Preference inference based on Pareto models

In this paper, we consider Preference Inference based on a generalised form of Pareto order. Preference Inference aims at reasoning over an incomplete specification of user preferences. We focus on two problems. The Preference Deduction Problem (PDP) asks if another preference statement can be deduced (with certainty) from a set of given preference statements. The Preference Consistency Problem (PCP) asks if a set of given preference statements is consistent, i.e., the statements are not contradicting each other. Here, preference statements are direct comparisons between alternatives (strict and non-strict). It is assumed that a set of evaluation functions is known by which all alternatives can be rated. We consider Pareto models which induce order relations on the set of alternatives in a Pareto manner, i.e., one alternative is preferred to another only if it is preferred on every component of the model. We describe characterisations for deduction and consistency based on an analysis of the set of evaluation functions, and present algorithmic solutions and complexity results for PDP and PCP, based on Pareto models in general and for a special case. Furthermore, a comparison shows that the inference based on Pareto models is less cautious than some other types of well-known preference model

Preference inference based on lexicographic and Pareto models

Preferences play a crucial part in decision making. When supporting a user in making a decision, it is important to analyse the user’s preference information to compute good recommendations or solutions. However, often it is impractical or impossible to obtain complete knowledge on preferences. Preference inference aims to exploit given preference information and deduce more preferences. More specifically, the Deduction Problem asks whether another preference statement can be deduced from a given set of preference statements. The closely related Consistency Problem asks whether a given set of user preferences is consistent, i.e., the statements are not contradicting each other. We present approaches for preference inference based on qualitative preference models that are based on lexicographic and Pareto orders. We consider user preference statements that are given in the form of comparisons of alternatives or alternative sets. For some model types and preference statements we formulate efficient algorithms; for others we show NP-completeness and coNP-completeness results. In particular, we find that the Deduction and Consistency problem are polynomial time solvable for comparative preference statements for lexicographic and simple Pareto preference models by a detailed analysis of the problem structures. The computational efficiency for these models makes them particularly appealing for practical uses. The Deduction and Consistency Problem are coNP-complete and NP-complete, respectively, for hierarchical and generalised Pareto models, which make these models less practical even for simple preference languages. However, we still formulate a quite efficient algorithmic approach to solve the Consistency Problem (and implicitly the Deduction) for hierarchical models. We also analyse deduction and consistency for preference statements that are (strongly) compositional under some set of preference models. (Strong) compositionality is a property of preference statements in connection with a set of preference models. It demands inference of preference statements for certain combinations of preference models. We find many interesting results for this case, which ultimately leads to a general greedy algorithm to solve the Consistency Problem for strongly compositional preference statements. This indicates that strong compositionality is an important property that can deliver immediate algorithmic approaches when present. We find many types of preference statements, e.g., conjunctions of strongly compositional statements, are strongly compositional. The considered comparative preferences statements are also strongly compositional for many of the discussed preference models - different lexicographic and hierarchical models. We can make use of the Deduction Problem to find a set of optimal alternatives, e.g., to be recommended to a user that are undominated with respect to different notions of optimality. We analyse this connection for general lexicographic models and find computationally efficient solutions

Sensitive and Scalable Online Evaluation with Theoretical Guarantees

Multileaved comparison methods generalize interleaved comparison methods to provide a scalable approach for comparing ranking systems based on regular user interactions. Such methods enable the increasingly rapid research and development of search engines. However, existing multileaved comparison methods that provide reliable outcomes do so by degrading the user experience during evaluation. Conversely, current multileaved comparison methods that maintain the user experience cannot guarantee correctness. Our contribution is two-fold. First, we propose a theoretical framework for systematically comparing multileaved comparison methods using the notions of considerateness, which concerns maintaining the user experience, and fidelity, which concerns reliable correct outcomes. Second, we introduce a novel multileaved comparison method, Pairwise Preference Multileaving (PPM), that performs comparisons based on document-pair preferences, and prove that it is considerate and has fidelity. We show empirically that, compared to previous multileaved comparison methods, PPM is more sensitive to user preferences and scalable with the number of rankers being compared.Comment: CIKM 2017, Proceedings of the 2017 ACM on Conference on Information and Knowledge Managemen

Intrahousehold Bargaining and Agricultural Technology Adoption : Experimental Evidence from Zambia

This study examines how technology adoption is determined in an intra-household bargaining process between spouses with different incentives and resource constraints. We develop a noncooperative bargaining model in which individual investments affect not only a household’s total income but also its members’ future bargaining position, which can yield Pareto-inferior outcomes. To test for possible inefficiency, we introduce rice seeds to farmers in rural Zambia and randomly distribute vouchers for transportation from the village to a miller in town to husbands and wives. The results show that the identity of the voucher recipients matters for rice seed take-up when wives choose which crop to grow on suitable plots for rice production. We also find that the voucher given to husbands is effective only when they manage the plots by themselves. Furthermore, intra-household information flows are distorted by the recipients. The heterogeneous effects and incomplete information sharing among spouses provide evidence against efficient resource pooling within the family. We present suggestive evidence that limited commitment to the production plan is a key mechanism behind strategic spousal behavior. Overall, this study highlights the importance of directly targeting individuals with productive resources relevant to a technology.This study was financially supported by JSPS KAKENHI No. 16H02733.http://www.grips.ac.jp/list/jp/facultyinfo/kijima-yoko

Refinement Type Inference via Horn Constraint Optimization

We propose a novel method for inferring refinement types of higher-order functional programs. The main advantage of the proposed method is that it can infer maximally preferred (i.e., Pareto optimal) refinement types with respect to a user-specified preference order. The flexible optimization of refinement types enabled by the proposed method paves the way for interesting applications, such as inferring most-general characterization of inputs for which a given program satisfies (or violates) a given safety (or termination) property. Our method reduces such a type optimization problem to a Horn constraint optimization problem by using a new refinement type system that can flexibly reason about non-determinism in programs. Our method then solves the constraint optimization problem by repeatedly improving a current solution until convergence via template-based invariant generation. We have implemented a prototype inference system based on our method, and obtained promising results in preliminary experiments.Comment: 19 page

A Multi-objective Exploratory Procedure for Regression Model Selection

Variable selection is recognized as one of the most critical steps in statistical modeling. The problems encountered in engineering and social sciences are commonly characterized by over-abundance of explanatory variables, non-linearities and unknown interdependencies between the regressors. An added difficulty is that the analysts may have little or no prior knowledge on the relative importance of the variables. To provide a robust method for model selection, this paper introduces the Multi-objective Genetic Algorithm for Variable Selection (MOGA-VS) that provides the user with an optimal set of regression models for a given data-set. The algorithm considers the regression problem as a two objective task, and explores the Pareto-optimal (best subset) models by preferring those models over the other which have less number of regression coefficients and better goodness of fit. The model exploration can be performed based on in-sample or generalization error minimization. The model selection is proposed to be performed in two steps. First, we generate the frontier of Pareto-optimal regression models by eliminating the dominated models without any user intervention. Second, a decision making process is executed which allows the user to choose the most preferred model using visualisations and simple metrics. The method has been evaluated on a recently published real dataset on Communities and Crime within United States.Comment: in Journal of Computational and Graphical Statistics, Vol. 24, Iss. 1, 201