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[RESEARCH HIGHLIGHTS]
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Our
research group is deeply engaged in a multifaceted exploration at the intersection
of statistics, geometry, and real world data, seeking to unravel complex
problems through a series of innovative projects
and seminars.
At
the heart of our work in the Interaction of Statistics and Geometry,
we explore manifold fitting
and estimation, developing state-of-the-art methods for constructing and
evaluating smooth submanifolds for data set approximation, inspired by the
geometric complexity of the Whitney problem. We extend our geometric
investigation through the study of principal
submanifolds
and classification challenges on Riemannian manifolds, developing
sophisticated statistical techniques to exploit the unique properties of
manifold structures for data analysis, including the development of
principal currents, submanifolds and nonlinear classifiers. Our research
also ventures into the geometrical
intricacies of Calabi-Yau manifolds,
aiming to decode the geometry of their moduli spaces. We are also
pioneering the development of graphical
models and classification strategies in high-dimensional settings,
introducing a novel two-stage classification approach that uses innovative
thresholding and quadratic discriminant analysis to navigate the
complexities of high-dimensional data. Apart from advancing theoretical understanding,
these methods have been applied to the analysis of complex, real-world
datasets, such as single-cell RNA sequencing
and UK Biobank data,
highlighting the practical impact of our work.
Under
the umbrella of Statistical Inference for Inverse Problem with
Singularity, our projects address pressing questions in brain imaging,
using advanced techniques to investigate time-varying source distributions
in magnetoencephalography (MEG) and to develop predictive behavioral models based on MEG/EEG data. At the same
time, we are pioneering non-traditional methods to address the inverse
problem in tomographic reconstruction, to revolutionize 3D particle
reconstruction from 2D random projections in cryo-electron microscopy (cryo-EM).
Our group's work is characterized by a relentless pursuit of knowledge at
the intersection of disparate fields, driven by the ambition to provide groundbreaking solutions to some of the most
challenging problems in science today.
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[PUBLICATIONS]
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A Principal Submanifold-Based Approach for Clustering and
Multiscale RNA Clash Correction (with Menghao
Wu) (2025) [Manuscript]
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) [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) [PDF][Manuscript] Proceedings of the National Academy of
Sciences of the United States of America, To appear.
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) [PDF][Manuscript][Code]
Distinguishing Calabi-Yau Threefolds: Topology and Machine-learning (with
Yang-Hui He and Shing-Tung Yau) (2024) [Manuscript]
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). [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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[GRANTS]
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Our work has been supported by Singapore Ministry of
Education (MOE) Academic Research Fund grants --
·
MOE Tier 1 (Startup), Modern
Statistical Methods for Complex Data, 2014-2017,
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MOE Tier 2, Magnetoencephalography (MEG) Inverse Problem,
2017-2020,
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MOE Tier 2, Learning in MEG/EEG imaging-- from
localization to behaviour prediction, 2021-2024,
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MOE Tier 2, Cryo-Electron Microscopy: Reconstruction and
Uncertainty Quantification via Manifold Learning, 2023-2027,
·
MOE Tier 2, Manifold Landscape in Data Science: Learning
beyond Euclidean Space (with Shing-Tung Yau),
2024-2028 (pending),
and by various grants from the National University of
Singapore.
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[RECRUITING]
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Ø
PhD Candidates: Interested
students are encouraged to contact me directly for possible funded positions. Preferences will be given to those with
solid mathematical/statistical background and who are willing to work
hard on challenging problems. Any exceptional
student without TOEFL/GRE scores will also be considered.
For NUS students, I normally expect at least one semester of
positive research interaction before discussing joining the group.
Ø
Postdocs: Candidates
interested in these open positions are encouraged
to get in touch directly.
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[RECENT/UPCOMING SEMINARS]
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1.
JSM Invited Talk, Nashville (Aug 2025)
2.
Statistics, Seoul National
University (March 2025)
3. Plenary Lecture (1-hour), International
Congress of Chinese Mathematicians (ICCM), Shanghai (Jan 2025)
4. Second Symposium of Geometry and Statistics in
China, Sanya/Shanghai (Jan 2025)
5.
Shanghai Institute for Mathematics and
Interdisciplinary Sciences (Dec 2024)
6. Statistical Methods for Network Analysis, Sanya (Dec 2024)
7. Sixth Conference on Computational and
Mathematical Bioinformatics and Biophysics, Sanya
(Dec 2024)
8. TOPS (Tsinghua Open Problems Seminar) Lecture,
Qiuzhen College, Tsinghua (Nov 2024)
9. IMS, Singapore (Sep and Oct 2024)
10. The International Congress of Basic Science,
Beijing (July 2024)
11.
Peking U (July 2024)
12.
Shanghai Institute for Mathematics and
Interdisciplinary Sciences (June 2024)
13.
SIAM Conference on Applied Linear Algebra,
Paris (May 2024)
14. Plenary Talk, Current Developments in
Mathematics and Physics, Beijing (April 2024)
15.
YMSC, Tsinghua (Feb 2024)
16. Invited Lecture (45-min), International
Congress of Chinese Mathematicians (ICCM), Shanghai (Jan 2024)
17. Kent, LSE and Cambridge, under London
Mathematical Society and Royal Statistical Society (Nov 2023)
18. First Symposium of Geometry and Statistics in
China, Beijing (July 2023)
19. Pujiang Innovation Forum, hosted by Ministry
of Science and Technology of China, Shanghai Municipal Government (July 2023)
20. The Inaugural International Congress of Basic
Science, Guest of Honor,
People's Hall of China, Beijing (July 2023)
21.
YMSC, Tsinghua (July 2023)
22.
YMSC, Tsinghua (June 2023)
23.
Statistics Centre, Peking U (May 2023)
24.
Applied/Computational Mathematics/Statistics,
Notre Dame (April 2023)
25. Mathematics,
Duke (March 2023)
26. Statistics
and Geometry Conference, Harvard (Feb 2023)
27.
Probability Seminar, Harvard (Feb 2023)
28.
Mathematics, Berkeley (Feb 2023)
29.
Biostatistics, Berkeley (Feb 2023)
30.
Statistics/Biostatistics, Stanford (Jan 2023)
31.
Simons Center, Stony Brook (Nov 2022)
32.
Statistics, George Mason (Nov 2022)
33.
Statistics, Columbia (Oct 2022)
34.
Statistics, UW-Madison (Oct 2022)
35.
CMSA, Harvard (Oct 2022)
36.
Statistics, Carnegie Mellon (Oct 2022)
37.
Statistics, Pitt (Sep 2022)
38.
Mathematical Sciences, WPI (Sep 2022)
39.
Statistics, Harvard (Sep 2022)
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[CONFERENCES & WORKSHOPS]
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Meeting the Statistical
Challenges in High Dimensional Data and Complex Networks, Singapore,
February 5-16, 2018 (Co-organizer) [IMPRINTS]
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Interactions of Statistics
and Geometry (ISAG I), February 14-18, 2022 (Co-organizer)
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The First Harvard
Conference on Geometry and Statistics, Center of Mathematical Sciences
and Applications, Harvard University, Feb 27-March 1, 2023 (Organizer)
[Poster]
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The
First Symposium of Geometry and Statistics in China, Yanqi Lake Beijing
Institute of Mathematical Sciences and Applications, Yau Center at Tsinghua
University, Beijing, July 29-31, 2023 (Organizer)
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Summer Seminar Series: Statistics + Geometry + X,
Shanghai Institute for Mathematics and Interdisciplinary Sciences, June
1-July 31, 2024 (Organizer)
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Interactions of Statistics
and Geometry (ISAG II), Singapore, October 14-25, 2024
(Co-organizer)
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Winter Seminar Series: Statistics + Geometry + X, Shanghai
Institute for Mathematics and Interdisciplinary Sciences, June 1-July
31, 2024 (Organizer)
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The Second Symposium of
Geometry and Statistics in China, A Satellite Conference of
2024 Annual Meeting of International Congress of Chinese Mathematicians,
Shanghai (SIMIS) and Sanya (TSIMF), January 8-12, 2024 (Organizer)
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The Second Harvard Conference on Geometry and
Statistics, Center of Mathematical Sciences
and Applications, Harvard University, scheduled in 2025 (Organizer)
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Dual Trimester Program on Geometric Statistics:
Theory, Application, and Computation, Hausdorff
Research Institute for Mathematics, scheduled in 2026 (Co-organizer)
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Interactions of Statistics and Geometry (ISAG III),
Bonn, 2026 (Co-organizer)
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Elected
Member, International Statistical Institute (ISI), 2018-present
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Member, University Research Committee (URC)
Expert Panel, 2024-present
Member, University Research Committee (URC)
Expert Panel (Informatics and Mathematics), 2022-2023
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