compute a correct error
bound such that it converges to 0 as the computation of algorithmic
probability converges to the correct number. More specifically--- we can
approximate the algorithmic probability from below, computing better lower
We all make conjectures all of the time, but we don't often don't have
anyway to establish credibility for the claims that are made. So I wanted
to examine one part of this field, and the idea that seemed most natural for
me was Solomonoff Induction. I have reached a conclusion about the subject
Jim,
The statements about bounds are mathematically provable... furthermore, I
was just agreeing with what you said, and pointing out that the statement
could be proven. So what is your issue? I am confused at your response. Is
it because I didn't include the proofs in my email?
--Abram
On Thu,
Last week I came up with a sketch that I felt showed that Solomonoff
Induction was incomputable *in practice* using a variation of Cantor's
Diagonal Argument. I wondered if my argument made sense or not. I will
explain why I think it did.
First of all, I should have started out by saying
as they are now understood.
-- Matt Mahoney, matmaho...@yahoo.com
From: Jim Bromer jimbro...@gmail.com
To: agi agi@v2.listbox.com
Sent: Wed, July 14, 2010 11:29:13 AM
Subject: [agi] Comments On My Skepticism of Solomonoff Induction
Last week I came up
Jim,
There is a simple proof of convergence for the sum involved in defining the
probability of a given string in the Solomonoff distribution:
At its greatest, a particular string would be output by *all* programs. In
this case, its sum would come to 1. This puts an upper bound on the sum.
Since
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