Hi (esp. Ben),
here's my feedback on
https://wiki.opencog.org/w/Measuring_Surprisingness
Let me jump right into the matter
1. maxSub = max{ g(coh(A1)) * g(coh(B1)) * g(coh(C1)) * P(A1 B1 C1) |
A1 is a subset of A, and B1 is a subset of B, and C1 is a subset of C) }
I think is wrong because
1.1. I don't think coh(A1) to coh(C1) should be used, but rather
coh(A) to coh(C). This depends on the exact definition of coh
of course but I would think that the coherence of a set should
be defined by the regularities within its subsets, not its
supersets, it seems to much to ask (I mean, I can't expect the
universe to be regular just cause my computer file system is
in order, etc, the other way around would work better though),
but again it's a question of definition...
1.2. Even if the coherences set to 1 (best case) P(A1 B1 C1) may
still badly underestimate P(A B C) (unless coh(A1) somehow
implies that P(A1)~=P(A) for superset A of A1, which I don't
see why). The example calculation maxSub(CAR, horror)=
P(Bangui horror) = .0004 is consistent with that
observation. I suspect the intended formula is
maxSub = max{ g(coh(A1)) * g(coh(B1)) * g(coh(C1)) * P(A1 B1 C1) *
P(A)/P(A1) * P(B)/P(B1) * P(C)/P(C1) | A1 is a subset of A, and B1 is a
subset of B, and C1 is a subset of C) }
that is rescaling factors P(A)/P(A1), etc, have been put.
Another option I guess would be to define maxSub as the mirror
of maxSuper (i.e. swapping supersets for subsets).
2. minSub = min{ h(coh(A1)) * h(coh(B1)) * h(coh(C1)) * [ P(A1 B1 C1) +
minInd_{A*, B*, C*} ] | A1 is a subset of A, and B1 is a subset of B,
and C1 is a subset of C) }
where A* = A - A1, etc.; and minInd_{A*, B*, C*} indicates minInd
evaluated at A*, B*, C* rather than A, B, C. The point of
The explanation ends with "The point of". But I think I understand,
however I don't think it's correct, it seems minInd_{A*, B*, C*} is
gonna underestimate too much the rest because it dismisses
combinations such as P(A* B1 C1), P(A1 B* C1), etc. Thus IMO better
use the scaling factors as in my correction of maxSub. Actually,
the example
minSub(CAR, horror) = P(Bangui horror) + ( P(CAR-Bangui horror) -
P(CAR-Bangui)P(horror) )
doesn't match the formula so maybe it has a typo, or I
misunderstood, still seems wrong/incomplete though.
Obviously I understand that these are heuristics and so they don't
have to be correct, though I suppose they could be better (kinda the
definition of a heuristic). Other than that I think it makes a lot of
sense.
More general remarks...
3. It seems the intervals (obtained from minInd, maxInd, etc) used to
measure the deviation between expectation and "reality" could be
replaced by second order distributions. This would avoid the
possible problem of having too wide intervals, and would also allow
concepts based on fewer data points to not be too misleading.
Actually I recall being asked by Misgana some code to calculate the
Jensen-Shannon divergence for some interestingness-based
attentional focus experiments, so maybe it has already been
attempted, even rudimentarily.
4. Last point, I just want to be sure I understand why surprisingness
is useful. It seems to me, if we agree that surprisingness is the
difference between expectation and reality, it then is a useful
indicator to gain knowledge (i.e. perfect our model of reality).
Also, surprisingness is subsumed by interestingness, right?
Something interesting isn't necessarily surprising, but something
surprising is (always?) interesting. And something interesting is
something worth focusing on, so surprisingness is a particular
mechanism to detect and deal with interestingness, right? Anyway, I
know it's pretty basic, and I don't expect much disagreement but
natural language is ambiguous (especially to me) so...
Thanks,
Nil
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