Research



Scholarly Publications:


    Preprints (Double-blind submissions are not listed)

  1. Bumsu Kim, Daniel Mckenzie, HQ Cai, and Wotao Yin. Curvature-Aware Derivative-Free Optimization, submitted. arXiv GitHub

    2. Journal and Selected Conference Papers

  2. HQ Cai, Zehan Chao, Longxiu Huang, and Deanna Needell. Robust Tensor CUR Decompositions: Rapid Low-Tucker-Rank Tensor Recovery with Sparse Corruption, SIAM Journal on Imaging Sciences (SIIMS), 17(1): 225–247, 2024. arXiv GitHub BibTEX

  3. Xinyu Chen, Zhanhong Cheng, HQ Cai, Nicolas Saunier, and Lijun Sun. Laplacian Convolutional Representation for Traffic Time Series Imputation, IEEE Transactions on Knowledge and Data Engineering (TKDE), to appear.

  4. Jialin Liu, Xiaohan Chen, Zhangyang Wang, Wotao Yin, and HQ Cai. Towards Constituting Mathematical Structures for Learning to Optimize, In International Conference on Machine Learning (ICML), 2023. arXiv GitHub BibTEX Poster

  5. HQ Cai, Longxiu Huang, Pengyu Li, and Deanna Needell. Matrix Completion with Cross-Concentrated Sampling: Bridging Uniform Sampling and CUR Sampling, IEEE Transactions on Pattern Analysis and Machine Intelligence (TPAMI), 45(8): 10100–10113, 2023. arXiv GitHub BibTEX

  6. HQ Cai, Jian-Feng Cai, and Juntao You. Structured Gradient Descent for Fast Robust Low-Rank Hankel Matrix Completion, SIAM Journal on Scientific Computing (SISC), 45(3): A1172–A1198, 2023. arXiv GitHub BibTEX

  7. HQ Cai, Daniel Mckenzie, Wotao Yin, and Zhenliang Zhang. A One-Bit, Comparison-Based Gradient Estimator, Applied and Computational Harmonic Analysis (ACHA), 60: 242–266, 2022. arXiv GitHub BibTEX

  8. HQ Cai, Daniel Mckenzie, Wotao Yin, and Zhenliang Zhang. Zeroth-Order Regularized Optimization (ZORO): Approximately Sparse Gradients and Adaptive Sampling, SIAM Journal on Optimization (SIOPT), 32(2): 687–714, 2022. arXiv GitHub BibTEX

  9. HQ Cai, Jialin Liu, and Wotao Yin. Learned Robust PCA: A Scalable Deep Unfolding Approach for High-Dimensional Outlier Detection. In Advances in Neural Information Processing Systems (NeruIPS), 2021. arXiv GitHub BibTEX Poster

  10. HQ Cai, Yuchen Lou, Daniel Mckenzie, and Wotao Yin. A Zeroth-Order Block Coordinate Descent Algorithm for Huge-Scale Black-Box Optimization. In International Conference on Machine Learning (ICML), 2021. arXiv GitHub BibTEX Poster

  11. HQ Cai, Keaton Hamm, Longxiu Huang, and Deanna Needell. Mode-wise Tensor Decompositions: Multi-dimensional Generalizations of CUR Decompositions. Journal of Machine Learning Research (JMLR), 22(185): 1–36, 2021. arXiv GitHub BibTEX

  12. HQ Cai, Keaton Hamm, Longxiu Huang, and Deanna Needell. Robust CUR Decomposition: Theory and Imaging Applications. SIAM Journal on Imaging Sciences (SIIMS), 14(4): 1472–1503, 2021. arXiv BibTEX

  13. HQ Cai, Keaton Hamm, Longxiu Huang, Jiaqi Li, and Tao Wang. Rapid Robust Principal Component Analysis: CUR Accelerated Inexact Low Rank Estimation. IEEE Signal Processing Letters (SPL), 28: 116–120, 2021. arXiv GitHub BibTEX

  14. HQ Cai, Jian-Feng Cai, Tianming Wang, and Guojian Yin. Accelerated Structured Alternating Projections for Robust Spectrally Sparse Signal Recovery. IEEE Transactions on Signal Processing (TSP), 69: 809–821, 2021. arXiv GitHub BibTEX

  15. HQ Cai, Jian-Feng Cai, and Ke Wei. Accelerated Alternating Projections for Robust Principal Component Analysis. Journal of Machine Learning Research (JMLR), 20(1): 685–717, 2019. arXiv GitHub BibTEX Poster Demo

    16. Other Referred Conference and Workshop Papers

  16. HQ Cai, Longxiu Huang, Chandra Kundu, and Bowen Su. On the Robustness of Cross-Concentrated Sampling for Matrix Completion. In Conference of Information Sciences and Systems (CISS), 2024. arXiv

  17. Chandler Smith, Samuel Lichtenberg, HQ Cai, and Abiy Tasissa. Riemannian Optimization for Euclidean Distance Geometry. In Conference on Neural Information Processing Systems (NeruIPS) Workshops, 2023. BibTEX Poster

  18. Zheng Tan, Longxiu Huang, HQ Cai, and Yifei Lou. Non-convex Approaches for Low-Rank Tensor Completion under Tubal Sampling. In International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2023. arXiv BibTEX Poster

  19. Keaton Hamm, Mohamed Meskini, and HQ Cai. Riemannian CUR Decompositions for Robust Principal Component Analysis. In International Conference on Machine Learning (ICML) Workshops, 2022. arXiv BibTEX Poster

  20. HQ Cai, Zehan Chao, Longxiu Huang, and Deanna Needell. Fast Robust Tensor Principal Component Analysis via Fiber CUR Decomposition. In International Conference on Computer Vision (ICCV) Workshops, 2021. arXiv GitHub BibTEX

    21. Technical Reports

  21. Dylan King, Caroline Hills, Michael Kielstra, and Matt Torrence. Parallel Time Integration for Constrained Optimization. Lawrence Livermore National Lab, Report No. LLNL-SR-822456, 2020. Academic Mentor: HQ Cai. Sponsoring Mentors: Rob Falgout, Jeff Hittinger, and Cosmin Petra. PDF

  22. Elijah Gross-Sable, Jacky Lee, Xia Li, Tyler Sam, and Nate Sands. Trained to Kill: Analyzing Homicide Data in Los Angeles County. UCLA Computational and Applied Mathematics REU, Final Report for LA Homicide Narratives, 2019. Principal Investigators: Andrea Bertozzi and Jeffrey Brantingham. Academic Mentors: Michael Lindstrom and HQ Cai. PDF

Dissertation:


Editorship:


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