Would you argue that any of your examples produce good results that are
not comprehensible by humans? I know that you sometimes will argue that the
systems can find patterns that are both the real-world simplest explanation
and still too complex for a human to understand -- but I don't believe that
such patterns exist in the real world (I'd ask you to provide me with an
example of such a pattern to disprove this belief -- but I wouldn't
understand it :-).
Well, it really depends on what you mean by "too complex for a human
to understand."
Do you mean
-- too complex for a single human expert to understand within 1 week of effort
-- too complex for a team of human experts to understand within 1 year of effort
etc.
-- fundamentally too complex for humans to understand, ever
??
My main point in this regard is that a machine learning algorithm can
find a complex predictive pattern, in a few seconds or minutes of
learning, that is apparently inscrutable to humans -- and that remains
inscrutable to an educated human after hours or days of scrutiny.
This doesn't mean the pattern is **fundamentally impossible** for
humans to understand, of course... though in some cases it might
conceivably be (more on that later)
As an example consider ensemble-based prediction algorithms. In this
approach, you make a prediction by learning say 1000 or 10,000
predictive rules (by one or another machine learning algorithm), each
of which may make a prediction that is just barely statistically
significant. Then, you use some sort of voting or estimate-merging
mechanism (and there are some subtle ones as well as simple ones,
e.g. ranging from simple voting to an approach that tries to find a
minimum-entropy prob. distribution for the underlying reality
explaining the variety of individal predictions)
So, what if we make a prediction about the price of Dell stock tomorrow by
-- learning (based on analysis of historical price data) 10K weak
predictive rules, each of which is barely meaningful, and each of
which combines a few dozen relevant factors
-- merging the predictions of these models using an
entropy-minimization estimate-merging algorithm
Then we are certainly not just using nearest-neighbor or CBR or
anything remotely like that.
Yet, can a human understand why the system made the prediction it did?
Not readily....
Maybe, after months of study -- statistically analyzing the 10K models
in various ways, etc. -- a human could puzzle out this system's one
prediction. But the predictive system may make similar predictions
for a whole bunch of stocks, every day....
There is plenty of evidence in the literature that ensemble methods
like this outperform individual-predictive-model methods. And there
is plenty of evidence suggesting that the brain uses ensemble methods
(i.e. it combines together multiple unreliable estimates to get a
single reliable one) in simple contexts, so maybe it does in complex
contexts too...
I would also note that, on a big enough empirical dataset, an
algorithmic approach like SVM or the ensemble method described above
definitely COULD produce predictive rules that were "fundamentally
incomprehensible to humans" --- in the sense of having an algorithmic
information content greater than that of the human brain. This is
quite a feasible possibility. But I don't claim that this is the case
with these algorithms as applied in the present day, in fact I doubt
it.
-- Ben G
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