au revoir from skyharbor..

Folks

 The grades have been posted and you should be able to see them.

The homework 4 is available for pickup from the TA. The final exam has to be kept with me according to university rules.

It was fun teaching you all this semester and I hope to see you around and may be even in other courses.

cheers
Rao

AI homework 4 and project make up

Hi, folks.

If you need to pick up your hardcopy of homework 4 and project make up,
you can stop by my office (BYENG561AC) on Monday and Tuesday
(Dec.18th/19th). I should be around most of the time.

The instructor keeps the copies of final. You need to check with him if
you want to see the final.

Have a good holiday!!
-Lei

Hold--I say--*hold*--the presses (egregious error in the previous cumulatives)...

So it has just been pointed out to me by the ever-watchful TA that I took the midterm grade twice instead of
midterm and final--in computing the exam total and thereby the cumulative. My apologies.

Here I believe are the *real* cumulatives. Also, this does change the "top" person in one of the sections.  They now can
proffer their advice to me about where the grade cutoffs should be... (and my apologies to the person who
had the "Dewey Wins" dejavu--I think he/she did a great job in the class over all).


Rao

ps: By the way, if you were tormented with too much work, just think of the poor TA who had to grade everything you guys did
       (and continued to look out for your interests even in the eleventh hour). Lei more than continues the tradition of
      outstanding TAs for cse471..

Final cumulative ranking (required marks)

Here is the final cumulative ranking according to my Excel (I will have it checked by the TA once but it sort of looks correct).

I will let you in on an early secret.  The very top student in both sections (471 and 598) are guaranteed to get an A+ (although
they both should be chastised for not doing well on the final).

I am willing to hear (hear--not necessarily follow) from them about where the grade cutoffs should be in their sections 
for A+, A, A-, B+, B, B-, C+, C,  D and E. 

Rao

ps: Mails requesting a favorable consideration of your own case will likely result in me thinking unfavorably of you. So, don't do it ;-)

Final exam marks..

Final has been graded. Before witnessing the bloodbath, let us
pause--in the true Bhagavadgita fashion--
and take stock of the big answers ;-)

Here are some general observations:

1. Many people messed up the bomb in the toilet problem.
Here is one complete answer.

1. B(p1,S0) V B(p2,S0)
2. forall s, p B(p,s) => sf(Result(d(p),s))
3. ?sf(s)

1 is already in the clausal form. 2 becomes ~B(p,s) V sf(Result(d(p),s))
3, after negation becomes forall s ~sf(s) which in clausal form is ~sf(s)

You can resolve 3 with 2, and then resolve ~B(p,s) twice with 1 to
get an empty clause

The proof doesn;t give you a plan as it is existential proof.

Backward chaining won't work because the first clause is non-horn!

2. for part two of the flu epidemic question, many people missed the point that
the CPTs already take care of the ignorance and lazyness..

3. The likelihood of Flu in the enumeration question works out to be
about ~0.733

4. In the likelihood weighting question, you ignore the last few
samples since you
have to clamp RN and BA to "False"

5. The answer to how likely is flu on the first day given the
evidence of the kit on the second
day turns out to be ~0.824 [You guys could have used the project 3
applet to check your answers
before submitting ;-)]

6. for the third part of the DBN question, the best way to argue with
your friend is to
point out that belief revision can happen in diagnostic as well as
causal direction.

7. For the Neuman's party, the size of the hypothesis space is
2^(2^3)=256 (where
3 is the number of features of the problem)

8. For the same question, some people used their commonsense rather
than calculations

9. The answers to deep thoughts section made for interesting reading.
Seemed like some people really did
get something out of the course--and that is as apt a gift for the
winter solstice as any..

cheers
Rao

------
(*) Bhagavadgita is considered the Cliff's notes essence of Hindu
philosophy--and it is
a discourse on good and bad between Krishna and Arjuna--two
characters in the Indian
epic Mahabharata--at the outset of the big war--with two opposing
armies pitched and ready to
go at each other. Imagine, if you will, a philosophical discussion
between G.W. and Saddam in the deserts
of arabia, with the republican guard and marines ready to go at each
other once they stop talking..

Hw4 grading details

Below are the statistics of hw4:

HW4	Without Extra Credits(139)
	Mean	Median	Highest
Overall	95.4	106	136
Under	77.4	76
Graduate	109	117

For this homework, as you can see, the full score is very big: 139 + 12(for extra credit)
Note that the weight I finally adopt for grading is a little different as shown in the solution.

P1(30): 3+4+5+6+3++ 3+ 6
P2(15): 3+3+3+3+3
P3(24): 3+3+3+3+6+6
P4(15): 3+3+3+3+3
P5(15): 6+3+3+3
P6(6): 3+3
P7(30): 3+6+3+3+3+3+4+5
P8(4).

Thus, the total is 30+15+24+15+15+6+30+4 = 139.

One common error:
P1, part C to compare p1, p2, and p3.
Lots of students provide p1<=p3 or p3<=p1. Actually, unless you know the exact CPT, both cases are possible. I took 2 pts off for this unless you provide solid justification.

Re: Final Exam

You don't need this information. For perceptrons, it is customary to assume that the learning rate alpha
already contains the gradient information (i.e., just use alpha in place of alpha*gradient_of_activation_fn)


Rao

On 12/10/06, Nanan <nanan9177@gmail.com> wrote:

Dear Dr. Kambhampati,

 

Would you please tell me the activation function of the Neuman's Parties question? Thanks :)

 

Cheers,

Nan

Re: Clarification needed on DBN question

In this part of the question you calculate the probability that the patient has
flu on the *second* day given that the test on the *second* day came positive.

(In the next part, you have an argument with your friend about the flu probability
on the first day).

Rao

On 12/10/06, Srinath Reddy Bodala <Srinath.Bodala@asu.edu> wrote:

Dear Prof,

I need clarification regarding a question on DBN. I am reproducing the
question here for your convenience.

Question:

Given your representation above, after one days' stay in the hospital
the patient is tested and the test came positive. (1) What is the
probability that the patient actually has flu? Show your calculation.

I have doubt regarding whether I have to calculate probability of
patient having flu on the first day or second day.

Hope I am clear.

Thanks,
Srinath Reddy B.

Correction to the last question on page 5

There is an error in the specification of the last question for page 5.

Here is the correct version (I also changed the online version). (Thanks to Mandar
for pointing it out).

Rao

[3] Suppose we decide to do inference by sampling techniques—specifically  
likelihood weighting. Suppose we are trying to compute probability 
that Rhino Virus is true given that the patient has no fever and no body aches. 
Suppose we generate a sample from the network using likelihood weighting.  
Assume we sample the network in the order of Rhino Virus, Dyspotensia, Flu, 
Runny Nose, Body Aches and Fever. 
Suppose our samples return True, False, False, True, True, False 
(take only the samples you need). What is the complete sample and what is its weight?  

flu vs. flue

yes-- flu is the correct short speling of influenza (for some wierd reason
I tend to misspell it as flue).

rao

On 12/9/06, Yunsong Meng < Yunsong.Meng@asu.edu> wrote:

Hi profrssor Rao,
  In the part C of Arizona Flu Epidemic, when you say "flu", do you mean "flue" in the question?


--
Meng,Yunsong
Research Assistant
Department of Computer Science and Engineering
School of Computing & Informatics
Arizona State University

Interesting story..

http://www.cnn.com/2006/EDUCATION/12/06/grades.for.cash.ap/index.html

This is *not* a subliminal suggestion ;-)

rao

final exam

Some people asked me if I intend to add any more questions to the final exam.
At this point, the probability is vanishingly small.

I will of course send any clarifications or bugs others unearthed.

Remember that the exam is due on Tuesday 5pm unless you have been
explicitly granted an extension.

good luck
Rao

(oops trying again) Re: The missing figure in the seinfeld problem in homework 4 solutions

Trying again...

rao

On 12/8/06, Subbarao Kambhampati <rao@asu.edu> wrote:

Here is the missing figure on how to represent George's party as a neural net

rao

The missing figure in the seinfeld problem in homework 4 solutions

Here is the missing figure on how to represent George's party as a neural net

rao

Final exam--beta preview..

I decided to release the final now so you can start mulling over it.

you can get it from
   http://rakaposhi.eas.asu.edu/cse471/f06-final-rt.pdf

I may add a few more questions if I realize tomorrow that some aspects
have not been covered adequately.

I am also willing to hear comments--until tomorrow morning--on the fairness
of the distribution of marks on the test ( e.g. is it PAC..)

If I make any changes, I will of course let you know.

Good luck

Rao

Status on final exam...

Folks:

 This is just a heads-up on the status of the final exam. I am running behind schedule in setting it--I have about half of it ready, but  may have to do an all-nighter to complete it
and release it to you by tomorrow morning. (In the worst case, if I don't have it all ready, I will have to release what I do have in a "socket" fashion--I am trying to avoid that)

I am also aware of the fact that some of the figures in the homework are not showing. Unfortunately those figs seem to have disappeared. I will try to
redraw them and send them to you

thanks for your patience.

Rao

Homework 4 solutions posted

The homework 4 solutions are posted.

rao

Some additional comments

Here are some more of the interactive review comments that were emailed that I am redirecting to the blog... (three other comments were directly
added to the blog and can be found at https://beta.blogger.com/comment.g?blogID=7807789293679070909&postID=1259600912214366833 )

Eventually, with Lei's help, we hope to post a summary description as acquired wisdom.

rao

===================

Srinath Reddy Bodala

to Subbarao

show details

Dec 5 (2 days ago)

Dear Prof,

 

Going straight into the topics I liked the most, I enjoyed adversial search, alpha-beta pruning. I also enjoyed doing the project on building tic-tac-toe program. But there were too many no result games so it was a bit boring there, so may be we should have used more interesting game for the project. I also liked learning various types of logic, working on pattern databases heuristic.

 

Thanks,

Srinath ReddyB. 


==============

						Reply   Reply to all  Forward  Print Add Al to Contacts list  Delete this message  Report phishing  Show original Message text garbled?
		Al Welle	to Subbarao, Lei	show details	9:20 am (40 minutes ago)

I found there were many things about AI that I had been mis-informed about before taking the class. Primarily about the usefulness of Neural Networks. I was greatly surprised to see how much better, more efficient and flexible, SVM was compared with Neural Networks.

 

I think I learned a great deal, but I think I either missed or could have learned more by a large factor. I believe that to fully do justice to the material there should be a 3 course sequence for Artificial Intelligence.

 

I was surprised at how little detail we went into regarding the math behind some of the equations. The basic understanding of what the equations do is fairly simple, but the math behind it seems to get exponentially complex for every level of depth you dive into it. (Which is probably why we use a computer to do the math, huh?)

 

I gained some insight into PAC and Bias and how they relate to both my own introspective thought process (I had always thought I kept an open mind and considered alternative theories equally until I had sufficient evidence but now, after having forced myself to actually observe my own thoughts with an eye to bias / logical-leaps I find I make these mistakes much more often than I would originally have believed)

 

I've never loved a class as much while hating it so throughly. The material is fascinating and that's at the level of "just barely indicitive of how useful this could be" but at the same time it's maddening for me to not almost instantly grasp concepts and implementations. I'm not used to having to THINK about a problem for a long time. Even worse I often found myself not being able to fully comprehend something and having to accept that I wasn't going to master the material in a week, or two, or even over the whole course, but would have to keep burning "mental clock cycles" on problems long after the semester ends.

 

For instance in planning I think I have a good idea of "regression planning" and "mutexes" and when graphs level off. But when actually having to explain it I'm reduced to "proof by inspection." .. That is "um, can't you just see that's the answer, cause I'm really not able to draw you a graph in two-dimensions black-and-white with a pencil." 

 

In short "the toughest class you'll ever love to hate" best describes my aqquired wisdom for the course.

 

Apologies for the length,

 

Al

==========================

office hours today..

I will hold office hours at 3pm as announced.
Additionally, I should be in my office most of the day--if you
have questions drop by.

rao

Re: For those people who wanted to take part in the interactive review but didn't get a chance..

One correction: Lei.Tang@asu.edu is not my email address.

Please send to L.Tang@asu.edu

-Lei

Subbarao Kambhampati wrote:

If logging onto the class blog acts as an additional disincentive, just send your
input to me and lei ( rao@asu.edu, lei.tang@asu.edu -- use the same subject as this mail)


rao

On 12/5/06, Subbarao Kambhampati <rao@asu.edu> wrote:

Folks:
 Those of you who wanted to take part in the interactive review but didn't get a chance because
we ran out of time--please add your comments to the blog--preferaby as a response to this mail.

We will then collect those in making the acquired wisdom page for this year (it seems odd to have
acquired wisdom of only half the clas...)

thanks
Rao

On the "berkeley" comment at the end of the class..

My comment comparing 471 to the berkeley intro to AI may have come across a bit more jarring than I intended.

Looking beyond the bluster, I think I do have something serious to say here, so let me try once more.

My philosophy is that *what* is taught in a course shouldn't depend on *where* it is taught. The demands and
coverage of the course should not be diluted based on anyone's reduced expectations of a student population
(since this is a vicious slippery slope and is ultimately detrimental to the students themselves). 

Your grade may well depend on who else took the course with you, but the material and demands should not.

I should also make it clear that there was no real deluge of students requesting me to reduce the demands or coverage.
In all the semester, I probably heard about one and a half comments of this vein. Most others seemed to take it in stride;
and I respect that immensely.

regards
Rao

Re: For those people who wanted to take part in the interactive review but didn't get a chance..

If logging onto the class blog acts as an additional disincentive, just send your
input to me and lei ( rao@asu.edu, lei.tang@asu.edu -- use the same subject as this mail)


rao

On 12/5/06, Subbarao Kambhampati <rao@asu.edu> wrote:

Folks:
 Those of you who wanted to take part in the interactive review but didn't get a chance because
we ran out of time--please add your comments to the blog--preferaby as a response to this mail.

We will then collect those in making the acquired wisdom page for this year (it seems odd to have
acquired wisdom of only half the clas...)

thanks
Rao

Attendance statistics...

Here are the self-reported attendance statistics, for your edification:

17  had perfect attendance (18 if you include me ;-)
4 missed 1 class
6 missed 2 classes
3 missed 3 classes
1 missed 4 classes
1 missed 7 classes

This gives a mean absence rate of 1.125 classes/person

[Of course, I only had 32 responses and the roster says I have 37 students.
So either five of you apparently either didnt show up today or  were in class but forgot to
turn in the following information. Either way, please do, or I will assume you missed all classes ;-)]

 

CSE 471/598 Attendance/Participation Sheet

 

 

Name:____________________________

 

 

Total number of classes missed:_______________________

 

 

                  The number missed with prior notification:___________________

 

 

Number of times you asked a question in the class (circle one):

 

    Never        Maybe once or twice          5-10 times        >10 times

 

(Please give your best estimate)

For those people who wanted to take part in the interactive review but didn't get a chance..

Folks:
 Those of you who wanted to take part in the interactive review but didn't get a chance because
we ran out of time--please add your comments to the blog--preferaby as a response to this mail.

We will then collect those in making the acquired wisdom page for this year (it seems odd to have
acquired wisdom of only half the clas...)

thanks
Rao

Reminder: Interactive Review tomorrow..

Folks

 Just a reminder that there will be an interactive review tomorrow. You will be asked to say a couple of words
(1-2min max) about the topics/ideas that you particularly enjoyed or got bored stiff.

(If you are completely bereft of ideas, you may look at http://rakaposhi.eas.asu.edu/cse471/acquired-wisdom-031.htm
for what Fall 2003 folks said. Don't copy their opinions though ;-)

Also, please note that this is session is *not* meant for expressing your opinions on the quality of instruction/instructor.
You have the CEAS evaluations for that.

see you all tomorrow bright, chirpy and enlightened..

rao

One last extension: Homework 4 will be accepted until Wednesday 4:30pm

I have been getting a huge number of questions on homework 4 today which makes me think
that people have only started working on it seriously today.

Since the homework covers a lot of topics I really would like for you guys to try and do some justice
to them. (That and I would hate to see people falling asleep in the last class after staying up all night today.)

So, I am going to allow people to submit homework 4 until wednesday 4:30pm.

Note of course  that  you can still submit it tomorrow and be done with it...

rao

clarification on b and d of qn 3 (the robot question).

Several people asked for clarification as to how b and d differ.

The idea is that in "b" you only consider the question from a pure graph-theoretic
perspective (e.g., purely in terms of directroute(x,y)). Here, we don't need to consider
situation calculus at all.

In "d" you are thinking in terms of actions and effects and specific plans (so you need to consider situation calculs).

Hope this helps. (People who are still confused might want to skip b and do the rest..)

Rao


=====the problem from homework

In this exercise, we will consider the problem of planning a route for

a robot to take from one city to another. The basic action taken by
the robot is Go(x,y) which takes it from city x to city y if there is 
a direct route between the cities. DirectRoute(x,y) is true if and
only if there is a direct route from x to y; you can assume that all

such facts are already in the KB (see the map on page 63 of the text
 book). The robot is in Arad and must reach Fagaras.

a. Write a suitable logical description of the initial situation of
the robot

 b. Write a logical query whose solutions will provide possible paths
to the goal

c. Write a sentence describing the Go action

d. Write a suitable query whose answer can provide the plan for the
robot to go from Arad to Fagaras. 


e. Use resolution refutation to answer the query and output the plan.

f. Suppose the Robot was wearing a redshirt and green pants when it
was in Arad. We want it to be wearing the same dress when it reaches 

Fagaras. Explain how your answers to the parts a-e change.

Fwd: Homework 4 Weight

---------- Forwarded message ----------
From: Subbarao Kambhampati <rao@asu.edu>
Date: Dec 4, 2006 4:14 PM
Subject: Re: Homework 4 Weight
To: Kartik Talamadupula <tkartik@asu.edu>

Homework 4 will have more weight than normal homeworks. (it covers a large number of topics)

I would say something closer to 10%+. (Also note that there is a *required* part in homework--as part of the learning question).

rao

On 12/4/06, Kartik Talamadupula <tkartik@asu.edu> wrote:

Dr Rao,

 

Can you please tell me how much homework 4 will be worth in terms of percentage of the total grade? I know you don't like giving out numbers, but this would genuinely help.

 

Am I right in assuming that it would have to be lesser than or equal to about 5%, since you said there is 25% remaining credit to be earned and I am estimating the final should be at least 20%, given how much the midterm was worth.

 

Kartik

Current cumulatives (with Project 3 and Project 4 marks thrown in--75% of the grade accounted for)

Folks
 Here--FYI--is the current cumulatives. I included the project 3 (at 7%) and project 4 (at 12%). The 5 projects thus come to 1+10+10+7+12=40pts.
Project 4 will be returned tomorrow.

Let me or the TA know if there are any discrepancies in the entered grades.

cheers
Rao

Homework 4 socket closed.. with two extra credit problems..

Folks:
 I added an additional part to the Seinfeld party problem (part I)--which is about naive bayes classifiers.

I also added the long promised dyanamic bayes net problem.

Both of these are made "extra-credit" and optional.

No more changes will be made to the homework. It will be due in class on Tuesday.

cheers,
Rao

A reference for the discussion on support vector m/c

Here is a reasonably easy to read tutorial article on support vector machines (the pictures I had in the class were taken from it).

http://www.acm.org/sigs/sigkdd/explorations/issue2-2/bennett.pdf

Rao

Fwd: Instructor/Course Evaluations

Folks:
 As per the mail below, I am encouraging you to complete the course evaluations before next wednesday.
Your feedback--especially written comments--will be carefully read.

(By the way, to state the obvious, we get these only after all the grades are submitted etc. So, you can be candid ;-)

rao



---------- Forwarded message ----------
From: James Collofello <JAMES.COLLOFELLO@asu.edu >
Date: Nov 29, 2006 5:41 PM
Subject: Instructor/Course Evaluations
To: "DL.WG.CEAS.Faculty" <DL.WG.CEAS.Faculty@mainex1.asu.edu>



Colleagues,



The Fall 2006 teaching evaluations are scheduled to be available to students starting Wed 11/29 around 9:00 am and will close at Wed 12/6 (reading day) at 12:00 midnight.  Students will be able to access the evaluation tool at:   https://intraweb.eas.asu.edu/eval

Please encourage your students to complete the evaluations or face several nagging email requests.  Good luck on your scores!





James S. Collofello

Associate Dean for Academic Affairs

Ira A. Fulton School of Engineering

Re: Next Tuesday's class format: Interactive Review...

You may also want to bring in notes for more than 2 minutes worth of
interesting things to say, since it is somewhat probable that if you
find something interesting, someone else in the class, speaking before
you, will have found interesting as well.

-Will

On 11/29/06, Subbarao Kambhampati <rao@asu.edu> wrote:
> Folks
>
> It is customary to do an end-of-course review in the last class. My version
> of this is to let *you* do the review. This is called the
> "interactive review" session.
>
> A significant portion of Tuesday's class--which will also be the last class
> of the semester--will consist of interactive review and discussion.
>
> If you are registered for this course, attendance to this class is
> mandatory.
>
> Each of you will get about 2min to hold forth on any of the following:
>
> -->topics covered in the course that particularly caught your fancy (and
> why)
> --> intriguing connections *between* the various topics covered in the
> course that struck you
> --> what topics--if any--got overplayed or should have gotten more coverage
>
> It may be useful for you to make some notes along these lines *before*
> coming to class--so
> you have everything ready to hold-forth when called on.
>
>
> rao
>
> ps: Tomorrow--Thursday--we will have our regular class which will continue
> discussion of Machine Learning
>

Next Tuesday's class format: Interactive Review...

Folks

It is customary to do an end-of-course review in the last class. My version of this is to let *you* do the review. This is called the
"interactive review" session.

A significant portion of Tuesday's class--which will also be the last class of the semester--will  consist of interactive review and discussion.

If you are registered for this course, attendance to this class is mandatory.

Each of you will get about 2min to hold forth on any of the following:

-->topics covered in the course that particularly caught your fancy (and why)
--> intriguing connections *between* the various topics covered in the course that struck you
--> what topics--if any--got overplayed or should have gotten more coverage

It may be useful for you to make some notes along these lines *before* coming to class--so
you have everything ready to hold-forth when called on.


rao

ps: Tomorrow--Thursday--we will have our regular class which will continue discussion of Machine Learning

One more problem added to the homework 4

Pointer to Geoff Hinton lJCAI research excellence award lecture..

Folks

 On Wednesday's make-up class, I mentioned that Geoff Hinton is foremost among the people working on brain-inspired neural networks (there isn't that much work on neural nets in the ML community these days because you can get by with max-margin kernel classifiers instead of multi-layer neural nets. However, understanding the training of multi-layer and recurrent nets does offer the possibility of understanding how human brain works).

Anyways, I mentioned Hinton's research excellence award lecture at IJCAI last year. Here is a link to his slides (he calls this version the
"gentle/after-dinner version" of his talk.

http://www.cs.toronto.edu/~hinton/talks/gentle.ppt

(The other versions of the talk can be found at http://www.cs.toronto.edu/~hinton/talks.html )

enjoy..

Rao

Project 4 help

I have done part of Task 2 and came up with a varsubst function which looks
like:

(defun varsubst (pattern binding)
(if (null pattern) nil
(if (atom (car pattern))
(if (eq '? (car pattern)) ;find matching and return var
;if pattern is (? var)
(if (equal pattern (caar binding)) (list (cadar binding))
;if binding doesn't match, traverse through bindings
(list (match-var pattern (rest binding))))
;else, atom in pattern isn't ?, so append car pattern to return list
(append (list (car pattern))
(varsubst (rest pattern) binding)))
;else, not an atom...pattern is a list
(append (varsubst (car pattern) binding) (if (null (varsubst (rest
pattern) binding)) nil (list(varsubst (rest pattern) binding)))))))

(defun match-var (pattern binding)
(if (equal pattern (caar binding)) (cadar binding) (match-var pattern (rest
binding))))

I'm not sure if it is supposed to look that customized, but it works.

I am now on the rename function and understand that the same generated number
suffix is appended to each variable. I can generate a number such as "112"
but it is in String format. I've been looking around and can't figure out how
to combine "112" and 'rao to produce a variable like 'rao112.

Thanks in advance.

Optional reading on Max-margin classifiers..

Here is an *optional* reading on max-margin classifiers (Support vector machines; kernelization etc)

http://www.acm.org/sigs/sigkdd/explorations/issue2-2/bennett.pdf

Rao

Learning homework problem added (includes playing with the applets)

A Smarter Computer to Pick Stocks

Very interesting article
http://www.nytimes.com/2006/11/24/business/24trading.html?_r=1&oref=slogin

re: Recitation Session, Tuesday 28th November, 1:40->

Just a clarification so you are not going to think I am sneaking in an
extra class ;-) Recitation session is purely optional. 
The regular class for 28th is what was made up yesterday. 

 
rao



==========

Rao brings up the excellent point that everyone ought to be free to
meet on the 28th of November at the normal class time.

So the next recitation session will be held then, in the classroom
itself.  As always, send any specific questions you'd like covered in
more depth, for example, questions on the midterm that you still don't 
understand fully.   Other than that the plan is as usual; cover the
material from the end of the last recitation up till now and comment
on the connections to the homework.

-Will

Audio and video of yesterday's make-up class available online

For those of you who couldn't make it for the make-up class yesterday:

 The audio, video and slides of the lecture are available online. Some notes:

1. The video is a 320x160 video (if you see it at 200% the size and resolution are reasonable).
    The size of the video is a whopping 718mb (so if you want to download it, you will have to be
   on a high-speed internet connection)

2. In two places, in the slides, I replaced the slide used in the class with a better one. In both cases,
   I left the older version in with a warning saying that the replacement slide right next is better.

that is all.

Happy thanksgiving!

Rao

Recitation Session, Tuesday 28th November, 1:40->

Rao brings up the excellent point that everyone ought to be free to
meet on the 28th of November at the normal class time.

So the next recitation session will be held then, in the classroom
itself. As always, send any specific questions you'd like covered in
more depth, for example, questions on the midterm that you still don't
understand fully. Other than that the plan is as usual; cover the
material from the end of the last recitation up till now and comment
on the connections to the homework.

-Will

request for feedback on the first two learning lectures..

Hi all

I know that several of you are simultaneously taking either the grad
or undergraduate level data-mining courses. I was wondering, for those
of you, whether the learning lectures were useful at all or are they
too much of the same thing that you have learned. If you have any
comments let me know--either directly or via the anonymous email
http://rakaposhi.eas.asu.edu/cgi-bin/mail?rao

(Feedback is also welcome from others who are learning about learning
for the first time. I was struck by the unusually stoic demeanors of
the students in the class and was wondering whether the cause was
enlightenment or boredom).

thanks
Rao
[Nov 21, 2006]

*Important*--Please read (about Project 4; upcoming gigantic homework assignment; making up for early projects etc)

Folks

Here are several announcements:

1. It looks like there will not be enough time for a coding oriented project 5. So, project 4 will be the last coding project.
(I can see your disappointed looks; I am sorry it had to be this way..)

2. The main assignment after project 4 is a double homework that has been evolving. I will extend it with problems (and perhaps  mini-applet assignments) on learning. This homework will be done on the last day of the class (5th December--no exceptions).  Furthermore, there may not be an explicit one week gap between the addition of last question and the due date. So, I strongly suggest that you all start working on the problems that are already there.

3. Since there is no project after the prolog one, I am willing to allow students who did very badly in any of the earlier projects a  chance to improve their project grades. If you want to do that, let me and the TA know (and also let us know which project(s) you want to work on and what your grade on it was); we may be able to tell you whether it will be worth your time. (Your final project grade will be a weighted average of the two grades). *All* work must be submitted by the last day of the class--no exceptions.


4. Since project 4 is the last project, I am also willing to take it without penalty until Wednesday make-up class; and with a flat 3*pi % late penalty until next Monday.  Those who have banked an extension can give it until next Monday without penalty.(I know there is no class on Monday--it is your responsibility to hand-in the hard copy--either at the dept office or to the TA)
 [Of course, you can hand it in tomorrow and  spend your time on other things such as the homework.]


that is all

regards
rao

Re: project 4 report question

Thanks for this question. The trace produced by prolog with all the failing paths can be quite large and is pointless to include. I would suggest that appropriately edited trace (where the editing operations only involve *removing* parts of the trace) be submitted.

Rao

On 11/19/06, Mandar Joshi <mandar.joshi@asu.edu> wrote:

Hi Lei and Prof Rao ,

I just wanted to ask what exactly we are expected to show regarding
the output of prolog with domain 2 that is family tree .

(For earlier parts i am including edited output as the trace was very crisp )

The dribble file for domain2 questions  is very large. Should we just mention logical steps that prolog has taken
to prove/answer the question.(not actual console statements ..)   Or we just mention our final answer (along with observations if any)

The actual output can be verified as we are submitting the code also.

If any one of you can throw some light on how much we include in report it would be great .


--
Regards,

Mandar

Fwd: CSE598 - Project 4 - small correction

I haven't quite checked this but am forwarding it none the less
since adding additional background knowledge is not going to
hurt you (and, if Peyman is right, will help you in this case).

Rao


---------- Forwarded message ----------
From: Peyman Nayeri <Peyman.Nayeri@asu.edu>
Date: Nov 16, 2006 4:26 PM
Subject: CSE598 - Project 4 - small correction
To: Subbarao Kambhampati <rao@asu.edu>

Hi,
  For the 4th task in the 4th project there is a hint
saying to add knowledge to the effect that sibling is
a transitive relation. This won't help. We need to add
knowledge to make sibling a symmetric relation.
Cheers,
Peyman




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Bias, generalization and stereotypes: A half-baked lesson in Ethics

[[extra-curricular]]

[ACM suggests that some percentage of CS courses should be spent on discussing
ethics. May be this will fill that role... ]


Inductive  generalizations are what allow the
organisms with their limited minds to cope with the staggering complexity 
of the real world. Faced with novel situations, our ancestors had to
make rapid "fight or flight" decisions, and they had to do biased
learning to get anywhere close to survival. So, we can't really
 seriously ask people not to generalize or not to have biases!

The problem of course is where does this leave us vis-a-vis
stereotypes--the "all Antarciticans are untrustworthy", "all
Krakatoans are smelly" variety. Afterall, they too are instances of 

our mind's highly useful ability to induce patterns from limited
samples. 

So, what, if any, is the best computational argument against stereotyping? One
normal argument is that the stereotype may actually be wrong--in 

otherwords, they are actually wrong (non-PAC) generalizations, either
because they are based on selective (non-representative) samples, or
because the learner intentionally chose to ignore training samples
 disagreeing with its hypothesis.  True, some 
stereotypes--e.g. "women
can't do math", "men can't cook" variety--are of this form.

However, this argument alone will not suffice, as it leaves open the 
possibility that it is okay to stereotype if the stereotype is

correct. (By correct, we must, of course, mean "probably approximately
correct," since there are few instances where you get metaphysical 
certainty of generalization.)

What exactly could be wrong in distrusting a specific Antarcitican because

you have come across a large sample of untrustworthy Antarciticans?

I think one way to see it is perhaps in terms of "cost-based 
learning". In these types of scenarios, you, the learning agent, have

a high cost on false negatives--if you missed identifying an
untrustworthy person, or a person who is likely to mug you on a dimly
 lit street, or a person who is very likely to be a "bad" employee in
 your organization, your success/survival chances slim down. At the
same time, the agent has much less cost on false positives, despite
the fact that the person who is classifed falsely positive by your
(negative) stereotype suffers a very large cost. Since the false 

positive *is* a member of the society, the society incurs a cost for
your false positives, and we have the classic case of individual good
clashing with societal good.

This then is the reason civil societies must go the extra mile to 

discourage acting on negative stereotypes, so we do not round up all
antarciticans and put them in bootcamps, or stop all Krakatoans at
airport securities and douse them with Chanel 5.  And societies, the
 good ones, by and large do, or at least try to do. The golden rule,

the "let a thousand guilty go free than imprison one innocent", and
the general societal strictures about negative streotypes--are all 
measures towards this. 

You need good societal laws precisely when the individual

good/instinct clashes with the societal good.

So, you are forced to learn to sometimes avoid acting on the highly
 efficient, probably PAC, generalizations that your highly evolved
brain makes. I think. 
 
Yours illuminatingly... ;-)
Rao

Epilogue/can skip:

It was a spring night in College Park, Maryland sometime in
1988. Terrapins were doing fine.  The Len Bias incident was slowly
getting forgotten.  It was life as usual at UMD. About the only big 

(if a week-old) news was that of a non-caucasian guy assaulting a
couple of women students in parking lots.  I was a graduate student,
and on this particular night I did my obligatory late-evening visit to
 my lab to feign some quality work. My lab is towards the edge of the campus;

just a couple more buildings down the Paint Branch Drive, and you get
to the poorly lit open-air parking lots. 

On that night I parked my car, walked down the couple of blocks to my 
lab, only to remember that I left a book in the car. So, I turned, and

started walking back to the parking lot. As I was walking, I noticed
that this woman walking in front turned a couple of times to look back at me. I remembered 
that I had passed her by in the opposite direction. Presently I

noticed her turning into the cryogenics building, presumably her
lab. As I passed by the cryo lab, however, I saw the woman standing
behind the glass doors of the lab and looking at me.  

Somewhere after I took a few more steps it hit me with lightning

force--I was a false positive! The woman was basically ducking into
the lab to avoid the possibility that I might be the non-caucasian
 male reportedly assaulting campus women. I knew, at a rational level,
that what she was exhibiting is a reasonably rational survival

instinct. But it did precious little to assuage the shock and
diminution I felt (as evidenced by the fact that I still remember the 
incident freshly, after over 15 years.). There is no substitute
for assessing the cost of false positives than being a false positive

yourself sometime in your life...

--------------
     ....not to make up your minds, but to open them.  
    To make the agony of decision-making so intense that  
    you can escape only by thinking. 
  
                        -Tag line from Columbia School of Journalism Seminars 

   "Induction  extends your expectation, not your experience" 

Colorless green ideas sleeping furiously (Chomsky, Universal Grammars etc. (Long.))

As I mentioned in the class today, for the longest time, and by that I
mean, until well into late 50's, the conventional scientific wisdom
was that infants come into this world with a "Tabula Rasa" (blank 
slate) mind, and pick up everything by learning (supervised or
reinforced) and observation. The reigning doctrine was
"behaviorism"--you can condition/reinforce any behavior into any
organism. To behaviorists, children were but cuter (pavlovian) rats, 
and language acquisition was no different than a acquisition of maze
following skills. B.F. Skinner was the leading exponent of behaviorism
and was, in early fifties, writing book after book expounding on how
 behaviorism can explain all sorts of human behavior.
[Skinner was such an ardent behaviorist that there was even an
apocryphal urban legend that said he raised his own daughter in a
"skinner box" to test his behaviorism hypotheses--see 
http://www.snopes.com/science/skinner.htm ]

 When Skinner came around to applying behaviorism explanations to
language acquisition and wrote the book on "Verbal Behavior", it was 
expected to further shore up the behaviorism doctrine, and become a
classic. What became a classic instead is a critical scholarly 1959
"review" of the book by a then little-known linguist named Noam
 Chomsky (
http://cogprints.ecs.soton.ac.uk/archive/00001148/00/chomsky.htm ).

 Chomsky essentially killed the book as well as much of the euphoria 
of behaviorism by an arugment that has since then come to be known as
the "poverty of stimulus" argument.  He said that behaviorism and
stimulus/response reinforcement does not quite explain how it is that 
children seem to be able to generate sentences that they have never
heard of. In other words, there are not enough examples (hence a
poverty of "stimuli") for the children to learn entire
language--grammar and sentences together (even for children--such as 
mine--with overly talkative parents ;-) [You note that the argument
that something cannot be learned is being done in terms of the 
the inordinate number of examples needed to learn it. As we saw in
the class, difficulty of learning tasks is measured in terms of 
"sample complexity".]

 As an alternative explanation, Chomsky cited his own work on
"generative grammars"--a set of grammar rules that can generate
"grammatically correct" sentences from a language. He said that it 
must be the case that children come into the world with grammar rules
already in their head. Since the grammars of different world languages
are different, he posited that the children come into this world with
 a "universal" grammar. Using the language being spoken around them,
they then set the "parameters" (or knobs, if you will) on their
universal grammar such that it becomes customized to the specific 
language environment they are in.  Once they have the customized
grammar, they then are in the business of learning word sense (or
semantics). "Colorless green ideas sleep furiously" is one of
Chomsky's famous examples, which he uses to show that even small kids 
with limited vocabularies can tell automatically whether a sentence is
grammatically correct.  [Even here, in learning semantics, children
come into the world with pretty strong biases--including the so-called
 "whole object hypothesis". If I point towards a big moving bus and say
"Bus", the kid hypothesizes that the whole big thing is called
bus--not just the wheels, or the hubcaps, or some subset of the 
parts. Pretty strong bias, come to think of it--what if I said
"Driver" pointing towards the driver side of the bus?]

Chomsky of course went on to become the demi-god of cognitive science
in general, and mathematical linguistics in particular (and you 
obviously heard of him in your CSE 355, when you probably learned
about the Chomskian hierarchy of languages--which is in terms of their
grammar complexity). A lot of research has been done since Chomsky's
original work, to shore up the support for the universal grammar 
hypothesis.  It is so much of an accepted fact (dogma) now that it
(universal grammar) in turn is seen as yet another evidence that all
humans evolved from a common set of ancestors--as against evolving
separately and independently (the "Lucy" theory, 
http://www.pbs.org/wgbh/evolution/library/07/1/l_071_01.html ; by the
way Don Johanson, who found Lucy skeleton in Ethiopia, is right here
 at ASU--check out http://www.asu.edu/clas/iho/dcj.html ). The basic
argument is that the rank similarity of the human languages cannot be
explained without it. (Of course, there are much stronger arguments 
for the common ancestor theory--including the fact that we are all
same species--any man from anywhere in the world can mate with any
woman from anywhere in the world and produce healthy offspring).

So that is some of the background on the universal grammar. By the 
way, note that none of the above says that conditioning will not be
effective in changing ones behavior--you probably saw the recent press
accounts of the infamous Wendell Johnson orphan stuttering experiments
 (http://www.jsonline.com/news/nat/jun01/stutter11061001.asp). All
Chomsky's argument says is that conditioning and reinforcement are
only part of the story and cannot alone explain language acquisition; 
evolution did a whole other part too.

Now for a couple of references. Probably the best-written lay-person
book on human language acquisition is Steven Pinker's "Language
Instinct"( http://www.amazon.com/exec/obidos/tg/detail/-/0060976519/104-1220170-3641559).
A very nice and eminently watchable 3-part PBS series on language
acquisition is "Human Language"
( http://equinoxfilms.home.mindspring.com/HLseries.html). 

That is all for now. Now for more important things like Seinfeld rerun
already in progress.

Rao

Epilogue/Postscript: These days of course, a search on Chomsky on the 
web is more likely to turn up references to his political views than
his linguistic ones. He is sort of a one-man vocal and loyal
opposition for many of the US government policies. For example, he
wrote one of the first dissenting "non-party line" opinions of the 
9/11. Whether I agree with him or not, I am grateful that there is
someone unafraid of speaking his mind--especially in these days of
hyper-patriotism, where FBI thinks it normal to monitor you because
you are against war, and your freedoms are being re-defined as the 
ones Ashcroft hasn't yet gotten around to excising into the "Patriot
Act".

----------------
  "I simply want to tell you that there are some men in this world who
 were born to do our unpleasant jobs for us. Your father's one of 
them."
 [..] "I always thought Maycomb folks were the best folks in the world,
least that's what they seemed like."
 "We're the safest folks in the world" said Miss Maudie. "We're so 
rarely called on to be Christians, but when we are, we've got men like 
Atticus to go for us."

        --Miss Maudie and Jem talking about Atticus Finch, as 
           Scout and Dill look on.. 

 

          

Re: CSE 598

The class of Tuesday 28th will not be held (as I need to attend a meeting
in Florida).  We are doing a make-up on
Wednesday 22nd (same time; room to be decided)

Rao

On 11/16/06, Coleman, James A <james.a.coleman@intel.com> wrote:

Dr. Rao,

            What day is class not being held which is causing us to have the make up class on November 22^nd?

-James

Several clarification of project 3 & Solution for the extra credit problem

I take 1 pts off Task III for most students. What I need is actually to show how you obtain the topology of the network. I am not satisfied with just a final network. I would consider a good project report showing the process and the reason as well.

Concerning the 2 pts off for comment of Task IV. I would take it back(I guess I am expecting too much). So the final effective full score would be 25.

Also, since this is a mini-project, its contribution to your final grade will be less than other projects.

The solution for the extra credit problem is below:

If we do not take the test, the expected cost would be $10,000 (take the insurance).

If we take the test, then depending on the test result, we can decide whether or not to take insurance.

So with 0.4 probability, the LHW would be T. Then, the P(CM|LHW) = 0.27. Since, 100,000*0.27>10,000, we definitely need to take the insurance. Hence, when LHW turns out to be true, the cost would be 10,000.

With 0.6 prob, LHW is False. Then, P(CM| not LHW) = 0.09. In this case, it is not necessary to take insurance any more. And the expected cost would be 100,000*0.09 = 9,000.

Therefore, the expected cost after taking a test would be
0.4*10,000+0.6*9,000 = 9,400.

Thus, we can pay at most 10,000-9,400 = 600 for the test. But here, the test price is $1000>$600, so it is not necessary to take the test.

AI Project 3 statistics

Hello, below are the statistics for AI project 3.

P3	Without Extra Credits(27)			With Extra Credits(33)
	Mean	Median	Highest	Mean	Median	Highest
Overall	19.6	21	25	22.4	24	30
Under	17.4	16		19.4	17
Graduate	21.2	22		24.7	26

-Lei

Project 3 Grading Standard

The full score for Project 3 is 27+6.

Task I: 6 = 2 (for the network&CPT) + 2 (for the probability) + 2 (for comment)

Task II: 8 = 2 (for CPT) + 2 (for Propositional logic) + 2 (for probability) + 2 (for logic proof to show equivalence)

Task III: 7 = 3(for the network) + 2 (for probability) + 2(for comment)

Task IV: 6 = 2(for network) + 2(for change to singlely connected tree) + 2 (for comment)

Extra: 6= 2+4.

Re: Grade cutoffs from Fall 2003 (with *no* implicit guarantees about your future..)

[The bitmap with last year's cumulatives didn't show up--trying again]

Several of you wanted some guidance about how the scores translate into
letter grades at the end of the semester. As I said in the class, there is no automatic translation program. It requires all the deliberative powers of a bleary-eyed full professor to convert them into letter grades.

If it helps, the following are the cumulative scores and lower-bound grade cutoffs that were used last time around.

This is strictly to give you a non-binding example. Every class is different and
the actual grades this time will again be determined adaptively. (In particular, the last times lowerbounds may or may not be admissible heuristics on this times grades...)

Feel free to ask me question either anonymously or in person. Like I said, at this point, after these many classes, tests, projects and exams, if you are still enjoying the class,  it will be a shame to lose you purely because of grade anxiety...

regards
Rao


From: Subbarao Kambhampati <rao@asu.edu>
To:  cse471-f03@parichaalak.eas.asu.edu
Date: Fri, 19 Dec 2003 08:52:33 -0700
Subject: Admissible heuristic for letter grades...

People started asking me for letter grades.
Your final letter grades will be available sometime next week online.

However, I think it is reasonable to give you a lowerbound on your grade.
Here then is an admissible--and reasonably informed (since I am making it
;-) heuristic on estimating your grade:

For Graduate students:

If your cumulative is >80% your lower bound grade will be an A

Above 70, lowerbound grade is B.


For UG students:

If your cumulative is >75% your  lower bound grade will be an A

if your cumulative is > 65, your lowerbound grade will be B

if your cumulative is >50, your lowerbound grade will be C

if your cumulative is >35, your lowerbound grade will be D

else E.


***In both cases, if your cumulative+extra credit pushes you over a threshold, then
you get that higher grade.

Rao

ps: I am willing to take comments  from people about grade thresholds that
are _below_ the category they
are in (i.e., A folks can tell me whether the A,B,C thresholds should be
changed. B folks can tell me if B and C thresholds can be changed
and so on). You can comment on whether the current thresholds are too
generous or too tight etc.


(The top part is graduate and the bottom part is UG in the bitmap below)

Grade cutoffs from Fall 2003 (with *no* implicit guarantees about your future..)

Several of you wanted some guidance about how the scores translate into
letter grades at the end of the semester. As I said in the class, there is no automatic translation program. It requires all the deliberative powers of a bleary-eyed full professor to convert them into letter grades.

If it helps, the following are the cumulative scores and lower-bound grade cutoffs that were used last time around.

This is strictly to give you a non-binding example. Every class is different and
the actual grades this time will again be determined adaptively. (In particular, the last times lowerbounds may or may not be admissible heuristics on this times grades...)

Feel free to ask me question either anonymously or in person. Like I said, at this point, after these many classes, tests, projects and exams, if you are still enjoying the class,  it will be a shame to lose you purely because of grade anxiety...

regards
Rao


From: Subbarao Kambhampati <rao@asu.edu>
To:  cse471-f03@parichaalak.eas.asu.edu
Date: Fri, 19 Dec 2003 08:52:33 -0700
Subject: Admissible heuristic for letter grades...

People started asking me for letter grades.
Your final letter grades will be available sometime next week online.

However, I think it is reasonable to give you a lowerbound on your grade.
Here then is an admissible--and reasonably informed (since I am making it
;-) heuristic on estimating your grade:

For Graduate students:

If your cumulative is >80% your lower bound grade will be an A

Above 70, lowerbound grade is B.


For UG students:

If your cumulative is >75% your  lower bound grade will be an A

if your cumulative is > 65, your lowerbound grade will be B

if your cumulative is >50, your lowerbound grade will be C

if your cumulative is >35, your lowerbound grade will be D

else E.


***In both cases, if your cumulative+extra credit pushes you over a threshold, then
you get that higher grade.

Rao

ps: I am willing to take comments  from people about grade thresholds that
are _below_ the category they
are in (i.e., A folks can tell me whether the A,B,C thresholds should be
changed. B folks can tell me if B and C thresholds can be changed
and so on). You can comment on whether the current thresholds are too
generous or too tight etc.

(The top part is graduate and the bottom part is UG in the bitmap below)

Current cumulatives (only required portion--extra credits not included)

Folks
  Some of you wanted to know your class standing currently. I weighted the materials graded until now
as follows: Pr0 --1pt; Pr 1,2-10pt each; hws 5pt each; exam 20pt (which comes to 56pts; with the remaining
points to come from the rest of the semester). The last two columns give your percentage assuming you
score at the same rate; and also your relative percentage w.r.t. the top scorer in each section.

The extra credit is not taken into account (I try not to look at them
until I decide the grades). Your extra credit points will be scaled
the same way your normal points are scaled.

As I mentioned, I like the +/- system and expect to give all the
grades A+/A/A- etc.

Let me know if you have any questions and need any anxiety
amelioration.

regards
rao


CSE471


CSE598



===============================================================

Re: code for unify

 There was a question on the blog about where to find the code for unify. All the code you need is at the bottom of the project 4 writeup (just cut and paste it to
your lisp file)

rao

Readings for tomorrow--10.3 and 15.5

<li>11/9: Chapter 10 (10.3--pg 328--334); Chapter 15 (15.5 first and
then 15.1-->15.4 as time permits)

rao

In case the (ir)rationality of sqrt(2)^sqrt(2) is bugging you... + Constructive vs. Existential math.

..In case you are dying to know whether sqrt(2)^sqrt(2) is rational or irrational, you can be rest assured
that it is irrational (actually transcendental  (*)). So a constructive proof for
our theorem is with p=sqrt(2)^sqrt(2) and q=sqrt(2)

see http://www.math.hmc.edu/funfacts/ffiles/10004.3-5.shtml

(which also points out a more general and easy to understand constructive proof. Consider
  e^{log_e q} for any transcendental number e and rational number q--which will be q. All you need to show is log_e(q) is irrational and you can show this easily (If log_e(q) = m/n with integers m and n without common factors, then
q = e^{m/n}. This would mean that e is the root of an algebraic equation x^m - q^n = 0. But the definition of trancendental number is that it cannot be the root of any algebraic equation!).

Rao

(*) By the way, transcendental => irrational but not vice versa. In particular, transcendentals are those irrational numbers that cannot be roots of any algebraic equation. Two famous examples of course are e and pi.  Notice that proving that a number e *is* transcendental involves showing that e^r for any rational number r cannot be rational (since if it is, then e will be the root of an algebraic equation). Thus, proving transcendentality is not all that easy.

(ps 2:

Check out

 http://digitalphysics.org/Publications/Cal79/html/cmath.htm

for a nice discussion on the Constructive vs. Classical mathematics--and how during Hilbert's time there was a pretty big controversy in mathematics--with mathematicians such as Brouer insisted that all math that depended on existential proofs be thrown out.Papa Hilbert had to come to rescue--pretty heady stuff.

You might also look at

http://plato.stanford.edu/entries/mathematics-constructive/

which also talks about the "slick" irrational power irrational can be rational proof...

Fwd: Project 2 & Take home mid-term statistics

The following are the statistics of Project 2 (game playing) and take home mid-term.

P2	Without Extra Credits(45)			With Extra Credits(65)
	Mean	Median	Highest	Mean	Median	Highest
Overall	38	40	45	41	42	63
Under	35	36.5		35.25	36.5
Graduate	40.2	42		45.3	45

Mid-term(Take-home)	Mean	Median	Highest
overall	59	61	82
Under	49.3	45	78
Graduate	66	71	82