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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

Related Work

- Recommendation systems
- E.g. Personalogic (no longer in business?)
- Problem
- Solutions are too specific -- needs a more generic preference framework

preferences

The Preference ProblemModel #

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 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(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)

- 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 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)

- 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

Alice’s preference function

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

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.

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?

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