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JIAJI SU

su_jiaji(at)nus.edu.sg. A Research Fellow at DSDS, NUS.

S16, 6 Science Drive 2

Faculty of Science, NUS

Singapore 117546

I am Su Jiaji (苏佳骥), a freshman in the statistical research community.

Currently I hold a position as a research fellow in the Department of Statistics
and Data Science at the National University of Singapore (NUS). My academic
journey at NUS began in August 2018, culminating in a Ph.D. in Statistics in
January 2024 under the guidance of associate professor Zhigang YAO. Prior to my
journey in Singapore, I earned a B.S. in Statistics from Zhejiang University in
2018. For additional details about my academic and professional journey, please
refer to my CV.

My research primarily focuses on statistical inference related to singularities,
including manifold fitting in Euclidean spaces, real data dimension reduction,
and solving ill-posed inverse problems. In addition, I have a keen interest in
machine learning, particularly in the theoretical and practical applications of
neural networks.


NEWS

Jan 31, 2024 My PhD. in Statistics is conferred! Jan 24, 2024 Our PNAS paper is
online! Oct 01, 2023 I have onboard the RF job at DSDS NUS.


LATEST POSTS

Apr 10, 2024 What is manifold fitting?


SELECTED PUBLICATIONS

 1. Manifold Fitting
    Zhigang Yao, Jiaji Su, Bingjie Li , and Shing-Tung Yau
    2023
    
    Abs arXiv Bib Code
    
    While classical data analysis has addressed observations that are real
    numbers or elements of a real vector space, at present many statistical
    problems of high interest in the sciences address the analysis of data that
    consist of more complex objects, taking values in spaces that are naturally
    not (Euclidean) vector spaces but which still feature some geometric
    structure. Manifold fitting is a long-standing problem, and has finally been
    addressed in recent years by Fefferman et. al
    (\citefefferman2020reconstruction,fefferman2021reconstruction). We develop a
    method with a theory guarantee that fits a d-dimensional underlying manifold
    from noisy observations sampled in the ambient space \mathbbR^D. The new
    approach uses geometric structures to obtain the manifold estimator in the
    form of image sets via a two-step mapping approach. We prove that, under
    certain mild assumptions and with a sample size N=\mathcalO(σ^-(d+3)), these
    estimators are true d-dimensional smooth manifolds whose estimation error,
    as measured by the Hausdorff distance, is bounded by \mathcalO(σ^2\log(1/σ))
    with high probability. Compared with the existing approaches proposed in
    \citefefferman2018fitting, fefferman2021fitting, genovese2014nonparametric,
    yao2019manifold, our method exhibits superior efficiency while attaining
    very low error rates with a significantly reduced sample size, which scales
    polynomially in σ^-1 and exponentially in d. Extensive simulations are
    performed to validate our theoretical results. Our findings are relevant to
    various fields involving high-dimensional data in machine learning.
    Furthermore, our method opens up new avenues for existing non-Euclidean
    statistical methods in the sense that it has the potential to unify them to
    analyze data on manifolds in the ambience space domain.
    
    @misc{yao2023manifold,
      title = {Manifold Fitting},
      author = {Yao, Zhigang and Su, Jiaji and Li, Bingjie and Yau, Shing-Tung},
      year = {2023},
      archiveprefix = {arXiv},
      primaryclass = {math.ST}
    }

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