mlsanityData to 7 Oct 2026

Covariate-assisted Sparse Tensor Completion

arXiv 2103.06428 ↗First posted 11 Mar 2021stat.ML cs.LG math.STcited by 4

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Abstract (arXiv)

We aim to provably complete a sparse and highly-missing tensor in the presence of covariate information along tensor modes. Our motivation comes from online advertising where users click-through-rates (CTR) on ads over various devices form a CTR tensor that has about 96% missing entries and has many zeros on non-missing entries, which makes the standalone tensor completion method unsatisfactory. Beside the CTR tensor, additional ad features or user characteristics are often available. In this paper, we propose Covariate-assisted Sparse Tensor Completion (COSTCO) to incorporate covariate information for the recovery of the sparse tensor. The key idea is to jointly extract latent components from both the tensor and the covariate matrix to learn a synthetic representation. Theoretically, we derive the error bound for the recovered tensor components and explicitly quantify the improvements on both the reveal probability condition and the tensor recovery accuracy due to covariates. Finally, we apply COSTCO to an advertisement dataset consisting of a CTR tensor and ad covariate matrix, leading to 23% accuracy improvement over the baseline. An important by-product is that ad latent components from COSTCO reveal interesting ad clusters, which are useful for better ad targeting.

Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). Builds on 32 of its 64 references that are in the map. First posted on arXiv 11 Mar 2021.

Builds on

32 of 64 references.

References · 32

  1. 2016Tensor Decomposition for Signal Processing and Machine Learningcited by 223
  2. 2017Tensor Completion Algorithms in Big Data Analyticscited by 48
  3. 2019Nonconvex Low-Rank Tensor Completion from Noisy Datacited by 35
  4. 2014Provable Tensor Factorization with Missing Datacited by 31
  5. 2020Community Detection on Mixture Multi-layer Networks via Regularized Tensor Decompositioncited by 30
  6. 2014Multilinear tensor regression for longitudinal relational datacited by 28
  7. 2016Spectral algorithms for tensor completioncited by 27
  8. 2017On Polynomial Time Methods for Exact Low Rank Tensor Completioncited by 27
  9. 2017Statistically Optimal and Computationally Efficient Low Rank Tensor Completion from Noisy Entriescited by 23
  10. 2014Guaranteed Non-Orthogonal Tensor Decomposition via Alternating Rank-1 Updatescited by 21
  11. 2015Parsimonious Tensor Response Regressioncited by 20
  12. 2019Factor Models for High-Dimensional Tensor Time Seriescited by 20
20 more
  1. 2015Provable Sparse Tensor Decompositioncited by 16
  2. 2017Multilayer tensor factorization with applications to recommender systemscited by 16
  3. 2013Optimal computational and statistical rates of convergence for sparse nonconvex learning problemscited by 14
  4. 2020Uncertainty quantification for nonconvex tensor completion: Confidence intervals, heteroscedasticity and optimalitycited by 13
  5. 2017Dynamic Tensor Clusteringcited by 12
  6. 2018Sparse and Low-rank Tensor Estimation via Cubic Sketchingscited by 11
  7. 2019Integrating multi-source block-wise missing data in model selectioncited by 11
  8. 2016Incoherent Tensor Norms and Their Applications in Higher Order Tensor Completioncited by 10
  9. 2016Cross: Efficient Low-rank Tensor Completioncited by 10
  10. 2018Covariate-Adjusted Tensor Classification in High-Dimensionscited by 10
  11. 2014Spectral norm of random tensorscited by 8
  12. 2020Sparse Nonnegative Tensor Factorization and Completion with Noisy Observationscited by 7
  13. 2021TenIPS: Inverse Propensity Sampling for Tensor Completioncited by 7
  14. 2014High Dimensional Expectation-Maximization Algorithm: Statistical Optimization and Asymptotic Normalitycited by 6
  15. 2018Optimal Sparse Singular Value Decomposition for High-dimensional High-order Datacited by 6
  16. 2017Effective Tensor Sketching via Sparsificationcited by 5
  17. 2017Convex Coupled Matrix and Tensor Completioncited by 4
  18. 2020Partially Observed Dynamic Tensor Response Regressioncited by 4
  19. 2019Individualized Multilayer Tensor Learning with An Application in Imaging Analysiscited by 3
  20. 2020Generalized Liquid Association Analysis for Multimodal Data Integrationcited by 2

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 1; 2022: 0; 2023: 0; 2024: 2; 2025: 0; 2026: 1.

4 papers.

  1. 2021Provable Tensor-Train Format Tensor Completion by Riemannian Optimizationcited by 17
  2. 2024Statistical Inference For Noisy Matrix Completion Incorporating Auxiliary Informationcited by 2
  3. 2024Causal Customer Churn Analysis with Low-rank Tensor Block Hazard Modelcited by 2
  4. 2026Tensor Completion using Subspace Informationcited by 0