Related papers: How to choose a completion method for pairwise com…
We attack the problem of getting a strict ranking (i.e. a ranking without equally ranked items) of $n$ items from a pairwise comparisons matrix. Basic structures are described, a first heuristical approach based on a condition, the…
A well-known method for completing low-rank matrices based on convex optimization has been established by Cand{\`e}s and Recht. Although theoretically complete, the method may not entirely solve the low-rank matrix completion problem. This…
We study how good a lexicographically maximal solution is in the weighted matching and matroid intersection problems. A solution is lexicographically maximal if it takes as many heaviest elements as possible, and subject to this, it takes…
We consider the problem of matrix completion on an $n \times m$ matrix. We introduce the problem of Interpretable Matrix Completion that aims to provide meaningful insights for the low-rank matrix using side information. We show that the…
We study the matrix completion problem when the observation pattern is deterministic and possibly non-uniform. We propose a simple and efficient debiased projection scheme for recovery from noisy observations and analyze the error under a…
We study sign symmetric $P_{0,1}^+$-matrix completion problem. It is shown that any non-asymmetric incomplete digraph lacks sign symmetric $P_{0,1}^+$-completion, digraphs of order at most four are completely classified and finally…
A general framework based on Gaussian models and a MAP-EM algorithm is introduced in this paper for solving matrix/table completion problems. The numerical experiments with the standard and challenging movie ratings data show that the…
Large, heterogeneous datasets are characterized by missing or even erroneous information. This is more evident when they are the product of community effort or automatic fact extraction methods from external sources, such as text. A special…
Audio signal processing algorithms are frequently assessed through subjective listening tests in which participants directly score degraded signals on a unidimensional numerical scale. However, this approach is susceptible to…
In this paper we study methods for estimating causal effects in settings with panel data, where some units are exposed to a treatment during some periods and the goal is estimating counterfactual (untreated) outcomes for the treated…
In this paper we study the low rank matrix completion problem using tools from Schur complement. We give a sufficient and necessary condition such that the completed matrix is globally unique with given data. We assume the observed entries…
In this paper, we investigate the recovery of a sparse weight vector (parameters vector) from a set of noisy linear combinations. However, only partial information about the matrix representing the linear combinations is available. Assuming…
A method for aggregation of expert estimates in small groups is proposed. The method is based on combinatorial approach to decomposition of pair-wise comparison matrices and to processing of expert data. It also uses the basic principles of…
Alternating Minimization is a widely used and empirically successful heuristic for matrix completion and related low-rank optimization problems. Theoretical guarantees for Alternating Minimization have been hard to come by and are still…
We present a method for learning max-weight matching predictors in bipartite graphs. The method consists of performing maximum a posteriori estimation in exponential families with sufficient statistics that encode permutations and data…
Handling missing values in training datasets for constructing learning models or extracting useful information is considered to be an important research task in data mining and knowledge discovery in databases. In recent years, lot of…
Efficiency is a core concept of multi-objective optimization problems and multi-attribute decision making. In the case of pairwise comparison matrices a weight vector is called efficient if the approximations of the elements of the pairwise…
Many datasets suffer from missing values due to various reasons,which not only increases the processing difficulty of related tasks but also reduces the accuracy of classification. To address this problem, the mainstream approach is to use…
The pairwise comparisons method is a convenient tool used when the relative order among different concepts (alternatives) needs to be determined. One popular implementation of the method is based on solving an eigenvalue problem for the…
We examine three methods for ranking by pairwise comparison: Principal Eigenvector, HodgeRank and Tropical Eigenvector. It is shown that the choice of method can produce arbitrarily different rank order.To be precise, for any two of the…