a framework for expressing and combining preferences

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!