## Toward Case-Based Preference Elicitation: Similarity Measures on Preference Structures (1998)

Venue: | In Proceedings of the Fourteenth Conference on Uncertainty in Artificial Intelligence |

Citations: | 50 - 6 self |

### BibTeX

@INPROCEEDINGS{Ha98towardcase-based,

author = {Vu Ha and Peter Haddawy},

title = {Toward Case-Based Preference Elicitation: Similarity Measures on Preference Structures},

booktitle = {In Proceedings of the Fourteenth Conference on Uncertainty in Artificial Intelligence},

year = {1998},

pages = {193--201}

}

### Years of Citing Articles

### OpenURL

### Abstract

While decision theory provides an appealing normative framework for representing rich preference structures, eliciting utility or value functions typically incurs a large cost. For many applications involving interactive systems this overhead precludes the use of formal decision-theoretic models of preference. Instead of performing elicitation in a vacuum, it would be useful if we could augment directly elicited preferences with some appropriate default information. In this paper we propose a case-based approach to alleviating the preference elicitation bottleneck. Assuming the existence of a population of users from whom we have elicited complete or incomplete preference structures, we propose eliciting the preferences of a new user interactively and incrementally, using the closest existing preference structures as potential defaults. Since a notion of closeness demands a measure of distance among preference structures, this paper takes the first step of studying various distance mea...

### Citations

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Citation Context ...by S. The central result of utility theory is a representation theorem that identifies a set of conditions guaranteeing the existence of a function consistent with the preferences of a decision maker =-=[19, 14]. The theo-=-rem states that if the preference order of a decision maker satisfies a few "rational" properties, then there exists a real-valued function, called a utility function u :\Omega ! !, over out... |

1217 | Grouplens: an open architecture for collaborative filtering of netnews
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Citation Context ...he retrieved structure in some minimal way. Minimality could be defined relative to our distance measure. The case-based approach we are advocating was inspired by the work on collaborative filtering =-=[13, 9]-=-, in which the filtering system predicts how interesting a user will find items he has not seen based on the ratings that other users give to items. Each user in a population rates various alternative... |

1106 |
Theory of Games and Economic Behavior
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Citation Context ...by S. The central result of utility theory is a representation theorem that identifies a set of conditions guaranteeing the existence of a function consistent with the preferences of a decision maker =-=[19, 14]. The theo-=-rem states that if the preference order of a decision maker satisfies a few "rational" properties, then there exists a real-valued function, called a utility function u :\Omega ! !, over out... |

639 | Grouplens: Applying Collaborative Filtering to Usenet News
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(Show Context)
Citation Context ...he retrieved structure in some minimal way. Minimality could be defined relative to our distance measure. The case-based approach we are advocating was inspired by the work on collaborative filtering =-=[13, 9]-=-, in which the filtering system predicts how interesting a user will find items he has not seen based on the ratings that other users give to items. Each user in a population rates various alternative... |

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Citation Context ...hms based on the Markov chain Monte Carlo technique 4 . In the Appendix we describe the best known algorithm, due to Bubley and Dyer [2] that has a run3 The complexity class #P, introduced by Valiant =-=[18]-=-, consists of all counting problems whose solutions are the number of accepting states of some non-deterministic polynomial-time Turing Machine. A counting problem is #P-complete if the problem of cou... |

242 | The Markov chain Monte Carlo method: an approach to approximate counting and integration
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Citation Context ...lt, especially in the view of Toda's results [17], which implies that one call to a #Pcomplete oracle suffices to solve any problem in the polynomial hierarchy in deterministic polynomial time. 4 See =-=[7]-=- for a recent survey of this method. ning time of O(n 3 log nffl \Gamma1 ), where n is the poset's cardinality, and ffl is the desired accuracy. Now with the help of the routine that almost uniformly ... |

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Citation Context ...i uniformly randomly from V i . It turns out that counting (approximately) and generating (uniformly randomly) elements of large combinatorial sets are two closely related problems. In fact, Sinclair =-=[15]-=- showed that an efficient algorithm for one problem can be used to construct an efficient algorithm for the other, provided the combinatorial sets have a certain structural property called self-reduci... |

148 | Interactive assessment of user preference models: The Automated Travel Assistant
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Citation Context ...ly on some preference information, we were forced to assume additive independence of the underlying utility function and to assume that the sub-utility functions are known. In contrast, Linden, etal. =-=[11]-=- supplement elicited preferences with default information to obtain a complete utility function, which is to be continually adjusted based on the user's feedback. This default preference information r... |

146 |
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Citation Context ... = 1=3 ? 1=9, which is what we would expect: Yvette's preferences are more similar to Xaviera's than Zelda's are. Closely related to the distance concept is the similaritysconcept in fuzzy-set theory =-=[20, 12]-=-. A similarity relation s is a binary fuzzy relation on a set U that satisfies the following three properties, 8u; v; w 2 U : (i) Reflexivity. s(u; u) = 1. (ii) Symmetry. s(u; v) = s(v; u). (iii) -Tra... |

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Citation Context ... Spearman's footrule : ffi S (OE 1 ; OE 2 ) := 1 2 n X i=1 jh 1j \Gammah 2j j: It is well-known that Spearman's footrule is a metric on strict orders and has the range [0; bn 2 =4c] (see, for example =-=[4]). The thr-=-ee requirements for a measure to be a metric are the following (for all strict orders OE i ; i = 1; 2; 3): (i) Reflexivity. d(OE 1 ; OE 2 )s0, "=" iff OE 1 and OE 2 are identical. (ii) Symme... |

60 |
On the computational power of PP and ⊕P
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Citation Context ... can be reduced to it in polynomial time. #P-complete problems, which are analog counting counterparts of NP-complete problems, are considered very difficult, especially in the view of Toda's results =-=[17]-=-, which implies that one call to a #Pcomplete oracle suffices to solve any problem in the polynomial hierarchy in deterministic polynomial time. 4 See [7] for a recent survey of this method. ning time... |

59 | Faster random generation of linear extensions
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(Show Context)
Citation Context ...lity. The set of linear extensions of a poset has this property and, not suprisingly, a number of algorithms for generating (almost) uniformly randomly linear extensions of posets have been developed =-=[8, 2]-=- in order to address the fundamental problem of counting linear extensions. These algorithms are all randomized algorithms based on the Markov chain Monte Carlo technique 4 . In the Appendix we descri... |

53 | Utility Elicitation As A Classification Problem
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(Show Context)
Citation Context ...ments, which is a set of at most 20 elements. This approach computes only an approximate of the actual distance, but can provide significant computational savings. In a recent paper, Chajewska et al. =-=[3]-=- discuss an approach to preference elicitation similar to ours. Given a data base of user utility functions, they propose clustering them and describing each cluster by a prototype. They propose build... |

45 |
Counting linear extensions
- Brightwell, Winkler
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(Show Context)
Citation Context ...ility of conflict is the proportion of conflicting pairs of outcomes (out of n(n \Gamma 1)=2 pairs). Proposition 1 The probabilistic distance on the set of weak orders on\Omega is a metric with range =-=[0; 1]-=-. Proof: It is evident that the probabilistic distance only takes values between 0 and 1, the distance between two identical orders is zero, and zero distance implies two identical weak orders. The sy... |

42 | Problem-Focused Incremental Elicitation of Multiattribute Utility Models
- Ha, Haddawy
- 1997
(Show Context)
Citation Context ...citation of a complete utility function can still be too time consuming and, furthermore, the assumptions preclude representation of many kinds of interesting and common preferences. In previous work =-=[6]-=-, we investigated an approach in which we first elicit partial preference information to produce a set of candidate solutions. We then use the set of candidate solutions to identify the additional inf... |

35 |
On the conductance of order Markov chains
- Karzanov, Khachiyan
- 1991
(Show Context)
Citation Context ...lity. The set of linear extensions of a poset has this property and, not suprisingly, a number of algorithms for generating (almost) uniformly randomly linear extensions of posets have been developed =-=[8, 2]-=- in order to address the fundamental problem of counting linear extensions. These algorithms are all randomized algorithms based on the Markov chain Monte Carlo technique 4 . In the Appendix we descri... |

23 |
Similarity Relations, Fuzzy Partitions and Fuzzy Orderings, Fuzzy Sets and Systems
- Ovchinnikov
- 1991
(Show Context)
Citation Context ... = 1=3 ? 1=9, which is what we would expect: Yvette's preferences are more similar to Xaviera's than Zelda's are. Closely related to the distance concept is the similaritysconcept in fuzzy-set theory =-=[20, 12]-=-. A similarity relation s is a binary fuzzy relation on a set U that satisfies the following three properties, 8u; v; w 2 U : (i) Reflexivity. s(u; u) = 1. (ii) Symmetry. s(u; v) = s(v; u). (iii) -Tra... |

21 |
footrule’ for measuring correlation
- Spearman
- 1906
(Show Context)
Citation Context ...e measures between these two preference orders: Spearman's footrule, Euclidean distance, and probabilistic distance. On the set of strict orders, the classical distance measure is Spearman's footrule =-=[16]-=-. Suppose that h ij ; i = 1; 2; j = 1; : : : ; n is the height of s j with respect to OE i . Then the Spearman's footrule is defined as: Spearman's footrule : ffi S (OE 1 ; OE 2 ) := 1 2 n X i=1 jh 1j... |

8 |
Notes on the theory of choice, Underground classics in economics
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(Show Context)
Citation Context ...ch. We discuss related work and future research in Section 5. 2 DISTANCE MEASURES ON PREFERENCE ORDERS We start out with a brief review of utility theory for decision making. The reader is refered to =-=[10]-=- for more details. The process of making decisions is generally modeled as the identification of the optimal alternative(s) from a set M of alternatives, using in effect a weak order OE, i.e. an asymm... |