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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

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Problem Explosion of information (the web) Impossible to construct a “social preference function” without leaving out individual preferences

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

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The Preference Problem Alice’s preference function A 0 Betty’s preference function B 0 Quality Model # Any color Best Choice: Model: 1 Color: Black Quality: Good combining preferences

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Record Type Record type is set of (name : type) pair that is used to express the preference parameters. Examples: dom(A 0 )={model: int, color: string union {*}} dom(B 0 )={model: int, quality: int}

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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(A 0 ))={color!model: score, star!!model: score} ScoreBoard(dom(B 0 ))={model!quality: score}

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RecordOf rt (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} RecordOf dom(A) (r,star!!model)={color = *,model = 134} (a more general r based on the field of the ScoreBoard)

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Scores Scores(p,r) applies the preference function p to the generalization of record r Scores(p,r).n’ 1 !...n’ k =p(RecordOf rt (r, n’ 1 !...n’ k )) Example: Scores(A 0,r)={color!model = 0.3, star!!model = 0.5} Where A 0 ({color = r.color, model=r.model})=0.3 and A 0 ({color=*, model=r.model})=0.5

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Putting Everything Together r = record: {color: white model: 1342 quality: 3} rt = record type: {color: white or * model: int} RecordOf rt (r,star!!model): color: * model: 1342 Field name: star!!model ScoreBoard(rt): {color!model: score, star!!model: score Scores(A 0,r): {color!model: veto, star!!model: 0.3} A 0 (preference function that has type rt) Scores(B 0,r): {color!quality: 0.5, star!!quality: 0.4} (combine(f))(a: Scores(A 0,r), b: Scores(B 0,r), r) = final score

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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 }

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Implementation using RDBMS Preference functions (p, or A 0 or B 0 ) are implemented in a table ColorModelScore Red1230.4 *123Veto Green234Veto White4560.8 White2340.6 ModelQualityScore 12330.7 12340.9 23440.5 34530.3 34540.5 Alice’s preference function Betty’s preference function

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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

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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. ColorModelQualityScore Red1231VETO Green1231VETO Purple1231VETO *1231VETO …………

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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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Thanks!

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