New tensor completion method reduces impact of outliers.
problem Recover tensors from incomplete data with outliers.
method Proposes a new correntropy-based objective function and half-quadratic minimization.
result Demonstrates robust performance with real and synthetic data.
Efficiently recovers low-tubal-rank tensors from few measurements.
problem Recovering tensors with low tubal-rank from limited measurements.
method Factorization and factorized gradient descent.
result Factorized gradient descent reduces computational costs and storage requirements.
Paper improves tensor approximation for streaming data.
problem Challenges in finding accurate low-tubal-rank tensor approximations in streaming settings.
method Extends Frequent Directions for efficient low-tubal-rank tensor approximation.
result The new algorithm achieves arbitrarily small approximation error with linear sketch size growth.
Small initialization improves tensor recovery from noisy data.
problem Recovering low-tubal-rank tensors from noisy measurements.
method Factorized gradient descent with small initialization.
result Achieves nearly minimax optimal recovery error.
Gradient descent in tensor factorization favors low-rank solutions.
problem Tackling implicit regularization in tensor factorization problems.
method Gradient descent with small random initialization for overparametrized tensor factorization.
result Gradient descent leads to implicit regularization towards low tubal rank solutions.
New model fills in missing traffic data efficiently.
problem Missing data in large-scale spatiotemporal traffic data.
method Developed scalable tensor learning model LSTC-Tubal for imputation.
result LSTC-Tubal achieves high accuracy with lower computational cost.
This paper conducts a rigorous analysis for provable estimation of multidimensional arrays, in particular third-order tensors, from a random subset of its corrupted entries. Our study rests heavily on a recently proposed tensor algebraic framework in which we can obtain tensor singular value decomposition (t-SVD) that …
In previous work, theoretical analysis based on the tensor Restricted Isometry Property (t-RIP) established the robust recovery guarantees of a low-tubal-rank tensor. The obtained sufficient conditions depend strongly on the assumption that the linear measurement maps satisfy the t-RIP. In this paper, by exploiting the…
Paper proposes robust tensor regression method for tensor data analysis.
problem Outliers in tensor data analysis can make existing methods sensitive.
method Nonconvex relaxation of tensor tubal rank in optimization framework.
result Global convergence of proposed estimation algorithm under mild assumptions.
In this paper we focus on the problem of completion of multidimensional arrays (also referred to as tensors) from limited sampling. Our approach is based on a recently proposed tensor-Singular Value Decomposition (t-SVD) [1]. Using this factorization one can derive notion of tensor rank, referred to as the tensor tubal…
The recent proposed Tensor Nuclear Norm (TNN) [Lu et al., 2016; 2018a] is an interesting convex penalty induced by the tensor SVD [Kilmer and Martin, 2011]. It plays a similar role as the matrix nuclear norm which is the convex surrogate of the matrix rank. Considering that the TNN based Tensor Robust PCA [Lu et al., 2…
Proposes tensor Q-rank for better tensor rank recovery in complex data.
problem Improving tensor rank recovery for complex data with low sampling rate.
method Introduces tensor Q-rank and two selection methods for Q, proposing VMTQN and MOTQN models. result Demonstrates superior performance in tensor completion problems compared to TNN-based methods.
Introduces t-CCS for flexible tensor sampling.
problem Lack of flexibility in tensor sampling methods.
method Tensor Cross-Concentrated Sampling (t-CCS).
result Effective tensor recovery from t-CCS samples.
New tensor recovery method improves efficiency under strict complementarity.
problem Efficiently recovering low-rank tensors using tensor nuclear norm.
method Developed strict complementarity condition for tensor nuclear norm ball and applied to gradient methods.
result Standard gradient methods achieve linear convergence and nearly linear runtime under strict complementarity.
Paper improves tensor completion by reducing sample entries needed.
problem Reducing the number of required sample entries for tensor completion.
method Utilizes multi-rank and unitary transformation in tensor singular value decomposition.
result Provides a bound on the number of required sample entries for tensor completion.
In this paper, we study robust tensor completion by using transformed tensor singular value decomposition (SVD), which employs unitary transform matrices instead of discrete Fourier transform matrix that is used in the traditional tensor SVD. The main motivation is that a lower tubal rank tensor can be obtained by usin…
Paper introduces G-LowTESTR for efficient tensor bandits.
problem Efficient decision-making in multi-dimensional data with non-linear reward functions.
method Generalized low-rank tensor contextual bandits model and G-LowTESTR algorithm.
result G-LowTESTR achieves superior regret bound compared to vectorization and matricization methods.
Indoor localization is a supporting technology for a broadening range of pervasive wireless applications. One promis- ing approach is to locate users with radio frequency fingerprints. However, its wide adoption in real-world systems is challenged by the time- and manpower-consuming site survey process, which builds a …
This paper protects rankings from differential privacy breaches.
problem Leakage of personal information in rankings.
method Develops ε-ranking differential privacy and a multistage ranking algorithm.
result Establishes the connection between Mallows model and ε-ranking differential privacy.
The paper addresses privacy in rank aggregation using randomized responses.
problem Preserving privacy while aggregating pairwise rankings.
method Adaptive debiasing method for randomized response rankings.
result Established minimax rates for estimation errors and optimal privacy guarantees.
This paper addresses the problem of rank aggregation, which aims to find a consensus ranking among multiple ranking inputs. Traditional rank aggregation methods are deterministic, and can be categorized into explicit and implicit methods depending on whether rank information is explicitly or implicitly utilized. Surpri…
We study the problem of rank aggregation: given a set of ranked lists, we want to form a consensus ranking. Furthermore, we consider the case of extreme lists: i.e., only the rank of the best or worst elements are known. We impute missing ranks by the average value and generalise Spearman's ρto extreme ranks. Our main …
Develops a method to infer partial rankings from sparse comparisons.
problem Challenges in ranking items with limited and noisy comparisons.
method Nonparametric Bayesian approach for learning partial rankings.
result Finds partial rankings that distinguish meaningful differences only when data supports it.
Research characterizes learnability of multilabel ranking problems.
problem Learnability of multilabel ranking problems with relevance-score feedback.
method Characterizes learnability in batch and online settings for a large family of ranking losses.
result Characterizes two equivalence classes of ranking losses based on learnability.
This paper compares rank aggregation methods for partial label ranking.
problem Handling partial label ranking with ties.
method Scoring-based and non-parametric probabilistic-based rank aggregation methods.
result Scoring-based variants consistently outperform the state-of-the-art method.
We study the problem of learning to rank from multiple information sources. Though multi-view learning and learning to rank have been studied extensively leading to a wide range of applications, multi-view learning to rank as a synergy of both topics has received little attention. The aim of the paper is to propose a c…
Paper tackles underranking in group-fair ranking systems, proving a trade-off and presenting an algorithm.
problem Underranking in group-fair ranking systems can worsen social and economic inequalities.
method Formulated underranking as a new problem, proved a lower bound, and presented a fair ranking algorithm.
result Algorithm achieves best of underranking and group fairness, confirming theoretical trade-off.
New ranking system balances fairness and user utility.
problem Achieving group fairness in ranking systems.
method Formulated a minimax game between a ranking player and an adversary.
result Better utility for highly fair rankings.
Introduces nondecreasing rank for matrices and tensors, developing methods and applications.
problem Finding low-rank approximations for matrices and tensors with monotonic constraints.
method Developed a variant of hierarchical alternating least squares algorithm for finding low ND rank approximations.
result Low ND rank factorizations can be found and interpreted for real-world datasets.
Analytic proof for minimal rank Sard conjecture.
problem Proving the minimal rank Sard conjecture in the analytic category.
method Using subanalytic abnormal distribution from [4], we establish a proof.
result The set of points accessible through singular horizontal curves of minimal rank has Lebesgue measure zero.
Rank-one measurements limit feasible sets for low-rank PSD matrices.
problem Feasibility of PSD matrices under rank-one measurements.
method Characterization of feasible sets for PSD matrices given rank-one projections.
result Radius of feasible sets determines singleton solution sets for low-rank matrices.
Sparse reduced-rank regression selects variables and ranks via manifold optimization.
problem Traditional rank selection fails when true rank is high.
method Sparse regularization and manifold optimization for rank and variable selection.
result Accurate estimation of coefficient parameter with high true rank.
We consider the problem of statistical inference for ranking data, specifically rank aggregation, under the assumption that samples are incomplete in the sense of not comprising all choice alternatives. In contrast to most existing methods, we explicitly model the process of turning a full ranking into an incomplete on…
The paper tackles learning true rankings from noisy, incomplete data.
problem Learning true rankings from incomplete and noisy data.
method Introduces a selective Mallows model for noisy rankings and derives upper and lower bounds on sample complexity.
result Strong asymptotically tight bounds on sample complexity for learning complete rankings and top-k rankings.
Paper introduces GAMs for interpretable learning-to-rank models.
problem Need for transparent ranking models in legal or policy scenarios.
method Developed generalized additive models (GAMs) for ranking tasks using neural networks.
result Neural ranking GAMs achieve better performance than traditional GAMs while maintaining interpretability.
Low-rank framework for task-specific LLM ranking from sparse comparisons.
problem Challenges in reliable task-specific ranking of LLMs under sparse, imbalanced comparisons.
method Low-rank modeling of task-by-model ability matrix, max-norm accurate estimator, task-wise top-K recovery guarantees, uncertainty quantification framework.
result Improves sample efficiency and produces tighter, better-calibrated ranking certificates.
New method solves nonsmooth low-rank matrix optimization problems efficiently.
problem Nonsmooth and low-rank matrix optimization problems in statistics and machine learning.
method Low-rank Extragradient Method with warm-start initialization.
result The extragradient method converges to an optimal solution with rate O(1/t) and requires only two low-rank SVDs per iteration. New methods rank players using covariates and comparisons, outperforming existing algorithms.
problem Ranking players based on incomplete and noisy pairwise comparisons.
method Three spectral ranking methods incorporating player covariates.
result Proposed methods outperform existing algorithms in simulations.
Proposes a cross entropy loss for better ranking algorithms.
problem Improving the theoretical understanding and performance of ranking algorithms.
method Introduces a cross entropy-based loss function that is a convex bound on NDCG and consistent with NDCG.
result Empirically, the proposed method outperforms existing algorithms in quality and robustness.
FedLoRU improves FL efficiency by using low-rank updates.
problem Communication inefficiency and performance reduction in Federated Learning.
method Proposes FedLoRU, a low-rank update framework for FL, which reduces communication costs while maintaining performance.
result FedLoRU achieves convergence rates similar to FedAvg and is robust to heterogeneous and large numbers of clients.
The paper addresses calibration in label ranking, a structured prediction task.
problem Calibration in label ranking is not well understood and often poorly calibrated.
method Formalized calibration for label ranking, developed a hierarchy of notions, and empirically evaluated models.
result Popular label ranking models are often poorly calibrated, with differences between sub-ranking and top-k metrics.
We propose Top-N-Rank, a novel family of list-wise Learning-to-Rank models for reliably recommending the N top-ranked items. The proposed models optimize a variant of the widely used discounted cumulative gain (DCG) objective function which differs from DCG in two important aspects: (i) It limits the evaluation of DCG …
We describe a seriation algorithm for ranking a set of items given pairwise comparisons between these items. Intuitively, the algorithm assigns similar rankings to items that compare similarly with all others. It does so by constructing a similarity matrix from pairwise comparisons, using seriation methods to reorder t…
Differentiable sorting and rank normalization are incompatible, with specific conditions for admissibility.
problem Incompatibility between differentiable sorting and rank normalization.
method Formalized admissibility through monotone invariance, batch independence, and rank-space stability conditions.
result Different gap-sensitive and batchwise relaxations of rank normalization violate the conditions for admissibility.
Confirming a conjecture, new CAT(0) spaces of higher rank are rigid.
problem CAT(0) spaces of higher rank with geometric group actions.
method Proving rigidity for spaces containing periodic flats and geodesics in flats.
result CAT(0) spaces of higher rank n≥2 are rigid if they contain a periodic n-flat. Boosting for label ranking outperforms existing methods.
problem Improving label ranking predictions using boosting techniques.
method Proposed a boosting algorithm tailored for label ranking tasks.
result Significantly outperforms existing label ranking algorithms.
The paper analyzes how low-rank layers in neural networks improve generalization.
problem Understanding how low-rank layers affect generalization in neural networks.
method Applying Maurer's chain rule for Gaussian complexity to analyze rank and spectral norm constraints.
result Deep networks with low-rank layers achieve better generalization than those with full-rank layers.
The problem of frequent pattern mining has been studied quite extensively for various types of data, including sets, sequences, and graphs. Somewhat surprisingly, another important type of data, namely rank data, has received very little attention in data mining so far. In this paper, we therefore addresses the problem…