We consider supervised learning of a ranking function, which is a mapping from instances to total orders over a set of labels (options). The training information consists of examples with partial (and possibly inconsistent) information about their associated rankings. From these, we induce a ranking function by reducing the original problem to a number of binary classification problems, one for each pair of labels. The main objective of this work is to investigate the trade-off between the quality of the induced ranking function and the computational complexity of the algorithm, both depending on the amount of preference information given for each example. To this end, we present theoretical results on the complexity of pairwise preference learning.

Preference learning is an emerging topic that appears in different guises in the recent literature. This work focuses on a particular learning scenario called label ranking, where the problem is to learn a mapping from instances to rankings over a finite number of labels. Our approach for learning such a mapping, called ranking by pairwise comparison (RPC), first induces a binary preference relation from suitable training data using a natural extension of pairwise classification. A ranking is then derived from the preference relation thus obtained by means of a ranking procedure, whereby different ranking methods can be used for minimizing different loss functions. In particular, we show that a simple (weighted) voting strategy minimizes risk with respect to the well-known Spearman rank correlation. We compare RPC to existing label ranking methods, which are based on scoring individual labels instead of comparing pairs of labels. Both empirically and theoretically, it is shown that RPC is superior in terms of computational efficiency, and at least competitive in terms of accuracy.

A wide range of algorithms have been developed for various types of automated negotiation. In developing such algorithms the main focus has been on their efficiency and their effectiveness. However, this is only part of the picture. Agents typically negotiate on behalf of their owners and for this to be effective the agent must be able to adequately represent the owners' preferences. However, the process by which such knowledge is acquired is typically left unspecified. To remove this shortcoming, we present a case study indicating how the knowledge for a particular negotiation algorithm can be acquired. More precisely, according to the analysis on the automated negotiation model, we identified that user trade-off preferences play a fundamental role in negotiation in general. This topic has been addressed little in the research area of user preference elicitation for general decision making problems as well. In a previous paper, we proposed an exhaustive method to acquire user trade-off preferences. In this paper, we developed another method to remove the limitation of the high user workload of the exhaustive method. Although we cannot say that it can exactly capture user trade-off preferences, it models the main commonalities of trade-off relations and reflects users' individualities as well.

A wide range of algorithms have been developed for various types of negotiating agents. In developing such algorithms the main focus has been on their efficiency and their effectiveness. However, this is only a part of the picture. Typically, agents negotiate on behalf of their owners and for this to be effective the agents must be able to adequately represent their owners ’ strategies and preferences for negotiation. However, the process by which such knowledge is acquired is typically left unspecified. To address this problem, we undertook a study of how user information about negotiation tradeoff strategies and preferences can be captured. Specifically, we devised a novel default-then-adjust acquisition technique. In this, the system firstly does a structured interview with the user to suggest the attributes that the tradeoff could be made between, then it asks the user to adjust the suggested default tradeoff strategy by improving some attribute to see how much worse the attribute being traded off can be made while still being acceptable, and, finally, it asks the user to adjust the default preference on the tradeoff alternatives. This method is consistent with the principles of standard negotiation theory and to demonstrate its effectiveness we implemented a prototype system and performed an empirical evaluation in an accommodation renting scenario. The result of this evaluation indicates the proposed technique is helpful and efficient in accurately acquiring the users’ tradeoff strategies and preferences.

Abstract. Label ranking studies the problem of learning a mapping from instances to rankings over a predefined set of labels. We approach this setting from a case-based perspective and propose a sophisticated k-NN framework as an alternative to previous binary decomposition techniques. It exhibits the appealing property of transparency and is based on an aggregation model which allows to incorporate a broad class of pairwise loss functions on label ranking. In addition to these conceptual advantages, we also present empirical results underscoring the merits of our approach in comparison to state-of-the-art learning methods. 1

While trying to satisfy a user’s preferences for a resource, partially stated or completely unknown preferences can be very disrupting. Unfortunately most of the time a user will not specify her preferences perfectly, and her partially stated or unknown preferences will be so numerous that she will not be willing to provide clarifications for all. To complicate things further we may not have perfect information about the resource as well and while we can ask an information source about the resource, the problem of “too many potential questions ” remains if we were to expect getting answers for all the imperfectly specified properties. In cases like these, we need a mechanism for figuring out which questions would yield a bigger improvement in allocating resources to users so that we can ask as few questions as it is possible to answer and get as high of a improvement as possible An example of such a problem is optimization for calculating the best assignment of a set of rooms to a set of sessions. The assignment depends on the various properties of rooms as well as the requirements for each session and the properties of these

Finding the optimal solution of a Multi-Attribute Decision Problem (MADP) is a key problem for electronic commerce systems. In this paper, we formally define the multi-attribute decision problem, and we report our survey of four different methods (soft-CSP framework, multi-attribute decision theory, CPnetwork, and Heuristic strategies) which potentially could be used to solve the MADP, and their advantages and disadvantages will be discussed respectively.

1 Introduction The nonparametric approach to statistics provides inferential procedures which rely on weaker assumptions about the underlying distributions than do standard parametric procedures for similar problems [8]. A particular class of nonparametric, distributionfree procedures is composed of hypothesis tests based on a statistic depending only on the rank order of observations in one or several samples. Examples of methods in this category are Kendall's test of independence using the rank correlation coefficient o / , Kendall's coefficient of concordance for measuring the agreement among several orderings of n objects and the associated significance test [18], the Wilcoxon twosample rank test for comparing two distributions, etc. Nonparametric procedures are typically adapted to situations in which little is known regarding the distributions of the data, such as small sample problems.

The problem of label ranking has recently been introduced as an extension of conventional classification in the field of machine learning. In this paper, we argue that label ranking is an amenable task from a CBR point of view and, in particular, is more amenable to supporting case-based problem solving than standard classification. Moreover, by developing a case-based approach to label ranking, we will show that, the other way round, concepts and techniques from CBR are also useful for label ranking. In addition to an experimental study in which case-based label ranking is compared to conventional nearest neighbor classification, we present an application in which label ranking is used for node ordering in heuristic search.

Abstract—Often, ranking is performed on the basis of some scores available for each item. The existing practice for comparing scoring functions is to compare the induced rankings by one of the multitude of rank comparison methods available in the literature. We suggest that it may be better to compare the underlying scores themselves. To this end, a generalized Kendall distance is defined, which takes into consideration not only the final ordering that the two schemes produce but also at the spacing between pairs of scores. This is shown to be equivalent to comparing the scores after fusing with another set of scores, making it theoretically interesting. A top k version of the score comparison methodology is also provided. Experimental results clearly show the advantages score comparison has over rank comparison. Index Terms—Score comparison, rank comparison, Kendall distance, top k lists. Ç