Related papers: Minimax Rates and Efficient Algorithms for Noisy S…
We study sorting of permutations by random swaps if each comparison gives the wrong result with some fixed probability $p<1/2$. We use this process as prototype for the behaviour of randomized, comparison-based optimization heuristics in…
This paper studies problems of inferring order given noisy information. In these problems there is an unknown order (permutation) $\pi$ on $n$ elements denoted by $1,...,n$. We assume that information is generated in a way correlated with…
We consider the problem of noisy matrix completion, in which the goal is to reconstruct a structured matrix whose entries are partially observed in noise. Standard approaches to this underdetermined inverse problem are based on assuming…
Sorting is the task of ordering $n$ elements using pairwise comparisons. It is well known that $m=\Theta(n\log n)$ comparisons are both necessary and sufficient when the outcomes of the comparisons are observed with no noise. In this paper,…
This paper proposes an estimation framework to assess the performance of sorting over perturbed/noisy data. In particular, the recovering accuracy is measured in terms of Minimum Mean Square Error (MMSE) between the values of the sorting…
This paper studies the problem of finding the exact ranking from noisy comparisons. A comparison over a set of $m$ items produces a noisy outcome about the most preferred item, and reveals some information about the ranking. By repeatedly…
In applications such as rank aggregation, mixture models for permutations are frequently used when the population exhibits heterogeneity. In this work, we study the widely used Mallows mixture model. In the high-dimensional setting, we…
Given a matrix the seriation problem consists in permuting its rows in such way that all its columns have the same shape, for example, they are monotone increasing. We propose a statistical approach to this problem where the matrix of…
In this paper, we consider large-scale ranking problems where one is given a set of (possibly non-redundant) pairwise comparisons and the underlying ranking explained by those comparisons is desired. We show that stochastic gradient descent…
In this paper we study noisy sorting without re-sampling. In this problem there is an unknown order $a_{\pi(1)} < ... < a_{\pi(n)}$ where $\pi$ is a permutation on $n$ elements. The input is the status of $n \choose 2$ queries of the form…
We consider a ranking problem where we have noisy observations from a matrix with isotonic columns whose rows have been permuted by some permutation $\pi$ *. This encompasses many models, including crowd-labeling and ranking in tournaments…
This paper considers a noisy data structure recovery problem. The goal is to investigate the following question: Given a noisy observation of a permuted data set, according to which permutation was the original data sorted? The focus is on…
We consider the problem of learning the true ordering of a set of alternatives from largely incomplete and noisy rankings. We introduce a natural generalization of both the classical Mallows model of ranking distributions and the…
We consider the problem of finding the $k^{th}$ highest element in a totally ordered set of $n$ elements (select), and partitioning a totally ordered set into the top $k$ and bottom $n-k$ elements (partition) using pairwise comparisons.…
Parsimony, including sparsity and low rank, has been shown to successfully model data in numerous machine learning and signal processing tasks. Traditionally, such modeling approaches rely on an iterative algorithm that minimizes an…
We consider the problem of ranking $N$ objects starting from a set of noisy pairwise comparisons provided by a crowd of equal workers. We assume that objects are endowed with intrinsic qualities and that the probability with which an object…
The existence of noisy labels in real-world data negatively impacts the performance of deep learning models. Although much research effort has been devoted to improving robustness to noisy labels in classification tasks, the problem of…
Motivated by applications in single-cell biology and metagenomics, we investigate the problem of matrix reordering based on a noisy disordered monotone Toeplitz matrix model. We establish the fundamental statistical limit for this problem…
We study the problem of learning an unknown mixture of $k$ rankings over $n$ elements, given access to noisy samples drawn from the unknown mixture. We consider a range of different noise models, including natural variants of the "heat…
In this paper, we consider a statistical problem of learning a linear model from noisy samples. Existing work has focused on approximating the least squares solution by using leverage-based scores as an importance sampling distribution.…