1. About Me
  2. Papers
  3. Teaching Fellow
  4. Other Skills
  5. Selected Awards
  6. Contact Me

About Me

Hi! My name is Tianle Liu (/tʰjɛn14 ljoʊ2/, Tyler, 刘天乐 or 劉天樂). I am a fourth-year Ph.D. candidate in statistics at Harvard University, coadvised by Natesh S. Pillai and Morgane Austern. I also work closely with Xiao-Li Meng, José R. Zubizarreta, Promit Ghosal, and Krishna Balasubramanian. Previously, I obtained my B.S. degree in pure and applied mathematics at Tsinghua University in 2020. There I worked under supervision of Mingsheng Long and Hanzhong Liu. In 2019 I visited Simons Institute, UC Berkeley and Wharton School, University of Pennsylvania (hosted by Edgar Dobriban).

My research interest lies at the intersection of probability, machine learning and causal inference. On one hand, I study probability tools that are potentially useful in statistical learning and inference. On the other hand, I develop learning algorithms and causal methodology inspired by probability theory. As a person with broad interest, I always enjoy learning by research as well as learning for research. Here is a list of topics that I am familiar with:



  • Central limit theorems, Stein’s method, Concentration inequalities
  • Markov chain mixing
  • Random matrix, Free probability

Machine Learning:

  • Deep learning theory, Implicit bias of SGD, Benign overfitting
  • Probabilistic flow, Particle-based methods, Variational inference
  • Kernel methods, MMD, KSD
  • Domain adaptation, Distributionally robust optimization

Causal Inference:

  • Covariate balancing in observational studies, Targeted learning
  • Randomized experiments, Design-based inference
  • Efficient influence functions, Debiased machine learning


  • Multiple testing, Combination tests, FDR control

I might also learn about the following topics in the future. Feel free to discuss with me!

  • Anytime-valid confidence sequences
  • Malliavin calculus, Malliavin-Stein method
  • Large language models, Theory for transformers
  • Diffusion models, Schrödinger bridge, Entropic optimal transport
  • Graph neural networks
  • Persistent homology


* denotes equal contribution.


  • Tianle Liu, Morgane Austern (2022).
    Wasserstein-\(p\) Bounds in the Central Limit Theorem Under Local Dependence. Electronic Journal of Probability, 2023+.
    arXiv Cite

  • Tianle Liu, Morgane Austern (2022).
    Smooth Edgeworth Expansion and Wasserstein-\(p\) Bounds for Mixing Random Fields. Submitted, 2023.
    arXiv Cite

Machine Learning

  • Yuchen Zhang*, Tianle Liu*, Mingsheng Long, Michael I. Jordan (2019).
    Bridging Theory and Algorithm for Domain Adaptation. International Conference on Machine Learning (ICML), 2019. [Long Talk 4.6%]
    Link arXiv Cite

  • Tianle Liu, Promit Ghosal, Krishna Balasubramanian, Natesh S. Pillai (2023).
    Towards Understanding the Dynamics of Gaussian-Stein Variational Gradient Descent. Neural Information Processing Systems (NeurIPS), 2023.
    arXiv Cite

Causal Inference

  • Xin Lu, Tianle Liu, Hanzhong Liu, Peng Ding (2021).
    Design-Based Theory for Cluster Rerandomization. Biometrika, 2023.
    Link arXiv Cite

Teaching Fellow

  • STAT 210: Probability Theory (2021 Fall)
  • STAT 111: Introduction to Statistical Inference (2022 Spring)
  • STAT 185: Introduction to Unsupervised Learning (2022 Fall)
  • STAT 170: Quantitative Analysis of Capital Markets (2023 Spring)

Other Skills

  • Languages: Mandarin Chinese (native), English (fluent).
  • Coding: Python (NumPy, SciPy, Pandas, PyTorch), R, JavaScript, OCaml, Wolfram, C/C++; HTML/CSS, Shell, \(\mathrm{\LaTeX}\).
    I like versatile multi-paradigm languages including Python, JavaScript and OCaml. Interestingly among the three Python is strongest in object-oriented programming, JavaScript has more imperative syntax, and OCaml is essentially functional. C/C++ is the first programming language I’ve learned. I also use R to collaborate with statisticians and Wolfram for symbolic computing. Btw I am a big fan of VSCode.
  • Hobbies: Badminton, Bodybuilding, Chinese Calligraphy, Painting & Sketching, Tennis.
    Notably I learned Chinese calligraphy from my grandpa when I was young and trained for badminton from 2020. I have also been learning tennis since August 2023.

Please check out this fun page if you want to learn more about my hobbies.

Selected Awards

  • New England Statistical Society Student Research Award, 2023
  • Beijing Outstanding Graduate Award (Top 5% of Tsinghua), 2020
  • S.-T. Yau College Student Mathematics Contest, Bronze Medal (Team), 2018
  • Xuetang Talent Scholarship for Tsinghua Undergraduates, 2017
  • Chinese Mathematics Olympiad, Silver Medal, 2015

Contact Me

Harvard University
Science Center #704
1 Oxford St Cambridge, MA 02138, USA

tianleliu [at] fas [dot] harvard [dot] edu