Efficient inference for expressive comparative preference languages

A fundamental task for reasoning with preferences is the following: given input preference information from a user, and outcomes α and β, should we infer that the user will prefer α to β? For CP-nets and related comparative preference formalisms, inferring a preference of α over β using the standard definition of derived preference appears to be extremely hard, and has been proved to be PSPACE-complete in general for CP-nets. Such inference is also rather conservative, only making the assumption of transitivity. This paper defines a less conservative approach to inference which can be applied for very general forms of input. It is shown to be efficient for expressive comparative preference languages, allowing comparisons between arbitrary partial tuples (including complete assignments), and with the preferences being ceteris paribus or not

Learning Conditional Lexicographic Preference Trees

We introduce a generalization of lexicographic orders and argue that this generalization constitutes an interesting model class for preference learning in general and ranking in particular. We propose a learning algorithm for inducing a so-called conditional lexicographic preference tree from a given set of training data in the form of pairwise comparisons between objects. Experimentally, we validate our algorithm in the setting of multipartite ranking

Comparative preferences induction methods for conversational recommenders

In an era of overwhelming choices, recommender systems aim at recommending the most suitable items to the user. Preference handling is one of the core issues in the design of recommender systems and so it is important for them to catch and model the user’s preferences as accurately as possible. In previous work, comparative preferences-based patterns were developed to handle preferences deduced by the system. These patterns assume there are only two values for each feature. However, real-world features can be multi-valued. In this paper, we develop preference induction methods which aim at capturing several preference nuances from the user feedback when features have more than two values. We prove the efficiency of the proposed methods through an experimental study

Preference inference based on hierarchical and simple lexicographic models

Preference Inference involves inferring additional user preferences from elicited or observed preferences, based on assumptions regarding the form of the user’s preference relation. In this paper we consider a situation in which alternatives have an associated vector of costs, each component corresponding to a different criterion, and are compared using a kind of lexicographic order, similarly to the way alternatives are compared in a Hierarchical Constraint Logic Programming model. It is assumed that the user has some (unknown) importance ordering on criteria, and that to compare two alternatives, firstly, the combined cost of each alternative with respect to the most important criteria are compared; only if these combined costs are equal, are the next most important criteria considered. The preference inference problem then consists of determining whether a preference statement can be inferred from a set of input preferences. We show that this problem is coNP-complete, even if one restricts the cardinality of the equal-importance sets to have at most two elements, and one only considers non- strict preferences. However, it is polynomial if it is assumed that the user’s ordering of criteria is a total ordering (which we call a simple lexicographic model); it is also polynomial if the sets of equally important criteria are all equivalence classes of a given fixed equivalence relation. We give an efficient polynomial algorithm for these cases, which also throws light on the structure of the inference. We give a complete proof theory for the simple lexicographic model case, and analyse variations of preference inference

REPRESENTING AND LEARNING PREFERENCES OVER COMBINATORIAL DOMAINS

Agents make decisions based on their preferences. Thus, to predict their decisions one has to learn the agent\u27s preferences. A key step in the learning process is selecting a model to represent those preferences. We studied this problem by borrowing techniques from the algorithm selection problem to analyze preference example sets and select the most appropriate preference representation for learning. We approached this problem in multiple steps. First, we determined which representations to consider. For this problem we developed the notion of preference representation language subsumption, which compares representations based on their expressive power. Subsumption creates a hierarchy of preference representations based solely on which preference orders they can express. By applying this analysis to preference representation languages over combinatorial domains we found that some languages are better for learning preference orders than others. Subsumption, however, does not tell the whole story. In the case of languages which approximate each other (another piece of useful information for learning) the subsumption relation cannot tell us which languages might serve as good approximations of others. How well one language approximates another often requires customized techniques. We developed such techniques for two important preference representation languages, conditional lexicographic preference models (CLPMs) and conditional preference networks (CP-nets). Second, we developed learning algorithms for highly expressive preference representations. To this end, we investigated using simulated annealing techniques to learn both ranking preference formulas (RPFs) and preference theories (PTs) preference programs. We demonstrated that simulated annealing is an effective approach to learn preferences under many different conditions. This suggested that more general learning strategies might lead to equally good or even better results. We studied this possibility by considering artificial neural networks (ANNs). Our research showed that ANNs can outperform classical models at deciding dominance, but have several significant drawbacks as preference reasoning models. Third, we developed a method for determining which representations match which example sets. For this classification task we considered two methods. In the first method we selected a series of features and used those features as input to a linear feed-forward ANN. The second method converts the example set into a graph and uses a graph convolutional neural network (GCNN). Between these two methods we found that the feature set approach works better. By completing these steps we have built the foundations of a portfolio based approach for learning preferences. We assembled a simple version of such a system as a proof of concept and tested its usefulness

Archives of Data Science, Series A. Vol. 1,1: Special Issue: Selected Papers of the 3rd German-Polish Symposium on Data Analysis and Applications

The first volume of Archives of Data Science, Series A is a special issue of a selection of contributions which have been originally presented at the {\em 3rd Bilateral German-Polish Symposium on Data Analysis and Its Applications} (GPSDAA 2013). All selected papers fit into the emerging field of data science consisting of the mathematical sciences (computer science, mathematics, operations research, and statistics) and an application domain (e.g. marketing, biology, economics, engineering)

Représentation et apprentissage de préférences

La modélisation des préférences par le biais de formalismes de représentation compacte fait l'objet de travaux soutenus en intelligence artificielle depuis plus d'une quinzaine d'années. Ces formalismes permettent l'expression de modèles suffisamment flexibles et riches pour décrire des comportements de décision complexes. Pour être intéressants en pratique, ces formalismes doivent de plus permettre l'élicitation des préférences de l'utilisateur, et ce en restant à un niveau admissible d'interaction. La configuration de produits combinatoires dans sa version business to customer et la recherche à base de préférences constituent de bons exemples de ce type de problème de décision où les préférences de l'utilisateur ne sont pas connues a priori. Dans un premier temps, nous nous sommes penchés sur l'apprentissage de GAI-décompositions. Nous verrons qu'il est possible d'apprendre une telle représentation en temps polynomial en passant par un système d'inéquations linéaires. Dans un second temps, nous proposerons une version probabiliste des CP-nets permettant la représentation de préférences multi-utilisateurs afin de réduire le temps nécessaire à l'apprentissage des préférences d'un utilisateur. Nous étudierons les différentes requêtes que l'on peut utiliser avec une telle représentation, puis nous nous pencherons sur la complexité de ces requêtes. Enfin, nous verrons comment apprendre ce nouveau formalisme, soit grâce à un apprentissage hors ligne à partir d'un ensemble d'objets optimaux, soit grâce à un apprentissage en ligne à partir d'un ensemble de questions posées à l'utilisateur