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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) [Manuscript][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) [Manuscript][Platform]
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 [PDF][Manuscript]
--
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 Clash Correction (with Menghao
Wu) (2026). Annals of Applied
Statistics, In press. [PDF][Manuscript]
Distinguishing Calabi-Yau Threefolds: Topology and Machine-learning (with
Yang-Hui He and Shing-Tung Yau) (2026) Harvard Data Science Review,
8.1 [PDF]
[Manuscript]
Estimation of Riemannian Quantities from Noisy Data via
Density Derivatives (with Junhao Chen and Ruowei
Li) (2026). [Manuscript]
Curvature-driven Manifold Fitting under Unbounded
Isotropic Noise (with Ruowei Li) (2026). [Manuscript]
Differentially Private Manifold Denoising (with Jiaqi Wu
and Yiqing Sun) (2025). [Manuscript][PDF]
Questionnaire Non-response: A Warning Sign of Cognitive
Decline and Age-related Chronic Disease (with Bingjie Li and Yukun Lu) (2025). [Manuscript]
Enhanced High-Dimensional Data Visualization through
Adaptive Multi-Scale Manifold Embedding (with Tianhao
Ni and Bingjie Li) (2025). IEEE Transactions on Visualization and
Computer Graphics, To appear. [Manuscript]
Principal Decomposition with Nested Submanifolds (with Jiaji Su) (2025). [Manuscript]
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 [PDF][Manuscript][Code]
CellScope: A High-Performance Cell Atlas Builder
with Tree-Structured Representation (with Bingjie Li, Runyu
Lin, Tianhao Ni, Guanao Yan, Mannix Burns and
Jingyi Jessica Li) (2024). Nature Communications, 11, 1130
[PDF][Manuscript][Code][Tutorial]
Single-Cell Analysis via Manifold Fitting: A New 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
[PDF][Manuscript][Code][NUS News][Tsinghua News]
Manifold Fitting with CycleGAN
(with Jiaji Su and Shing-Tung Yau) (2023). Proceedings
of the National Academy of Sciences of the United States of America, 121
(5) e2311436121 [PDF][Manuscript][Code][NUS News][Tsinghua News]
Uncertainty Quantification in Cryo-EM: A Framework for
Continuous Variability (with Bertrand Sim) (2023). [Manuscript][Code]
Fitting Manifolds on Manifolds (2023). [Manuscript]
Manifold Fitting (with Jiaji Su,
Bingjie Li and Shing-Tung Yau) (2023). [PDF][Manuscript][Code]
Hunting Principal Sub-manifolds: New Theories and Methods
(with Bingjie Li, Do Tran and Zhenyue Zhang)
(2023). [Manuscript][Code]
Random Fixed Boundary Flows (with Yuqing Xia and Zengyan Fan) (2023). Journal of the American Statistical Association, To appear. [PDF][Code]
A Statistical Approach of Estimating Adsorption Isotherm
Parameters in Gradient Elution Preparative Liquid Chromatography (with Jiaji Su, Cheng Li and Ye Zhang) (2022). Annals of Applied Statistics, In
press. [PDF][Manuscript][Code]
High Dimensional Quadratic Discriminant Analysis:
Optimality and Phase Transitions (with Wanjie
Wang and Jingjing Wu) (2021). Electronic Journal of Statistics, Accepted in 2026 [PDF][Manuscript][Code]
Manifold Fitting and Projection via Quadratic
Approximation (with Zheng Zhai) (2021). [PDF][Manuscript][Code]
Manifold Fitting by Ridge Estimation: A
Subspace-constrained Approach (with Zheng Zhai) (2020). [PDF][Manuscript][Code]
Manifold Fitting under Unbounded Noise (with Yuqing Xia)
(2019). Journal of Machine Learning Research, 26, 1-55, 2025 [PDF][Manuscript][Code]
Community Detection Based on the L∞ Convergence of Eigenvectors in DCBM (with Yan
Liu et al.) (2019). [PDF][Manuscript]
Manifold Learning in Ambient Space (with Bingjie Li and
Wee Chin Tan) (2019). [PDF][Manuscript]
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 [PDF][Supplementary Material]
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
[PDF][Supplementary
Material]
Principal Boundary on Riemannian Manifolds (with Zhenyue Zhang) (2020). Journal of the American Statistical Association, 115 1435-1448 [PDF] [Supplementary Material]
Sufficient Dimension Reduction for Classification (with
Xin Chen, Jingjing Wu and Jia Zhang) (2018). Statistica Sinica, Accepted
in 2024 [PDF]
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 [PDF]
Principal Sub-manifolds (with Benjamin Eltzner and Tung
Pham) (2016). Statistica Sinica, Accepted in 2024 [PDF][Manuscript][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 [PDF][Supplementary Material]
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 [PDF][Manuscript]
A Statistical Approach to the Inverse Problem in
Magnetoencephalography (with William F. Eddy) (2014). Annals of Applied Statistics 8 1119-1144 [PDF][Manuscript]
Principal Flows (with Victor Panaretos, Tung
Pham) (2014). Journal of the
American Statistical Association 109
424-436 [PDF]
Optimal Classification in Sparse Gaussian Graphic Model
(with Jiashun Jin, Yingying Fan) (2013). Annals of Statistics 41 2537-2571 [PDF][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 [PDF]
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