Re: cse471 homework 4

[Subbarao Kambhampati <rao@asu.edu>]

From: Monika <monika.s@asu.edu>
Subject: Re: cse471 homework 4
Date: Mon, 03 Dec 2001 18:01:34 -0700 (MST)
Message-ID: <Pine.GSO.4.21.0112031758270.12970-100000@general1.asu.edu>

monika.s> Hello Rao,
monika.s> 
monika.s> I guess you missed my e-mail. I still haven't figured out what the enumeration
monika.s> is. I have asked a few students and Terry, but neither of them could tell me
monika.s> what the enumeration is. Could you briefly explain what does 'a' stand for in
monika.s> the enumeration algorithm and give an example of an enumeration calculation? I
monika.s> couldn't figure out what we are summing over in the example in your slides.
monika.s> 
monika.s> Monika

I think a stands for the different values of alarm variable (i.e., a=T 
and a=False) 

In general, if you wanted to compute the 

P(J,M)  (i.e., probability john and mary call)

then the enumeration algorithm simply marginalizes (sums over all the
values of) the remaiming variables 


Since the rest of the variables are a, b and e (alarm, burglary and
earthquake)

we just have to do 

 Sum-over-a  Sum-over-b Sum-over-e P(a,b,e,J,M)

this 

will expand into 6 joint distribution entries

P(A,B,E,J,M)
P(~A,B,E,J,M)
P(A,~B,E,J,M)
and so on ..

you can easilty compute the joint distribution entries using the
normal semantics of bayes nets.

Rao

ps: enumeration method is just _barely_ better than computing the full 
joint. It just computes the entries of the joint that are needed to
answer the query. But what it saves, it loses in not being able to
capitalize on repeated computations. Variable elimination method is
the first reasonable method in that sense.