A framework for expressing and combining preferences
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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.

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A Framework for Expressing and Combining Preferences

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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

Problem

  • Explosion of information (the web)

  • Impossible to construct a “social preference function” without leaving out individual preferences


Related work

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

combining

preferences

The Preference Problem

Model #

Any color

Alice’s preference function

A0

Model #

Best Choice:

Model: 1

Color: Black

Quality: Good

Quality

Betty’s preference function

B0


Record type

Record Type

  • 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

ScoreBoard

  • 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}


Recordof rt r n 1 n 2 n k

RecordOfrt(r,n’1! n’2!...n’k)

  • 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

  • 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 together

Putting Everything Together

r = record:

{color: white

model: 1342

quality: 3}

Field name: star!!model

rt = record type:

{color: white or *

model: int}

RecordOfrt(r,star!!model):

color: *

model: 1342

ScoreBoard(rt):

{color!model: score,

star!!model: score

Scores(A0,r):

{color!model: veto,

star!!model: 0.3}

Scores(B0,r):

{color!quality: 0.5,

star!!quality: 0.4}

A0 (preference function that

has type rt)

(combine(f))(a: Scores(A0,r),

b: Scores(B0,r), r)

= final score


Example value function f

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

Implementation using RDBMS

Alice’s preference function

  • Preference functions (p, or A0 or B0) are implemented in a table

Betty’s preference function


Generating the scores

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

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.


Questions for discussion

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

Thanks!


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