首页/论文/1408.2467

arXiv 1408.24672014-08math.OCcs.AIcs.IR

Matrix Completion under Interval Uncertainty

IBM Research（IBM研究院）；Lehigh University（里海大学）；University of Edinburgh（爱丁堡大学）

Jakub Marecek, Peter Richtarik, Martin Takac

发表信息：: European Journal on Operational Research (2017) 256 (1): 35-43
DOI：: 10.1016/j.ejor.2016.07.014

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

英文摘要相关论文

英文摘要：

Matrix completion under interval uncertainty can be cast as matrix completion with element-wise box constraints. We present an efficient alternating-direction parallel coordinate-descent method for the problem. We show that the method outperforms any other known method on a benchmark in image in-painting in terms of signal-to-noise ratio, and that it provides high-quality solutions for an instance of collaborative filtering with 100,198,805 recommendations within 5 minutes.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

Uncertainty quantification for nonconvex tensor completion: Confidence intervals, heteroscedasticity and optimality

Princeton University（普林斯顿大学）

We study the distribution and uncertainty of nonconvex optimization for noisy tensor completion -- the problem of estimating a low-rank tensor given incomplete and corrupted observations of its entries. Focusing on a two-stage estimation algorithm proposed by Cai et al. (2019), we characterize the distribution of this nonconvex estimator down to fine scales. This distributional theory in turn allows one to construct valid and short confidence intervals for both the unseen tensor entries and the unknown tensor factors. The proposed inferential procedure enjoys several important features: (1) it…

2020-06-15cs.ITcs.LGmath.IT

Metric completion of $Diff([0,1])$ with the $H1$ right-invariant metric

We consider the group of smooth increasing diffeomorphisms Diff on the unit interval endowed with the right-invariant $H^1$ metric. We compute the metric completion of this space which appears to be the space of increasing maps of the unit interval with boundary conditions at $0$ and $1$. We compute the lower-semicontinuous envelope associated with the length minimizing geodesic variational problem. We discuss the Eulerian and Lagrangian formulation of this relaxation and we show that smooth solutions of the EPDiff equation are length minimizing for short times.

2019-06-21math.APmath.OC

Inference and Uncertainty Quantification for Noisy Matrix Completion

Princeton University（普林斯顿大学）

Noisy matrix completion aims at estimating a low-rank matrix given only partial and corrupted entries. Despite substantial progress in designing efficient estimation algorithms, it remains largely unclear how to assess the uncertainty of the obtained estimates and how to perform statistical inference on the unknown matrix (e.g.~constructing a valid and short confidence interval for an unseen entry). This paper takes a step towards inference and uncertainty quantification for noisy matrix completion. We develop a simple procedure to compensate for the bias of the widely used convex and nonconve…

2019-11-14cs.ITcs.LGeess.SP

An Efficient Interval Uncertainty Optimization Approach Based on Quasi-sparse Response Surface

The structure uncertainty optimization problem is usually treated as double-loop optimization process, which is computation-intensive. In this paper, an efficient interval uncertainty optimization approach based on Quasi-sparse response surface (QSRS) is proposed for structure uncertainty optimization. In which, 1) with l_1 norm and l_2 norm penalty method, a few appropriate basis functions are selected form a large number of basis functions to construct QSRS accurately and only a few sampling points is required, 2) as the orthogonal chebyshev polynomials is employed as QSRS basis functions, t…

2019-09-13math.OC

Uncertainty Intervals for Robust Bottleneck Assignment

We examine the robustness of bottleneck assignment problems to perturbations in the assignment weights. We derive two algorithms that provide uncertainty bounds for robust assignment. We prove that the bottleneck assignment is guaranteed to be invariant to perturbations which lie within the provided bounds. We apply the method to an example of task assignment for a multi-agent system.

2020-05-24math.OC

On convexity and solution concepts in cooperative interval games

Cooperative interval game is a cooperative game in which every coalition gets assigned some closed real interval. This models uncertainty about how much the members of a coalition get for cooperating together. In this paper we study convexity, core and the Shapley value of games with interval uncertainty. Our motivation to do so is twofold. First, we want to capture which properties are preserved when we generalize concepts from classical cooperative game theory to interval games. Second, since these generalizations can be done in different ways, mainly with regard to the resulting level of un…

2018-11-09cs.GTmath.OC

更多相关论文收起更多论文

无环有向图中可恢复鲁棒最短路径问题的计算复杂性

Computational complexity of the recoverable robust shortest path problem in acyclic digraphs under interval budgeted uncertainty

Wrocław University of Science and Technology（弗罗茨瓦夫科技大学）

本文研究无环有向图中可恢复鲁棒最短路径问题的计算复杂性，证明其在分层无环有向图下仍为强NP难，并证明离散预算不确定性下该问题不可近似。

2026-09-28cs.DSmath.OC

具有预算区间不确定性的鲁棒单阶段选择问题

Robust single-stage selection problems with budgeted interval uncertainty

研究具有预算区间不确定性的鲁棒单阶段选择问题，在固定与不确定双成本及基数约束下，提供包含多项式算法及NP完备性证明的完整计算复杂度分类。

2025-11-03math.OC

Investigating the Recoverable Robust Single Machine Scheduling Problem Under Interval Uncertainty

We investigate the recoverable robust single machine scheduling problem under interval uncertainty. In this setting, jobs have first-stage processing times p and second-stage processing times q and we aim to find a first-stage and second-stage schedule with a minimum combined sum of completion times, such that at least Delta jobs share the same position in both schedules. We provide positive complexity results for some important special cases of this problem, as well as derive a 2-approximation algorithm to the full problem. Computational experiments examine the performance of an exact mixed-i…

2022-03-07cs.DMcs.DSmath.OC

约束含数据不确定性的非光滑区间值多目标优化中的近似Pareto解研究

On approximate Pareto solutions in nonsmooth interval-valued multiobjective optimization with data uncertainty in constraints

针对约束含数据不确定性的非光滑区间值多目标优化问题，定义多类近似Pareto解，推导其最优性条件与对偶关系，为含不确定约束的区间值多目标优化提供理论支撑。

2025-02-22math.OC

区间不确定性下线性互补问题性质的稳定性

Stability of the linear complementarity problem properties under interval uncertainty

研究区间不确定数据下线性互补问题的性质稳定性，通过分析区间矩阵的鲁棒性质（含S-矩阵、Z-矩阵等多类矩阵性质），给出其刻画并提出可高效识别的子类，以保障问题在不确定环境下仍具备期望性质。

2019-08-21cs.NAmath.NAmath.OC

区间库存情形下的成本分摊：SOC与Shapley方法

Cost allocations in interval inventory situations: the SOC and Shapley approaches

针对供需不确定性下的协作库存成本分摊问题，本文提出区间库存框架，研究区间SOC规则与区间Shapley规则的理论性质，并通过西班牙七机场香水库存案例验证其实际应用价值。

2025-07-29math.OC

Machine Learning based optimization for interval uncertainty propagation

Delft University of Technology（代尔夫特理工大学）

Two non-intrusive uncertainty propagation approaches are proposed for the performance analysis of engineering systems described by expensive-to-evaluate deterministic computer models with parameters defined as interval variables. These approaches employ a machine learning based optimization strategy, the so-called Bayesian optimization, for evaluating the upper and lower bounds of a generic response variable over the set of possible responses obtained when each interval variable varies independently over its range. The lack of knowledge caused by not evaluating the response function for all th…

2021-10-20cs.LGeess.SPmath.OC