Dear Dr. Zadeh,
Recently you posted the following causality-related question:
I am a manufacturer of raincoats. To increase sales, I
increased spending on advertising by 20%. Sales increased
by 10%. As a manufacturer, I would like to know if the
increase in sales was caused by the increase in spending on
advertising?
Moreover, you stated:
My contention is that no existing theory of causality can answer
this question.
We disagree. To our understanding, the current theories of causality can
in fact handle this example. Moreover, the answer to the question in your
example is precise, complete, formal, algorithmic and principled.
The precise answer is:
The information provided in this problem statement is
not sufficient to derive a unique answer to the
question asked. Both answers: Yes and No are
consistent with the problem statement.
This answer does not amount to skirting the question, in the same way that
"more information is needed" is the correct answer to the question "If I
have sold 100 raincoats today (some red and some black), how many red
raincoats have I sold today?"
And if we contended that no existing theory of arithmetic can answer the
above question, then what would that mean? We think that a proper theory
would be one that would tell us exactly how much information we would need
to uniquely answer the above question -- i.e., we would at least need to
know how many black raincoats were sold today.
Thus, a theory of causality that can handle your raincoat problem is one
that can determine when we have sufficient information in the problem
statement to derive definitive answers, when the information is merely
sufficient to derive bounds (on probabilities of causation) and what kind
of information we need to add to a problem statement to render the answer
definitive. If you are asking whether such a theory of causality exists,
then we believe that the answer is yes.
There are a number of resources out there which answer these questions in
a principled way. One example would be Pearl's book "Causality" (in
particular Chapter 9), but there might be others.
Chen Avin, Carlos Brito and Mark Hopkins
Cognitive Systems Laboratory
UCLA
-------------------------------
Dear all:
I am being told by very knowledgeable members of the UAI
community that causality theories X,Y,Z can handle the "raincoats"
example in my message(l0/3/03;l0/4/03.) But what I have not seen so far,
is a description of how it can be done. For convenience, let me
restate the example. Note that the "raincoats" example is typical of
causality-related problems which arise in real-world settings.
I am a manufacturer of raincoats. To increase sales, I
increased spending on advertising by 20%. Sales increased by l0%. As a
manufacturer, I would like to know if the increase in sales was caused
by the increase in spending on advertising?
My contention is that no existing theory of causality can
answer this question. The problem is that the increase in spending on
advertising was just one of many factors which resulted in the increase
in sales. Some of these factors are visible to me and some are not.
Since the increase in spending on advertising is just one of possibly
many factors, it would be unreasonable to assert that it and only it
caused the increase in sales. Thus, it is necessary to define a degree
to which the increase in spending on advertising caused the increase in
sales. Clearly, the degree cannot be defined precisely. Furthermore,
statistical techniques cannot be used since we are not dealing with an
experiment which can be repeated.
I would be perfectly willing to retract my contention if
someone could show how the "raincoats" example can be handled by an
existing theory.
Warm regards.
Lotfi
- --
Lotfi A. Zadeh
Professor in the Graduate School, Computer Science Division
Department of Electrical Engineering and Computer Sciences
University of California
Berkeley, CA 94720 -1776
Director, Berkeley Initiative in Soft Computing (BISC)
Address:
Computer Science Division
University of California
Berkeley, CA 94720-1776
[EMAIL PROTECTED]
Tel.(office): (510) 642-4959
Fax (office): (510) 642-1712
Tel.(home): (510) 526-2569
Fax (home): (510) 526-2433
Fax (home): (510) 526-5181
http://www.cs.berkeley.edu/People/Faculty/Homepages/zadeh.html
