Related papers: Real Preferences Under Arbitrary Norms
Ranking and comparing items is crucial for collecting information about preferences in many areas, from marketing to politics. The Mallows rank model is among the most successful approaches to analyse rank data, but its computational…
Ordinal Embedding places n objects into R^d based on comparisons such as "a is closer to b than c." Current optimization-based approaches suffer from scalability problems and an abundance of low quality local optima. We instead consider a…
The objective of ordinal embedding is to find a Euclidean representation of a set of abstract items, using only answers to triplet comparisons of the form "Is item $i$ closer to the item $j$ or item $k$?". In recent years, numerous…
In multi-objective decision planning and learning, much attention is paid to producing optimal solution sets that contain an optimal policy for every possible user preference profile. We argue that the step that follows, i.e, determining…
Given a data-set of consumer behaviour, the Revealed Preference Graph succinctly encodes inferred relative preferences between observed outcomes as a directed graph. Not all graphs can be constructed as revealed preference graphs when the…
The paper suggests a new --- to the best of the author's knowledge --- characterization of decisions which are optimal in the multi-objective optimization problem with respect to a definite proper preference cone, a Euclidean cone with a…
To investigate objects without a describable notion of distance, one can gather ordinal information by asking triplet comparisons of the form "Is object $x$ closer to $y$ or is $x$ closer to $z$?" In order to learn from such data, the…
In this paper, we study the problem of approximately computing the product of two real matrices. In particular, we analyze a dimensionality-reduction-based approximation algorithm due to Sarlos [1], introducing the notion of nuclear rank as…
Ranking alternatives is a natural way for humans to explain their preferences. It is being used in many settings, such as school choice, course allocations and residency matches. In some cases, several `items' are given to each participant.…
Reallocating resources to get mutually beneficial outcomes is a fundamental problem in various multi-agent settings. While finding an arbitrary Pareto optimal allocation is generally easy, checking whether a particular allocation is Pareto…
We present various results about Euclidean preferences in the plane under $\ell_1$, $\ell_2$ and $\ell_{\infty}$ norms. When there are four candidates, we show that the maximal size (in terms of the number of pairwise distinct preferences)…
In recent years rank aggregation has received significant attention from the machine learning community. The goal of such a problem is to combine the (partially revealed) preferences over objects of a large population into a single,…
We study the problem of aggregating individual preferences over alternatives into a collective ranking. A distinctive feature of our setting is that agents are matched to alternatives. Applications include rankings of colleges or academic…
Estimating consumer preferences is central to many problems in economics and marketing. This paper develops a flexible framework for learning individual preferences from partial ranking information by interpreting observed rankings as…
The Stable Roommates problem involves matching a set of agents into pairs based on the agents' strict ordinal preference lists. The matching must be stable, meaning that no two agents strictly prefer each other to their assigned partners. A…
Ordinal data analysis is an interesting direction in machine learning. It mainly deals with data for which only the relationships `$<$', `$=$', `$>$' between pairs of points are known. We do an attempt of formalizing structures behind…
Embedding spaces contain interpretable dimensions indicating gender, formality in style, or even object properties. This has been observed multiple times. Such interpretable dimensions are becoming valuable tools in different areas of…
In previous work cite{Ha98:Towards} we presented a case-based approach to eliciting and reasoning with preferences. A key issue in this approach is the definition of similarity between user preferences. We introduced the probabilistic…
In the past decade, matrix factorization has been extensively researched and has become one of the most popular techniques for personalized recommendations. Nevertheless, the dot product adopted in matrix factorization based recommender…
We consider the notions of agreement, diversity, and polarization in ordinal elections (that is, in elections where voters rank the candidates). While (computational) social choice offers good measures of agreement between the voters, such…