Languages for Preferences Utility-based Representations Preference Elicitation / Learning Preference Modelling and Learning Paolo Viappiani LIP6 - CNRS, Université Pierre et Marie Curie www-desir.lip6.fr/ ∼ viappianip/ DMRS workshop, Bolzano 18 September 2014 1/67 Paolo Viappiani Preference Modelling and Learning
Languages for Preferences Utility-based Representations Preference Elicitation / Learning Outline Languages for Preferences 1 Utility-based Representations 2 Preference Elicitation / Learning 3 Standard vs Automated Elicitation Minimax-Regret Bayesian Approaches Discussion and Future Works 2/67 Paolo Viappiani Preference Modelling and Learning
Languages for Preferences Utility-based Representations Preference Elicitation / Learning Preference Handling Systems are Everywhere Not only recommender systems Computational advertisement Intelligent user interfaces Cognitive assistants Personalized medecine Personal Robots What the theory has to say about preferences? 3/67 Paolo Viappiani Preference Modelling and Learning
Languages for Preferences Utility-based Representations Preference Elicitation / Learning What are Preferences? Preferences are “rational” desires. Preferences are at the basis of any decision aiding activity. There are no decisions without preferences. Preferences, Values, Objectives, Desires, Utilities, Beliefs,... 4/67 Paolo Viappiani Preference Modelling and Learning
Languages for Preferences Utility-based Representations Preference Elicitation / Learning Are We Rational Decision Makers? NO. Human decision makers are (often) irrational and inconsistent. (work of Nobel prize winner Daniel Kahneman) Moreover preferences are often constructed during the “decision process” itself (considering specific examples) 5/67 Paolo Viappiani Preference Modelling and Learning
Languages for Preferences Utility-based Representations Preference Elicitation / Learning Binary relations Preference Relation �⊆ A × A is a reflexive binary relation x � y stands for x is at least as good as y � can be decomposed into an asymmetric and a symmetric part Asymmetric part Strict preference ≻ : x � y ∧ ¬ ( y � x ) Symmetric part Indifference ∼ 1 : x � y ∧ y � x Incomparability ∼ 2 : ¬ ( x � y ) ∧ ¬ ( y � x ) 6/67 Paolo Viappiani Preference Modelling and Learning
Languages for Preferences Utility-based Representations Preference Elicitation / Learning Preference Statements People will not directly provide their preference relation � . Rather, they will provide statements about preferred states of affair. Consider sentences of the type: I like red shoes. I do not like brown sugar. I prefer Obama to McCain. I do not want tea with milk. Cost is more important than safety. I prefer flying to Athens than having a suite at Istanbul. 7/67 Paolo Viappiani Preference Modelling and Learning
Languages for Preferences Utility-based Representations Preference Elicitation / Learning Representation Problem Often impossible to state explicitly the preference relation ( � ), especially when A is large → need for a compact representation! Logical Languages Weighted Logics Conditional Logics ... Graphical Languages Conditional Preference networks (CP nets) Conditional Preference networks with trade-offs Generalized Additive Independence networks 8/67 Paolo Viappiani Preference Modelling and Learning
Languages for Preferences Utility-based Representations Preference Elicitation / Learning Representation Languages A Compact representation is useful so that preferences can be formulated with statements that encompass several alternatives A preference statement: “I prefer red cars over to blue cars” But....What does this exactly mean? All red cards are preferred to blue cars? Some red cards are preferred to blue cars? There is at lest one red car preferred to a blue car? I prefer the average red car to the average blue car? The need of a principled “semantic” for preference statements 9/67 Paolo Viappiani Preference Modelling and Learning
Languages for Preferences Utility-based Representations Preference Elicitation / Learning Logical Languages Preference Logics Logical languages for preferences aim at giving a “semantic” to preference statements Φ is a preference formula (for example: color red) In logic you write x � Φ to say that x has the “feature” expressed by formula Φ Mod (Φ) are the alternative where Φ holds Von Wright semantics The statement “I prefer Φ to Ψ ” actually means preferring the state of affairs Φ ∧ ¬ Ψ to Ψ ∧ ¬ Φ Still not enough... Several preference semantics: strong, optimistic, pessimistic, opportunistic, ceteris paribus 10/67 Paolo Viappiani Preference Modelling and Learning
Languages for Preferences Utility-based Representations Preference Elicitation / Learning From Statements to Relations: Semantics Preference Statements I prefer Φ to Ψ ( Φ and Ψ are propositional formula) Preference for Φ ∧ ¬ Ψ over Ψ ∧ ¬ Φ (von Wright’s interpretation) Common case boolean preferences, where Φ is a variable and Ψ its negation (I prefer furnished apartment rather the unfurnished) Different Semantics Let � be a preference relation. � satisfies the preference statements if it holds x � y for: for every x , y ∈ A : x � Φ ∧ ¬ Ψ , y � Ψ ∧ ¬ Φ (Strong semantics) iff x � Φ ∧ ¬ Ψ , y � Ψ ∧ ¬ Φ and additionally they have the same evaluation for the other variables (Ceteris Paribus) x and y are maximal elements of � satisfying Φ ∧ ¬ Ψ and Ψ ∧ ¬ Φ respectively (Optimistic) x and y are minimal elements of � satisfying Φ ∧ ¬ Ψ and Ψ ∧ ¬ Φ respectively (Pessimistic) x is maximal, y minimal elements of � satisfying Φ ∧ ¬ Ψ and Ψ ∧ ¬ Φ respectively (Opportunistic) 11/67 Paolo Viappiani Preference Modelling and Learning
Languages for Preferences Utility-based Representations Preference Elicitation / Learning Ceteris Paribus: From Statements to Networks Preferential Independence Key notion in preference reasoning. It is analogous to probabilistic independence. CP preference a preferred to a ′ ceteris paribus iff ab � a ′ b ∀ b Conditional Preference a preferred to a ′ given c iff ab ′ � a ′ b ′ c for a given c CP networks The notion of conditional preferential indipendence constitutes the main building block to develop graphical models for compactly representing complex preferences → CP networks 12/67 Paolo Viappiani Preference Modelling and Learning
Languages for Preferences Utility-based Representations Preference Elicitation / Learning CP nets Formalization Each variable X is associated with a set of parents Pa ( X ) and a conditional preference table (CPT). The CPT assigns, for each combination of values of the parents, a total order on the values that X can take. CP-nets Research question: is assignment x preferred to y ? how to find undominated assignment of variables to values? Start by nodes with no parents, assign best value, look at the children,.. Technique of “worsening flip” sequence Notice: strong analogy with Bayesian networks 13/67 Paolo Viappiani Preference Modelling and Learning
Languages for Preferences Utility-based Representations Preference Elicitation / Learning Utility Representation Utility function u : X → [ 0 , 1 ] Ideal item x ⊤ such that u ( x ⊤ ) = 1 and u ( x ⊥ ) = 0 (scaling) Representing, eliciting u difficult in explicit form Flat utility representation often unrealistic Color Shape Position Weight ... Utility item1 red round top 1kg ... 0.82 item2 blue square top 2kg ... 1 item3 green square bottom 5kg ... 0.96 ... ... ... ... ... ... ... 14/67 Paolo Viappiani Preference Modelling and Learning
Languages for Preferences Utility-based Representations Preference Elicitation / Learning Additive Utility Functions Additive representation (common in MAUT) Sum of local utility functions u i over attributes (or local value functions v i multiplied by scaling weights) Exponential reduction in the number of needed parameters n n � � (1) u ( x ) = u i ( x i ) = α i v i ( x i ) i = 1 i = 1 Color v 1 Shape v 2 red 1.0 round 0 blue 0.7 square 0.2 green 0.0 star 1 Importance for attribute “color”: α 1 = 0 . 2, for “shape”: α 2 = 0 . 3. Notice: many algorithms in the recommender system community (for example matrix factorization techniques) implicitly assume an additive model! 15/67 Paolo Viappiani Preference Modelling and Learning
Languages for Preferences Utility-based Representations Preference Elicitation / Learning Generalized Additive Utility Sum of local utility functions u I over sets of attributes (or local value functions v i multiplied by scaling weights) Higher descriptive power than strictly additive utilities, while still having a manageable number of parameters m n � � (2) u ( x ) = u J i ( x J i ) = α J i v J i ( x J i ) i = 1 i = 1 where J i is a set of indices, x J i the projection of x on J i and m the number of factors. Color Shape v color , shape red round 0.9 Position v position red square 1.0 top 1 red star 0.5 bottom 0 blue round 0.4 ... ... ... Importance for factor “color+shape”: α J 1 = 0 . 2, for “position”: α J 2 = 0 . 3. 16/67 Paolo Viappiani Preference Modelling and Learning
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