Top-k Queries over Uncertain Scores Top-k Queries over Uncertain Scores Qing Liu, Debabrota Basu, Talel Abdessalem, St´ ephane Bressan CoopIS 2016 Qing Liu et.al. Top-k Queries over Uncertain Scores 1 / 19
Top-k Queries over Uncertain Scores Introduction Introduction ◮ Modern recommendation systems leverage some forms of collaborative user (crowd) sourced collection of information. CoopIS 2016 Qing Liu et.al. Top-k Queries over Uncertain Scores 2 / 19
Top-k Queries over Uncertain Scores Introduction Introduction ◮ Modern recommendation systems leverage some forms of collaborative user (crowd) sourced collection of information. ◮ Crowdsourcing Platforms ◮ easily announce their needs to the crowd / get access to the information they need ◮ choose the highest quality / most competitively priced CoopIS 2016 Qing Liu et.al. Top-k Queries over Uncertain Scores 2 / 19
Top-k Queries over Uncertain Scores Introduction Introduction ◮ Modern recommendation systems leverage some forms of collaborative user (crowd) sourced collection of information. ◮ Crowdsourcing Platforms ◮ easily announce their needs to the crowd / get access to the information they need ◮ choose the highest quality / most competitively priced ◮ Examples: TripAdvisor CoopIS 2016 Qing Liu et.al. Top-k Queries over Uncertain Scores 2 / 19
Top-k Queries over Uncertain Scores Introduction Introduction ◮ Modern recommendation systems leverage some forms of collaborative user (crowd) sourced collection of information. ◮ Crowdsourcing Platforms ◮ easily announce their needs to the crowd / get access to the information they need ◮ choose the highest quality / most competitively priced ◮ Examples: TripAdvisor ◮ collaborative user or crowdsourced collection of information, e.g., user generated ratings and reviews, to recommend travel plans and hotels, vacation rentals and restaurants. CoopIS 2016 Qing Liu et.al. Top-k Queries over Uncertain Scores 2 / 19
Top-k Queries over Uncertain Scores Introduction Introduction ◮ Crowdsourcing and Collaborative Economy: ◮ communities or crowds rent, share, sell products or services CoopIS 2016 Qing Liu et.al. Top-k Queries over Uncertain Scores 3 / 19
Top-k Queries over Uncertain Scores Introduction Introduction ◮ Crowdsourcing and Collaborative Economy: ◮ communities or crowds rent, share, sell products or services CoopIS 2016 Qing Liu et.al. Top-k Queries over Uncertain Scores 3 / 19
Top-k Queries over Uncertain Scores Introduction Introduction ◮ Crowdsourcing and Collaborative Economy: ◮ communities or crowds rent, share, sell products or services CoopIS 2016 Qing Liu et.al. Top-k Queries over Uncertain Scores 3 / 19
Top-k Queries over Uncertain Scores Introduction Introduction ◮ Crowdsourcing and Collaborative Economy: ◮ communities or crowds rent, share, sell products or services CoopIS 2016 Qing Liu et.al. Top-k Queries over Uncertain Scores 3 / 19
Top-k Queries over Uncertain Scores Introduction Introduction ◮ Independent collection of information → uncertainty and diversity. CoopIS 2016 Qing Liu et.al. Top-k Queries over Uncertain Scores 4 / 19
Top-k Queries over Uncertain Scores Introduction Introduction ◮ Independent collection of information → uncertainty and diversity. ◮ Objects (services, vacation rentals and restaurants...) have uncertain scores (quality, price...). CoopIS 2016 Qing Liu et.al. Top-k Queries over Uncertain Scores 4 / 19
Top-k Queries over Uncertain Scores Introduction Introduction ◮ Independent collection of information → uncertainty and diversity. ◮ Objects (services, vacation rentals and restaurants...) have uncertain scores (quality, price...). CoopIS 2016 Qing Liu et.al. Top-k Queries over Uncertain Scores 4 / 19
Top-k Queries over Uncertain Scores Introduction Introduction ◮ Independent collection of information → uncertainty and diversity. ◮ Objects (services, vacation rentals and restaurants...) have uncertain scores (quality, price...). CoopIS 2016 Qing Liu et.al. Top-k Queries over Uncertain Scores 4 / 19
Top-k Queries over Uncertain Scores Introduction Introduction ◮ Independent collection of information → uncertainty and diversity. ◮ Objects (services, vacation rentals and restaurants...) have uncertain scores (quality, price...). CoopIS 2016 Qing Liu et.al. Top-k Queries over Uncertain Scores 4 / 19
Top-k Queries over Uncertain Scores Introduction Introduction ◮ Ranking is one of the building blocks of recommendation. ◮ A top-k query returns the sequence of the k objects with the highest scores, given a database of objects ranked by their scores for the feature of interest. CoopIS 2016 Qing Liu et.al. Top-k Queries over Uncertain Scores 5 / 19
Top-k Queries over Uncertain Scores Introduction Introduction ◮ Ranking is one of the building blocks of recommendation. ◮ A top-k query returns the sequence of the k objects with the highest scores, given a database of objects ranked by their scores for the feature of interest. ◮ Price of the apartments. −3 1.4 x 10 1.2 1 0.8 0.6 0.4 0.2 0 2000 3000 4000 5000 6000 CoopIS 2016 Qing Liu et.al. Top-k Queries over Uncertain Scores 5 / 19
Top-k Queries over Uncertain Scores Introduction Introduction ◮ Ranking is one of the building blocks of recommendation. ◮ A top-k query returns the sequence of the k objects with the highest scores, given a database of objects ranked by their scores for the feature of interest. ◮ Price of the apartments. −3 1.4 x 10 1.2 1 0.8 0.6 0.4 0.2 0 2000 3000 4000 5000 6000 ◮ With uncertain scores, a top-k query can only return an uncertain result. CoopIS 2016 Qing Liu et.al. Top-k Queries over Uncertain Scores 5 / 19
Top-k Queries over Uncertain Scores Related Work Related Work ◮ Soliman, Hyas and Ben-David [Soliman and Ilyas, 2009] study top- k queries over objects with uncertain scores given as probability distributions. CoopIS 2016 Qing Liu et.al. Top-k Queries over Uncertain Scores 6 / 19
Top-k Queries over Uncertain Scores Related Work Related Work ◮ Soliman, Hyas and Ben-David [Soliman and Ilyas, 2009] study top- k queries over objects with uncertain scores given as probability distributions. ◮ In this paper, we consider probabilistic top- k queries under the top-k semantics as in [Soliman and Ilyas, 2009]. CoopIS 2016 Qing Liu et.al. Top-k Queries over Uncertain Scores 6 / 19
Top-k Queries over Uncertain Scores Problem Definition Problem Definition ◮ O : a set of n objects; CoopIS 2016 Qing Liu et.al. Top-k Queries over Uncertain Scores 7 / 19
Top-k Queries over Uncertain Scores Problem Definition Problem Definition ◮ O : a set of n objects; ◮ s ( o i ) : the score of an object o i ∈ O ; CoopIS 2016 Qing Liu et.al. Top-k Queries over Uncertain Scores 7 / 19
Top-k Queries over Uncertain Scores Problem Definition Problem Definition ◮ O : a set of n objects; ◮ s ( o i ) : the score of an object o i ∈ O ; ◮ X i : a random variable, equals to s ( o i ) ; CoopIS 2016 Qing Liu et.al. Top-k Queries over Uncertain Scores 7 / 19
Top-k Queries over Uncertain Scores Problem Definition Problem Definition ◮ O : a set of n objects; ◮ s ( o i ) : the score of an object o i ∈ O ; ◮ X i : a random variable, equals to s ( o i ) ; ◮ f i : bounded continuous probability density function of X i ; CoopIS 2016 Qing Liu et.al. Top-k Queries over Uncertain Scores 7 / 19
Top-k Queries over Uncertain Scores Problem Definition Problem Definition ◮ O : a set of n objects; ◮ s ( o i ) : the score of an object o i ∈ O ; ◮ X i : a random variable, equals to s ( o i ) ; ◮ f i : bounded continuous probability density function of X i ; ◮ π ( k ) = [ o 1 , · · · , o k ] : sequence of k objects in O ; CoopIS 2016 Qing Liu et.al. Top-k Queries over Uncertain Scores 7 / 19
Top-k Queries over Uncertain Scores Problem Definition Problem Definition ◮ O : a set of n objects; ◮ s ( o i ) : the score of an object o i ∈ O ; ◮ X i : a random variable, equals to s ( o i ) ; ◮ f i : bounded continuous probability density function of X i ; ◮ π ( k ) = [ o 1 , · · · , o k ] : sequence of k objects in O ; ◮ Pr ( π ( k ) ) : probability of π ( k ) be the top- k sequence; � ∞ � x 1 � x k Pr ( π ( k ) ) = f 1 ( x 1 ) · · · f n ( x n ) dx n · · · dx 1 · · · −∞ −∞ −∞ (1) CoopIS 2016 Qing Liu et.al. Top-k Queries over Uncertain Scores 7 / 19
Top-k Queries over Uncertain Scores Problem Definition Problem Definition ◮ O : a set of n objects; ◮ s ( o i ) : the score of an object o i ∈ O ; ◮ X i : a random variable, equals to s ( o i ) ; ◮ f i : bounded continuous probability density function of X i ; ◮ π ( k ) = [ o 1 , · · · , o k ] : sequence of k objects in O ; ◮ Pr ( π ( k ) ) : probability of π ( k ) be the top- k sequence; � ∞ � x 1 � x k Pr ( π ( k ) ) = f 1 ( x 1 ) · · · f n ( x n ) dx n · · · dx 1 · · · −∞ −∞ −∞ (1) ◮ (Objective:) Probabilistic top- k sequence : the π ( k ) that maximizes Pr ( π ( k ) ) . CoopIS 2016 Qing Liu et.al. Top-k Queries over Uncertain Scores 7 / 19
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