We analyze incomplete ranking data, modeling coarsening and studying rank aggregation methods.
problem Statistical inference for incomplete ranking data, especially under rank-dependent coarsening.
method Modeling rank-dependent coarsening, studying Plackett-Luce distribution, and analyzing rank aggregation methods.
result The ability to recover a target ranking from incomplete observations, despite coarsening bias, is theoretically addressed.
Measures incompleteness of financial markets using asset rank and acceptance set dimension.
problem Measuring incompleteness of incomplete financial markets.
method Introduce rank of vector price process and dimension of acceptance set.
result Rank and dimension of acceptance set are equal.
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.
Framework for incomplete multi-view learning improves efficiency and clustering accuracy.
problem Incomplete representation in multi-view data.
method Joint Embedding Learning and Low-Rank Approximation (JELLA) framework.
result Improves efficiency and clustering accuracy in incomplete multi-view data.
New method clusters strong and weak views effectively, improving performance by up to 40%.
problem Clustering incomplete multi-view data with unbalanced incompleteness.
method View evolution scheme and weighted multi-view subspace clustering.
result Improves clustering performance by up to 40% on three metrics.
Investigates portfolio selection for rank-dependent utilities in incomplete markets.
problem Portfolio selection for agents with rank-dependent utility in incomplete financial markets.
method Characterizes deterministic strict equilibrium strategies for constant-coefficient and time-invariant probability weighting functions. Addresses the issue of selecting an optimal strategy from multiple equilibrium strategies for time-variant probability weighting functions.
result Characterizes deterministic strict equilibrium strategies and identifies optimal strategies from multiple equilibrium strategies.
New method clusters incomplete data by fusing subspaces.
problem Learning low-dimensional structures from highly incomplete data.
method Assign each datum to its own subspace, then fuse subspaces of the same cluster.
result Our method performs comparably to state-of-the-art with complete data and better with missing data.
New algorithm clusters data from full or incomplete datasets.
problem Clustering incomplete data with standard methods.
method Fusion penalties for subspace clustering.
result Approach performs comparably to state-of-the-art with complete data, and better with missing data.
New compact ECS manifolds with rank 2 discovered, differing from previous rank 1 examples.
problem Finding new compact ECS manifolds with rank 2.
method Constructing new examples of compact pseudo-Riemannian manifolds with parallel Weyl tensor, rank 1 or 2.
result New compact ECS manifolds of rank 2, locally homogeneous, and geodesically incomplete.
This paper extends the recently proposed and theoretically justified iterative thresholding and K residual means algorithm ITKrM to learning dicionaries from incomplete/masked training data (ITKrMM). It further adapts the algorithm to the presence of a low rank component in the data and provides a strategy for recove…
Study on tensor signal estimation from incomplete data.
problem Estimating a rank-one tensor signal from noisy, incomplete data.
method Reduction to random matrix model for spectral analysis.
result Loss of performance due to incomplete data.
CoreFlow models matrix-valued distributions efficiently, preserving shared low-rank structure.
problem Learning matrix-valued distributions from high-dimensional and incomplete data.
method Low-rank flow model that learns shared row/column subspaces and trains a normalizing flow on the core.
result CoreFlow improves generation quality in few-sample regimes and remains competitive in data-rich settings.
Kernel clustering algorithm improved for large datasets using incomplete Cholesky factorization.
problem Large memory usage in kernel-based clustering for large-scale datasets.
method Approximate the kernel matrix using incomplete Cholesky factorization and apply linear k-means clustering. result The proposed method achieves similar performance to kernel k-means clustering but handles large-scale datasets efficiently. BRTR improves robust tensor completion with automatic rank detection.
problem Robust tensor completion from incomplete data with outliers.
method Bayesian robust tensor ring decomposition (BRTR) with variational Bayesian (VB) algorithm.
result Automatic detection of TR rank and improved performance over state-of-the-art methods.
Many applications in data analysis rely on the decomposition of a data matrix into a low-rank and a sparse component. Existing methods that tackle this task use the nuclear norm and L1-cost functions as convex relaxations of the rank constraint and the sparsity measure, respectively, or employ thresholding techniques. …
This work presents GROUSE (Grassmanian Rank-One Update Subspace Estimation), an efficient online algorithm for tracking subspaces from highly incomplete observations. GROUSE requires only basic linear algebraic manipulations at each iteration, and each subspace update can be performed in linear time in the dimension of…
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.
New algorithm recovers tensor factors from incomplete measurements efficiently.
problem Recovering tensor factors from incomplete measurements.
method Scaled gradient descent (ScaledGD) algorithm with spectral initializations.
result ScaledGD provably converges linearly for tensor completion and regression.
Extracting the underlying low-dimensional space where high-dimensional signals often reside has long been at the center of numerous algorithms in the signal processing and machine learning literature during the past few decades. At the same time, working with incomplete (partly observed) large scale datasets has recent…
Online tensor subspace tracking algorithm for incomplete data.
problem Online subspace tracking of partially observed high-dimensional data.
method OLSTEC algorithm based on CP decomposition and recursive least squares.
result OLSTEC outperforms state-of-the-art algorithms in convergence rate.
CANDECOMP/PARAFAC (CP) tensor factorization of incomplete data is a powerful technique for tensor completion through explicitly capturing the multilinear latent factors. The existing CP algorithms require the tensor rank to be manually specified, however, the determination of tensor rank remains a challenging problem e…
We consider the classic problem of establishing a statistical ranking of a set of n items given a set of inconsistent and incomplete pairwise comparisons between such items. Instantiations of this problem occur in numerous applications in data analysis (e.g., ranking teams in sports data), computer vision, and machine …
Survey on efficient methods for estimating low-rank matrices from incomplete data.
problem Estimating low-rank matrices from incomplete data with provable guarantees.
method Convex and nonconvex approaches, including nuclear norm minimization and projected gradient descent.
result Unified overview of recent advances with rigorous performance analysis.
Survey on robust data representation learning from a knowledge flow perspective.
problem Learning robust visual representation from noisy, incomplete or mismatched data.
method Low-rank modeling for robust knowledge recovery, transfer, and fusion.
result Unified formulation for robust knowledge discovery and transfer/fusion.
Study tackles nonlinear factor models with unknown monotone links from incomplete and noisy data.
problem Learning nonlinear factor models with unknown monotone links from incomplete and noisy data.
method Formulated as joint recovery of low-rank factors, loadings, and nonlinear link function; proposed BCD algorithm with regularization.
result Established convergence guarantees and sublinear regret bounds for link-function updates.
Low-rank matrix factorizations arise in a wide variety of applications -- including recommendation systems, topic models, and source separation, to name just a few. In these and many other applications, it has been widely noted that by incorporating temporal information and allowing for the possibility of time-varying …
We present a Dirichlet process mixture model over discrete incomplete rankings and study two Gibbs sampling inference techniques for estimating posterior clusterings. The first approach uses a slice sampling subcomponent for estimating cluster parameters. The second approach marginalizes out several cluster parameters …
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…
Ranking recommendation algorithms across datasets using Bradley-Terry model
problem Comparing recommendation algorithms across different datasets
method Introduce a novel data-driven ranking methodology based on Bradley-Terry model
result The obtained ranking depends on key dataset statistics
Recovering low-rank and sparse matrices from incomplete or corrupted observations is an important problem in machine learning, statistics, bioinformatics, computer vision, as well as signal and image processing. In theory, this problem can be solved by the natural convex joint/mixed relaxations (i.e., l_{1}-norm and tr…
Optimal privacy-preserving ranking from noisy comparisons.
problem Protecting individual privacy in ranking from noisy comparisons.
method Differentially private ranking algorithms under edge and individual differential privacy.
result Achieved minimax optimal rates of convergence under privacy constraints.
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.
Model learns tensor representations from imperfect multimodal data.
problem Learning from imperfect multimodal data with noise or missing entries.
method Tensor rank minimization to regularize rank of tensor representations.
result Model effectively learns tensor representations from imperfect data.
A new algorithm improves top-k recommendation accuracy by considering item payoffs uncertainty.
problem Suboptimal performance in top-k recommendation rankings due to varying item payoffs. method Proposes a risk-seeking utility function for ranking items based on estimated preference scores.
result Risk-seeking ranking yields the best performance in top-k recommendations. Paper develops new patterns for unique matrix completions.
problem Developing unique completions for non-random matrix patterns.
method Formulated low-rank matrix completion using Plucker coordinates.
result Provides two families of patterns for any rank.
Riemannian gradient descent escapes some spurious critical points on low-rank matrix manifold.
problem Spurious critical points on the boundary of low-rank matrix manifold.
method Riemannian gradient descent with dynamical low-rank approximation and rescaled gradient flow.
result Riemannian gradient descent escapes some spurious critical points on the boundary of the manifold.
New method for tensor classification with missing data.
problem Handling incomplete tensor data in high-dimensional classification.
method High-dimensional tensor linear discriminant analysis with TGMM and Tensor LDA-MD.
result Established convergence rates and minimax optimal bounds for misclassification rate.
Extracting latent low-dimensional structure from high-dimensional data is of paramount importance in timely inference tasks encountered with `Big Data' analytics. However, increasingly noisy, heterogeneous, and incomplete datasets as well as the need for {\em real-time} processing of streaming data pose major challenge…
Estimates low-rank distributional matrices from incomplete samples.
problem Matrix completion for distributional entries with limited observed data.
method Kernel mean embeddings, Tucker rank, functional unfolding operators.
result Effective estimator for distributional matrix completion established.
This paper examines the problem of locating outlier columns in a large, otherwise low-rank, matrix. We propose a simple two-step adaptive sensing and inference approach and establish theoretical guarantees for its performance; our results show that accurate outlier identification is achievable using very few linear sum…
Completes the space of vector-valued one-forms on manifolds.
problem Metric incompleteness of the space of full-ranked one-forms.
method Distance equality and quotient structures.
result Concrete description of the metric completion of the space of full-ranked one-forms.
We propose a general framework for reconstructing and denoising single entries of incomplete and noisy entries. We describe: effective algorithms for deciding if and entry can be reconstructed and, if so, for reconstructing and denoising it; and a priori bounds on the error of each entry, individually. In the noiseless…
Flexible ranking models from choice data.
problem Difficulties in modeling, learning from, and predicting rankings.
method Choice-based ranking models using repeated selection.
result Choice-based ranking models outperform existing models in various ranking tasks.
Bayesian method combines expert and user rankings using copulas.
problem Combining expert and user rankings for accurate predictions.
method Bayesian inference with copula modeling latent variables.
result Predictive distribution of user rankings can be approximated accurately.
New methods extend kernel estimators for partial rankings, improving performance in machine learning tasks.
problem Incomplete rankings data in real-world applications.
method Antithetic and Monte Carlo kernel estimators for partial rankings, variance reduction scheme.
result Improved antithetic kernel estimator with lower variance and better performance.
Optimizes tensor completion using geodesics on Segre manifolds.
problem Incomplete tensor data in recommender systems and spectroscopy.
method Riemannian conjugate gradient optimization with explicit geodesic expressions.
result Recovery of tensor decomposition from as little as 10% of data.
Paper presents a method for imputing and forecasting structural response from incomplete sensor data.
problem Missing sensor data in structural health monitoring (SHM).
method Incremental Bayesian tensor learning for spatiotemporal missing data reconstruction and forecasting.
result The proposed method achieves accurate and robust imputation and prediction even with high rates of missing data.
New method estimates and completes tensors from ordinal data, improving accuracy and efficiency.
problem Estimating and completing tensors from incomplete, ordinal observations.
method Multi-linear cumulative link model with rank-constrained M-estimator.
result The proposed estimator achieves faster convergence and is minimax optimal.