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C00001 00001
C00003 00002	Talk ... given to DBL's Learning Seminar, 14-April 1982
C00004 00003	"In terms of level & type of material presented,
C00007 00004	Four subtopics -
C00008 00005				     *** Overview ***
C00011 00006			     *** [1] What is an analogy? ***
C00014 00007	Does the pair of object alone determine the analogy?
C00016 00008	Two intuitive notions:
C00017 00009	----- ***** ----- ***** -----
C00020 00010	NB: Relation may not be (explicit) in representation
C00022 00011	We'll use common theory, as helps guide analogy
C00024 00012	Open Questions:
C00026 00013	... We now know what an analogy is -- that derive "f".
C00028 00014	[3] Reformulation
C00030 00015	[4] Loose Ends
C00033 00016	Other stuff:
C00035 00017	[[ My task ]]
C00044 ENDMK
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Talk ... given to DBL's Learning Seminar, 14-April 1982

On Analogy, and things like that

*******
I.  Intro
"In terms of level & type of material presented,
 this talk, on analogy,
 will be like Tom Dietterich's presentation last week on Inductive Learning."

 As you recall, Tom presented a coherent framework within which one could
 categorize various forms of induction.

 I will try to convey a similarly coherent model of analogy.

	Information relayed at about the same level.
	Fairly formal..., if coarse
	Why it useful, & include a rough description of history & other work

	(over?) emphasis on speaker's interest/work/prejudices

A relevant question is how (and why) you could have deduced that;
... and not ...
Topic, Speaker, Date/Room, Proportion of time for SubPart
Cohesiveness
amount of preparation I (the speaker) expect of the audience ...

/// coincedental:
same length of time, day of week, institutional affiliation of speaker, ...
///

This deduction is an ANALOGICAL INFERENCE --

On hearing that two things are similar,
you fairly accurately derived the nature of this similarity.

This type of analogical process is topic of this presentation.

----
Also, I want this to be as informal as Tom's
	Slides reflect my cowardise more than formality.
   - ask questions, make comments 
	(much for me to learn)

[Note this is a 2nd analogy between this same pair of objects]
Four subtopics -

[1] What is an analogy?
	[[Propose a definition to toss around.]]
	[[this is bulk - covers/motivates much of the rest]]
[2] What is a good analogy?
[3] Reformulation
[4] Loose Ends
      for (less in-)completeness
	- grab bag of things skipped or glossed over initially
	- my work

---
Not "how to find an analogy", but what it is, being sought.
			     *** Overview ***

 Sketch What it is, and why important,
	both in genl, & wrt Learning.

Already sketched an example --
  * An analogy involves two objects which are somehow similar.
	- describing the analogy means telling the particular way
  * [Webster]

Why relevant:
 In general - much of cognitive processes based on it -
   All familar w/Linguistic - fast communication
	  Conscious metaphor
		"Bill is a pig."
	  Lakoff
	   [one structure mapped onto other...]
		"He was down in the dumps" vs
		"He had his head up in the clouds"

   ... more generally,
   Gen'l Reasoning as well
	- patient#1 like that patient#2 [so related treatments]
		mutatis mutandis
	Simon: Expertise = 50-100K friends 
	   have to be recognized and applied
	Carbonell: gen'l problem solving tool

	recognition, (e.g. face, similar program), ...
	understanding = fitting into familiar framework [= learning]

 wrt learning:
    [See Psych literature on Learning by Analogy]
    Heart of learning -
	Accomodation - recognizing new situation as like old
	  [drawing/exploiting analogy]
	Assimilation - incorporating this situation; & indexing
	  [storing analogy]
		[adaptation? - = reformulation?]

---

Why Machine use of analogy?

Theme of seminar (AI in general):
  People use it [Ubiquitous], so should machines
  Adequate for 1 intelligent processing system, why not another?
  [and in particular, in computer interface w/people]
		     *** [1] What is an analogy? ***

Focus:
 What does it mean to "understand an analogical event"?
	Problem statement
	What is it, *really*?
		Just analogues? [# args]
		Mapping / Common Theory

Not mechanism, just description

Specific problem is the
  Use of Analogy for Learning.

Analogical event:
    situation characterized by S telling H a new fact about A,
using the form "A is like B for reason R".

E.g.  "talk like Tom's, in terms of contents"
=> You realize that "Russ will present a broad description (model) of analogy".

note: "new"
	-- Analogy for purpose of learning.
	-- helps specify what type of analogy being communicated
	-- not major limitation

S and H might be same person -- remembering
 or Expert and KB -- KA


[Yes, many forms of analogy; and many other tasks]
	(See Loose Ends)

----

Address few issues:

Note "reason R" clause?  Needed?
Does the pair of object alone determine the analogy?

NO! 
- needs Context [a third argument]

I gave 2 ways that "This talk like Tom's":
-- coverage of material, & (meta) style of presentation

"Doug used the black board, but this talk like Tom's"
	-- i.e. using "slides medium", not black board
"We'd discussed moving this class, but instead this talk will be like Tom's"
	--i.e. in same room

or "in same language",
or "by an HPP student",
or ...

Here: can just conjoin - to form "single" analogy.

BUT, might make a difference (lead to contradictory conclusions)
   Who is first lady of England?
      i.e. US:England :: first-lady  ?
	  Mr Thatcher?  Lady Diana?  president's wife...
	... spouse of head of state
	... figure head ...
   Consider Washington:Lincoln pairing:
	  Find ? s.t. W:1 :: L:? - is it 19 or 5 or 9?

Why is Context often not mentioned:
  Understood implicitly -- to expect this perspective
  In general, one wants the BEST match by some pre-defined "obvious" measure
	- why bother w/others
	[see next section]
Two intuitive notions:

1. Mapping - certain features correspond.
2. Both analogues satisfy same formula.

	[Equivalency]

"Professionally, Doug is like Mike"

	Doug:Profession = Mike:Profession 

	Profession(x) = "Professor"
----- ***** ----- ***** -----
[1] Mapping

  Induction-Talk
    Topic:		Induction, wrt Machine Learning
    Depth of coverage:	Broad, if shallow
    Speaker:		TGD
    Style:		Directed Discussion
    Medium:		Slides, ...
    SubTopics:		Essense of Induction, ...
			  [[ history/other work, why useful ]]
    Bias:		TGD's interest/work
<< = prejudices>>
    Where:		MJH 301
    When:		2:30-5:30PM, Thursday, 7-April
    #NewIdeas:		<n>

  Analogy-Talk
    Topic:		Analogy, wrt Machine Learning
    Depth of coverage:	Broad, if shallow
    Speaker:		RDG
    Style:		Open Discussion
    Medium:		Slides, ...
    SubTopics:		Essense of Analogy, ...
			  [[ history/other work, why useful ]]
    Bias:		RDG's interest/work
    Where:		200-205
    When:		2:30-5:30PM, Thursday, 14-April
    #NewIdeas:		0

(i) Simple approach -- see Depth & Style.
	n-tuples of features (R H-R feature set)

(ii) If values must match EXACTLY, would miss lots
	Consider
 Speaker(ITalk) ~ Speaker(ATalk)
	Abstraction hierarchy - as n-th year HPP student
 LTalk:Emphasis & ATalk:Emphasis are ONLY similar 
	-- need to abstract out Speaker
 Similarly for LTalk:SubTopics & ATalk:SubTopics, wrt (abstraction of) Topic
 LTalk:Time & ATalk:Time -- ignore date field.

So values must be similar.

(iii) Could be stated as equality of values of other (more abstract) slots.

(iv) Relations useful, for perspecuity:
	avoids issue of CURRY-ing...

	UsefulPreparationFor( x, y, z )
	  y = Speaker(x)
	  z = Thesis(x)

	PertainsTo( Topic(x), ResearchInterest( Speaker(x)) )
	#Ideas: to whom, and what -- for each person

(v) arbitrary formula -- other connectives (in part, =>), existentials
 & to interrelate slots, ...
	∃ y. Speaker(x, y) & Profession( x, HPP-student)

<<similar to (iv)>>

****
But this is just the common feature (space) approach!
Same formula for both!
NB: Relation may not be (explicit) in representation
 Language of talk may be defined as native-language-of(Speaker), ...
 Affiliation-of-Speaker...

** so may need to define new values of existing slot, or new slot
	[rel'n in general, of course]

----- ***** ----- ***** -----
2. Both analogues satisfy same formula
[See above -- just take conjunction of terms]

f(x) == Depth-of-coverage(x) = "Shallow and Broad" & 
	Style(x) = "Open Discussion"

----- ***** ----- ***** -----
Equivalency obvious.
	I.e. same formula -- with same symbols, to establish connection.
	Similarity = equality, in some (perhaps higher) sense

May require reformulation, to see rep'n...

---
Will later [4] describe uses of each --
one better for some applications...

We'll use common theory, as helps guide analogy
(i.e. useful for given analogues, and type of connection, find analogy --
as can store abstractions like Group, or Perspective-as-Human)

----
For learning,
consider theory of hearer, H.

Hearing
  Analogous(A B R)		R is reason

Find formula f s.t.
  Expand(R f)			maybe A B as well

where
  Th |=  f(B)
~ Th |=  f(A)
~ Th |= ~f(A)

----------------------

form Th' s.t.
Th' |= Th  &
Th' |= f(A)


****
R = "speaker is (HPP) Student"

f(x) = Medium(x, Slides) & Preparation(x TooMuch DBL) &
	SubTopics( x, TheoreticalEssense( Topic(x) ) )

<<as student less secure than faculty [slide over bb],
	and more head-in-the-cloud theoritical [over empirical] >>

****

Claim that "f" is the analogy --
	NOT how to find it, but rather, what it is you're trying to find.

Can relate other work:
	Carbonell: "R" = structure of derivation/solution,
		f is more abstract fleshing
	Winston:-- too confused --
		"R" is behaviour of characters (in his abstraction language)
		f is specification: Villian(x) will kill King(x)...

Open Questions:
	Ideas?

 form of reason R?
	Reason same form as analogy -- a common relation (together w/meta...)
	Like perspective, or guide telling what to map over...
 Nature of "Expand" connection.
	"Expand" in the form of expanding - to be more specific,...
		Subjective, based on USER-INPUT heuristics

	EG from "Similar Structure" to "Related SubTopics" and "Level of Detail".
	or from "Style" to "Formality Index", ...

	Limiting cases: when it is conjectural vs deduction...

 Mechanizable form -- based on syntactic...

----
Contributions:

	*** obvious ***
(1) 3rd arg - perspective, context, guide for what to carry over.

(2) Unification of Map & Commonality
	[modulo reformulation]

	*** decomposition of problem ***
(3) Only R in Expand - not A,B

(4) Seperation of Novelty ++ later over conditions on A,B.
... We now know what an analogy is -- that derive "f".

[2] What is a good analogy?
   -- What is it that makes an analogy good?
	[useful, applicable, relevant]
   -- Is analogy#1 better than analogy#2?

Need: 
 As shown above, 
  There may be >1 analogy between 2 given analogues.

Much work - most of AI works
  See Gentner, Carbonell, (other work: Invariance Hierarchy) ... etc
Applications: 
  Evans: Educing [many R s.t. R(A,B) -- want one s.t. R(C,i)]
  Winston: most similar play - nature/behavior of characters
  AP: best similar program - functionality
...

In our model,
there are many possible "f"s, even given A B & R.

Clearly: task/goal dependent
	[often implicit, "obvious"]
	E.g. "Best analogy is one which solves the problem."

I see this is being quite subjective -- to be guided by heuristics...
[All syntactic, trying to emulate depth of association]

Intution:
	"Deeper" (more semantic) is better

How easy it is to find (or measure) is clearly dependent on the rep'n
[3] Reformulation

------
Problem: Analogy is a relation between Analogues,
NOT their representations!
(I.e. not dependent on formulation for acceptance.)

But, when mechanized,
(to implement)
	facts are input in a rep'n.

As w/any problem, the soln is obvious in correct rep'n.
	"Ewe:Lamb :: cow: ?" -- sheep, not bovine

In ideal rep'n,
	"when nature is cuts at its joints"
abstraction is obvious;
just need simple (parameter) instantiation... explaining why
	Any analogy is obvious in retrospect.

If wrong, need to change. (to find best abstraction)

saw some simple cases above - new slots from old variety
Consider ? circle/sphere -- clearly better in polar coordinates over cartesian!

Grab bag of techniques --

new relations from old,
Abstracting/focussing,
coordinate change
[see Amarel]

Major lesson here:
Analogy = Reformulation + (Simple) Instantiation

Especially for one person (program) to understand another.
[4] Loose Ends

My focus fairly sharp.
Mention other aspects:

[Why: all analogy relevant to learning, in that learning
involves recognizing and applying similar situation]

3 Types of analogy 
  - similar,
  - proportional (educing R from A & B -- another degree of freedom)
	... actually continuum...
	simile
  - familial
	Family resemblence, Quine's ostention, Wittgenstein "game"
	[other sense of analogical reasoning - by prototype, not primitive]

Types of Analogy tasks 
  - find (best) analogy from analogues (w/direction)
	for some task - eg A:B :: C:?, or ...
  - find (generate) analogue from other analogue
	AP, precedent in Legal reasoning
  - compare/rank analogies

  - use analogy for guidance
	  Kling, Carbonell

  - use the analogy to deduce/conjecture new facts
	about one of the analogues
	[quickly describe that analogue]

  - use the analogy to form an extended analogy
	(and then used as above)


Conclusivenss
	Deduction
	Conjectural
		(based on reliability of that Extend operator)
	 * consider R like T *

Level - model (broad) vs instance
	Model to Model: Electricity is like Water Flow.

	Instance to Instance: This talk like Tom's.

	Instance to Model: <These have the basic flavor of induction.>
		or instanceS -- to classify, find category, ...

	Model to Instance: <These seems simple instantiation.>
		Inheritance from prototype
Other stuff:

Literature search
My work
--------
Limitations of mappings
(1) if only slots, too limited.
(2) (either way) - how to get the analogy from analogues and "context"
	no way to store the commonality
	(which could be used for guidance -- to suggest needed reformulation)

Limitation of Common Theory
(1) hard to express differences (likewise: "don't-cares")
(2) hard to express correspondences

-------
*** Philosophy: ***
	ala Polya (see also Dershowitz, JSBrown, ...)
Two analogues are siblings in some abstraction space --
with a common abstraction, but different instantiations.

Q: ∃? a reality to an Analogy, or just linguistic convenience?

*** Psychology: ***
Tveseky - similarity studies
Anderson et al, 1978 - ACT

[[ My task ]]

My task:
Focus on use of given analogy.
First finding the connection --
	involves first finding the apt representation
& then match.

Then exploit -- trying to transfer other facts over,
to flesh out new analogue.
(based on heuristics).

Why?
  Clearly learning - updating KB.

  Most learning is fairly constrained... 
	∃ goal of solving some task to guide search.

  [Meta] testable, sorta

*****
  Examples of Learning - Understanding something new
	Shallow - ala copy&edit
	   VM like BM
	Deeper - pedagogic tool
	  Given FM, learn EC
	    - to "understand/predict", and diagnose
	    - then Unix (other pipes system)
	  Text editor from <typewriter>, <secr'y>
   [Will later discuss differences - relating to reformulation]