a framework for expressing and combining preferences
DESCRIPTION
A Framework for Expressing and Combining Preferences. By Rakesh Agrawal & Edward L. Wimmers Presented by William Lee For CS491cxz Spring 2004. Problem. Explosion of information (the web) Impossible to construct a “social preference function” without leaving out individual preferences. - PowerPoint PPT PresentationTRANSCRIPT
A Framework for Expressing and
Combining Preferences
By Rakesh Agrawal & Edward L. Wimmers
Presented by William Lee
For CS491cxz Spring 2004
Problem
Explosion of information (the web) Impossible to construct a “social preference
function” without leaving out individual preferences
Related Work
Recommendation systems E.g. Personalogic (no longer in business?)
Problem Solutions are too specific -- needs a more generic
preference framework
The Preference Problem
Alice’s preference functionA0
Betty’s preference functionB0
Quality
Model #
Model #
Any color
Best Choice:
Model: 1Color: BlackQuality: Good
combiningpreferences
Record Type
}:,...,:{ 11 kk tntnrt
Record type is set of (name : type) pair that is used to express the preference parameters.
Examples: dom(A0)={model: int, color: string union {*}}
dom(B0)={model: int, quality: int}
ScoreBoard
}')!""'(|:'!...!'{)( 1 iiiik nnstarnwildistscorennrtScoreBoard
ScoreBoard(rt) is by itself a record type! Define the data type to store Scores New names of the record type = all combinations of the wild
types in the original rt separated with “!”. 2^j number of fields, j = number of wild types Use “star!” for the wild type
Examples ScoreBoard(dom(A0))={color!model: score, star!!model: score}
ScoreBoard(dom(B0))={model!quality: score}
RecordOfrt(r,n’1! n’2!...n’k)
!'*
'.).'!...!',(Re 1 starnif
nnifnrnnnrcordOf
j
jjjjkrt
RecordOf() a particular record always results in a generalization of the record.
Example If r = {color = “red”, model = 134} RecordOfdom(A)(r,star!!model)={color = *,model = 134} (a more
general r based on the field of the ScoreBoard)
Scores
Scores(p,r) applies the preference function p to the generalization of record r
Scores(p,r).n’1!...n’k=p(RecordOfrt(r, n’1!...n’k)) Example:
Scores(A0,r)={color!model = 0.3, star!!model = 0.5}
Where A0({color = r.color, model=r.model})=0.3 and A0({color=*, model=r.model})=0.5
Putting Everything Togetherr = record:{color: whitemodel: 1342quality: 3}
rt = record type:{color: white or *model: int}
RecordOfrt(r,star!!model):color: *model: 1342
Field name: star!!model
ScoreBoard(rt):{color!model: score,star!!model: score
Scores(A0,r):{color!model: veto,star!!model: 0.3}
A0 (preference function that has type rt)
Scores(B0,r):{color!quality: 0.5,star!!quality: 0.4}
(combine(f))(a: Scores(A0,r),b: Scores(B0,r), r)= final score
Example Value Function (f)
Alice has the veto power to veto a color/model combination or on a particular model. If she thinks that it’s OK, then let Betty’s “quality” decide.FirstVeto(a: ScoreBoard(dom(A0)), b:
ScoreBoard(dom(B0)), c: merge(dom(A0), dom(B0))) returns score
{ if a.color!model = veto then return veto else if a.star!!model = veto then return veto else return b.model!quality}
Implementation using RDBMS
Preference functions (p, or A0 or B0) are implemented in a table
Color Model Score
Red 123 0.4
* 123 Veto
Green 234 Veto
White 456 0.8
White 234 0.6
Model Quality Score
123 3 0.7
123 4 0.9
234 4 0.5
345 3 0.3
345 4 0.5
Alice’s preference function
Betty’s preference function
Generating the Scores To generate the “Scores” for Alice:
color!model: = SELECT Score FROM Alice WHERE Color = r.color AND Model =
r.model Return score, or NO_PREF if query returns nothing star!!model =
SELECT Score FROM Alice WHERE Color = * AND Model = r.model Similarly for Betty, model!quality = SELECT Score FROM Betty
WHERE Model = r.model AND Quality = r.quality
Combining the Scores
Get the Scores for Alice Get the Scores for Betty Returns the value obtained
by FirstVeto(a,b,r) The FirstVeto function can
be realized by a table with 4 columns (Color, Model, Quality, and Score) that covers the domain of the records that we pass to it.
Color Model Quality Score
Red 123 1 VETO
Green 123 1 VETO
Purple 123 1 VETO
* 123 1 VETO
… … … …
Questions for Discussion
What about the running time? 1000 fridges = 1000 * (2^j) SELECTs for each
user where j is the number of fields that have type *.
Would this be a problem? Does this system works on web search?
(Think Alice == Google and Betty == you) How can the system learn the user’s
preference function?
Thanks!