Related papers: Matrix Rationalization via Partial Orders
Many-to-many matching with contracts is studied in the framework of revealed preferences. All preferences are described by choice functions that satisfy natural conditions. Under a no-externality assumption individual preferences can be…
Matrix Completion is the problem of recovering an unknown real-valued low-rank matrix from a subsample of its entries. Important recent results show that the problem can be solved efficiently under the assumption that the unknown matrix is…
The general notion of a stochastic ordering is that one probability distribution is smaller than a second one if the second attaches more probability to higher values than the first. Motivated by recent work on barycentric maps on spaces of…
A matching is said to be disconnected if the saturated vertices induce a disconnected subgraph and induced if the saturated vertices induce a 1-regular graph. The disconnected and induced matching numbers are defined as the maximum…
The main result of this paper is a probabilistic proof of the penalty method for approximating the price of an American put in the Black-Scholes market. The method gives a parametrized family of partial differential equations, and by…
Sparse matrix factorization is the problem of approximating a matrix $\mathbf{Z}$ by a product of $J$ sparse factors $\mathbf{X}^{(J)} \mathbf{X}^{(J-1)} \ldots \mathbf{X}^{(1)}$. This paper focuses on identifiability issues that appear in…
Whether the goal is to analyze voting behavior, locate facilities, or recommend products, the problem of translating between (ordinal) rankings and (numerical) utilities arises naturally in many contexts. This task is commonly approached by…
Prior work studies the question of ``fairly'' ordering transactions in a replicated state machine. Each of $n$ replicas receives transactions in a possibly different order, and the system must aggregate the observed orderings into a single…
Approval-based committee voting has received significant attention in the social choice community. Among the studied rules, Thiele rules, and especially Proportional Approval Voting (PAV), stand out for desirable properties such as…
In multiwinner approval voting, the goal is to select $k$-member committees based on voters' approval ballots. A well-studied concept of proportionality in this context is the justified representation (JR) axiom, which demands that no large…
In light of recent data science trends, new interest has fallen in alternative matrix factorizations. By this, we mean various ways of factorizing particular data matrices so that the factors have special properties and reveal insights into…
The matrix completion problem aims to reconstruct a low-rank matrix based on a revealed set of possibly noisy entries. Prior works consider completing the entire matrix with generalization error guarantees. However, the completion accuracy…
The maximum modularity of a graph is a parameter widely used to describe the level of clustering or community structure in a network. Determining the maximum modularity of a graph is known to be NP-complete in general, and in practice a…
We study a submodular maximization problem motivated by applications in online retail. A platform displays a list of products to a user in response to a search query. The user inspects the first $k$ items in the list for a $k$ chosen at…
Following the works by Lin et al. (Circuits Syst. Signal Process. 20(6): 601-618, 2001) and Liu et al. (Circuits Syst. Signal Process. 30(3): 553-566, 2011), we investigate how to factorize a class of multivariate polynomial matrices. The…
Selecting representatives based on voters' preferences is a fundamental problem in social choice theory. While cardinal utility functions offer a detailed representation of preferences, ordinal rankings are often the only available…
Combinatorial preference aggregation has many applications in AI. Given the exponential nature of these preferences, compact representations are needed and ($m$)CP-nets are among the most studied ones. Sequential and global voting are two…
This paper studies whether rationality can be computed. Rationality is defined as the use of complete information, which is processed with a perfect biological or physical brain, in an optimized fashion. To compute rationality one needs to…
One tuple of probability vectors is more informative than another tuple when there exists a single stochastic matrix transforming the probability vectors of the first tuple into the probability vectors of the other. This is called matrix…
We study the classical problem of matching $n$ agents to $n$ objects, where the agents have ranked preferences over the objects. We focus on two popular desiderata from the matching literature: Pareto optimality and rank-maximality. Instead…