Comments on Nirenberg et al.
Some people have asked why we
used the measure we did to assess the role of correlations. Why didn't
we just measure information
when the two cells were recorded at the same time, measure
information when the two cells were recorded at different times,
and then take the difference? We did do this. In fact, it was the
first thing we tried, and we called the
(click to see the plot:
You can see from the plot that
Ishuffled and I are about the same; sometimes
Ishuffled is greater than I, sometimes it's
less than I, but it never differs by more than 10%.
The reason we didn't use I-Ishuffled in
the paper is that there's a potential confound. One can, in principle,
get cases where I-Ishuffled=0, but
correlations are actually important. This could happen because of
cancellation effects (explicit examples can be provided, if you're
The reason we used our measure, Delta I, is that it's an
upper bound on
information loss. Thus, if Delta I=0, there is an
absolute guarantee that one can ignore correlations and recover
all the information in the responses.
One last thing ... the fact that the maximum information loss measured by
Delta I (11%) was not much more than the maximum value of
|I-Ishuffled| (10%) indicates that
the cancellation effects we were worried about
don't happen in real life. But there was no way to know that until
we did the analysis with Delta I.
Markus Meister and Toshihiko Hosoya and Mike Berry and Elad
Schneidman submitted comments to Nature, but they
were not published. Here we provide a copy of their comments and our
responses for the interested reader
Meister and Hosoya's comment:
Our reply to Meister and Hosoya:
Berry and Schneidman's comment:
Removed at their request
Our reply to Berry and Schneidman:
More fun facts about Delta I:
Delta I provides a universal bound on optimal cost functions.
Delta I is an upper bound on information loss.
When it comes to comparing codes, Delta I has been used
much more widely than you might think.
Or, get all of them with one simple mouse click.
to Sheila Nirenberg's home page.
to Peter Latham's home page.