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Re: [computer-go] Re: What is Thought?
> Respectfully, that's not Occam's razor. There are a
> multiplicity of possible new theories, in fact an
> infinite number of them. There are even an infinite
> number that fit the data. Occam's razor tells you
> which one to choose, so it's evidently a much more
> sophisticated principle than the one you are suggesting.
>
> But, moreover, Occam's razor has been studied
> intensively in the computer science community for
> 20-40 years, making considerable intellectual progress.
> The Occam's razor literature that *What is Thought?*
> explains thus deals with a more powerful principle than the
> one posited by Occam in the 14th century. And *What is
> Thought?* extrapolates this research to an even more
> powerful principle, explaining mind in a broad and
> meaningful way.
I appreciate the research in the field, which I have read but will not
reference, because I have drawn conclusions other than the authors
intended. However, I believe that it is a contradiction in itself, that
"The simplest explanation which fits the data should be prefered" requires
years of research to validate and pages upon pages of proofs.
There are experiments which consistently show that given a simple
algorithm such as neural nets or decision trees can perfectly learn a
concept on the training data, and at the same time aggregated versions of
the same algorithms will always do better on the test set.
There are proofs that "explain" these results by claiming that a
representation exist for the neural network and or decision tree which
represents the concept learned by the aggregated version, but the result
is computationally infeasible to find.
In any case the actuall more complicated explanation fits the data as well
as the actuall simple version, but the more complicated one generalizes
better and therefore is preferred. If Occam's Razor cannot explain this
result without much explanation, then we need to get a new theory.
Aggregation, is using multiple classifiers which are slightly different,
then through voting to choose a classification. The different classifiers
can be obtained by the order which the data is presented to the algorithm,
or by training the algorithm on a randomly selected subset of the testing
examples.
Furthermore much of the research supporting Occam's Razor is done on
decision tree's, where a person can take a decsion tree which has been
built greedily and prune off the some the branches making a simpler
concept, and improve the generality, but not as well as the aggregated
versions. The researchers, then claim that simpler theories are prefered
and thus Occam's Razor holds. Yet they do not fit the original data as
well, so Occam's Razor does not apply.
Regards,
Robin Kramer
P.S.
Are you citing yourself? Is that not a bit like I am correct, because I
am me.
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