|
Published Papers
Manifold Fitting: A Review of Methods and Applications
(with Jiaji Su) (2026) An Invited paper to the Special Theme -- Shaping
Data Science: A Geometric Perspective, Harvard
Data Science Review, 8.3 [Article]
[Preprint]
--
This
review paper surveys manifold fitting and concludes with a discussion of
several open problems and future directions that, in our view, naturally
emerge from the current state of the field
--
Read more on Editor’s Column and Introduction to Special
Theme
A Principal Submanifold-Based Approach for Clustering and
Multiscale RNA Correction (with Menghao Wu)
(2026). Annals of Applied
Statistics, 20 (2), 986–1009. (First preprint: 2025) [Article]
[PDF] [Preprint] [Code]
Distinguishing Calabi-Yau
Topology Using Machine Learning (with Yang-Hui He and Shing-Tung Yau)
(2026) Harvard Data Science Review, 8.1 [Article]
[Preprint]
CellScope: High-Performance Cell Atlas Workflow
with Tree-Structured Representation (with Bingjie Li, Runyu
Lin, Tianhao Ni, Guanao Yan, Mannix Burns and
Jingyi Jessica Li) (2026). Nature Communications, 17, 1130
(First preprint: 2025) [Article]
[PDF] [Preprint]
[Code] [Tutorial]
An Adaptive Multi-Scale Manifold Embedding Preprocessing
Framework for High-Dimensional Data Visualization (with Tianhao Ni and Bingjie Li) (2026). IEEE
Transactions on Visualization and Computer Graphics, 32 (10),
8099–8110. (First preprint: 2025) [Article] [Preprint]
High Dimensional Quadratic Discriminant Analysis:
Optimality and Phase Transitions (with Wanjie
Wang and Jingjing Wu) (2026). Electronic Journal of Statistics, 20 (1), 2789–2851. (First preprint: 2021) [Article]
[PDF] [Preprint]
Sufficient Dimension Reduction for Classification (with
Xin Chen, Jingjing Wu and Jia Zhang) (2026). Statistica Sinica, 36 (4), 1843–1859. (First
preprint: 2018) [Article]
[Preprint]
Principal Sub-manifolds (with Benjamin Eltzner and Tung
Pham) (2026). Statistica Sinica, 36 (3), 1069–1089. (First preprint: 2016) [Article]
[PDF]
[Preprint] [Supplementary Material]
Manifold Fitting Reveals Metabolomic Heterogeneity and
Disease Associations in UK Biobank (with Bingjie Li, Jiaji Su, Runyu Lin and Shing-Tung Yau) (2025). Proceedings
of the National Academy of Sciences of the United States of America, 122
(22) e2500001122 [Article]
[PDF] [Code]
Manifold Fitting under Unbounded Noise (with Yuqing Xia)
(2025). Journal of Machine Learning Research, 26(45), 1–55. (First preprint: 2019) [Article] [PDF] [Preprint] [Code]
Single-cell analysis via manifold fitting: A framework for
RNA clustering and beyond (with Bingjie Li, Yukun
Lu and Shing-Tung Yau) (2024). Proceedings of the National Academy of
Sciences of the United States of America, 121 (37) e2400002121
[Article]
[PDF] [Code] [NUS News] [Tsinghua News]
Manifold Fitting with CycleGAN
(with Jiaji Su and Shing-Tung Yau) (2024). Proceedings of the National
Academy of Sciences of the United States of America, 121 (5)
e2311436121 [Article]
[PDF] [Code] [NUS News] [Tsinghua News]
Random Fixed Boundary Flows (with Yuqing Xia and Zengyan Fan) (2024). Journal of the American Statistical Association, 119 (547), 2356–2368. (First preprint: 2019)
[Article]
[Preprint] [Code]
A Statistical Approach to Estimating Adsorption-Isotherm
Parameters in Gradient-Elution Preparative Liquid Chromatography (with
Jiaji Su, Cheng Li and Ye Zhang) (2023). Annals of Applied Statistics, 17 (4), 3476–3499.
(First preprint: 2022) [Article]
[Preprint] [Code]
Quantifying Time-Varying Sources in Magnetoencephalography
– A Discrete Approach (with Zengyan Fan,
Masahito Hayashi and William F. Eddy) (2020). Annals of Applied Statistics, 14, 1379-1408 [Article] [PDF] [Preprint] [Supplementary Material]
Principal Boundary on Riemannian Manifolds (with Zhenyue Zhang) (2020). Journal of the American Statistical Association, 115 1435-1448 [Article] [PDF] [Preprint]
Estimating the Rate Constant from Biosensor Data via an
Adaptive Variational Bayesian Approach (with Ye Zhang, Patrik Forssen and Fornstedt
Torgny) (2019). Annals of Applied
Statistics, 13, 2011-2042
[Article] [PDF] [Preprint] [Supplementary
Material]
Estimating the Number of Sources in Magnetoencephalography
Using Spiked Population Eigenvalues (with Ye Zhang, Zhidong Bai and
William F. Eddy) (2018). Journal of
the American Statistical Association, 113 505-518 [Article] [PDF]
[Preprint] [Supplementary Material]
A Level Set Based Variational Principal Flow Method for
Nonparametric Dimension Reduction on Riemannian Manifolds (with Hao Liu, Shingyu Leung and Tony F. Chan) (2017). SIAM Journal on Scientific Computing, 39, A1616–A1646 [Article] [PDF]
Partial Correlation Screening for Estimating Large
Precision Matrices, with Applications to Classification (with Shiqiong Huang, Jiashun
Jin) (2016). Annals of Statistics,
44 (Peter Hall Memorial Issue)
5 2018-2057 [Article]
[PDF] [Preprint]
A Statistical Approach to the Inverse Problem in
Magnetoencephalography (with William F. Eddy) (2014). Annals of Applied Statistics 8 1119-1144 [Article]
[PDF] [Preprint]
Principal Flows (with Victor Panaretos, Tung
Pham) (2014). Journal of the
American Statistical Association 109
424-436 [Article]
[PDF]
Optimal Classification in Sparse Gaussian Graphic Model
(with Jiashun Jin, Yingying Fan) (2013). Annals of Statistics 41 2537-2571 [Article] [PDF] [Preprint] [Supplementary
Material]
A Comparison of the Lasso and Marginal Regression (with
Christopher R. Genovese, Jiashun Jin and Larry
Wasserman) (2012). Journal of
Machine Learning Research 13
2107-2143 [Article]
[PDF]
Accepted / In Press
Principal Decomposition with Nested Submanifolds (with
Jiaji Su) (2026). Biometrika, Accepted. (First
preprint: 2025) [Preprint]
Discussion of "Deep Fréchet Regression"
(with Chunming Zhang) (2026). Journal of the American Statistical
Association, Accepted. [PDF]
Preprints
Includes preprints
and working manuscripts.
Beyond Curvature Bias: Higher-Order Manifold Fitting via
Multiscale Cancellation (with Zhijun Zhu, Haoyu Yang, Ruoyu
Xiong, and Bingjie Li) (2026). [PDF] [Preprint]
A Euclidean Quasi-Newton Method for Matrix-Manifold
Optimization via Approximate Global Parametrization (with Ziang Tian, Jiang Hu and Bingjie Li) (2026). [PDF]
[Preprint]
Almost-global Coordinates On
Matrix Manifolds (with Bingjie Li and Jiaxiang
Wang) (2026). [PDF] [Preprint]
Beyond Vectorization: Matrix-Structured Manifold Fitting
(with Yuqing Xia, Taoyu Zhu, Jinxi Zhang, Kehang Zhang)
(2026) [PDF] [Preprint]
Local Manifold Attention for Recovery and Generation of
Rare 3D Human Poses (with Feiyue Pan) (2026) [Preprint] [Code]
Manifold Fitting by Successive Tangent-space Projection
(with Yuqing Xia and Bingjie Li) (2026) [PDF]
[Preprint] [Code]
Multidimensional Physical Fitness is Associated with
Reduced Dementia Risk through Proteomic and Neuroimaging Pathways: A
Prospective Cohort Study of the UK Biobank (with Yiqing Sun, Runyu Lin, Jiayue Qin, Feiyue
Pan, Bingjie Li) (2026) [Preprint]
[Code]
[Platform]
Routine Blood Biomarkers Reveal a Preclinical Continuum of
Multiple Myeloma Risk (with Bingjie Li, Jiadai
Xu, Yiqing Sun, Feiyue Pan, Shing-Tung Yau and
Peng Liu) (2026) [Preprint]
[Platform]
Estimation of Riemannian Quantities from Noisy Data via
Density Derivatives (with Junhao Chen and Ruowei
Li) (2026). [PDF] [Preprint]
Curvature-driven Manifold Fitting under Unbounded
Isotropic Noise (with Ruowei Li) (2026). [PDF] [Preprint]
Differentially Private Manifold Denoising (with Jiaqi Wu
and Yiqing Sun) (2026). [PDF] [Preprint]
Questionnaire Non-response: A Warning Sign of Cognitive
Decline and Age-related Chronic Disease (with Bingjie Li and Yukun Lu) (2025). [PDF] [Preprint]
Uncertainty Quantification in Cryo-EM: A Framework for
Continuous Variability (with Bertrand Sim) (2023). [PDF]
[Preprint]
Fitting Manifolds on Manifolds (2023). Working manuscript.
Manifold Fitting (with Jiaji Su, Bingjie Li and Shing-Tung
Yau) (2023). [PDF] [Preprint] [Code]
Hunting Principal Sub-manifolds: New Theories and Methods
(with Yuqing Xia, Do Tran and Zhenyue Zhang)
(2023). Working manuscript.
Manifold Fitting and Projection via Quadratic
Approximation (with Zheng Zhai) (2021). [Preprint]
Manifold Fitting by Ridge Estimation: A
Subspace-constrained Approach (with Zheng Zhai) (2020). [Preprint]
Community Detection Based on the L∞ Convergence of Eigenvectors in DCBM (with Yan
Liu et al.) (2019). [Preprint]
Manifold Learning in Ambient Space (with Bingjie Li and
Wee Chin Tan) (2019). [Preprint]
|