Yuxin Chen

I am a Professor of Statistics and Data Science and of Electrical and Systems Engineering at University of Pennsylvania. Before moving to UPenn in 2022, I was an assistant professor of Electrical and Computer Engineering, and an associated faculty member of Computer Science and Applied and Computational Mathematics at Princeton University from 2017 to 2021. Prior to this, I was a postdoc in Statistics at Stanford University from 2015 to 2017, and obtained my Ph.D. in Electrical Engineering at Stanford University in Jan 2015. Contact: 313 Academic Research Building 265 South 37th Street, Philadelphia, PA 19104 Email: yuxinc at wharton dot upenn dot edu

Openings

I'm looking for highly motivated postdocs and Ph. D. students with strong mathematical background and interest in machine learning theory (particularly diffusion models, LLM, and RL), statistics, and optimization.

Recent news

Together with Prof. Yuejie Chi and Prof. Yuting Wei, we will present a tutorial on reinforcement learning at the 2025 INFORMS Annual Meetings. Together with Prof. Qing Qu and Prof. Liyue Shen, we presented a tutorial on diffusion models at ICML 2025. Check out our website. See also [slides of my part] Our paper on implicit regularization in nonconvex statistical estimation received the SIAM Activity Group on Imaging Science Best Paper Prize (SIAM news). Our paper on MagNet (an ML framework for power magnetics modeling) received the IEEE Transactions on Power Electronics Prize Paper Award (first place). (Project webpage by Prof. Minjie Chen's lab). Zihan Zhang will join HKUST as an Assistant Professor in August 2025. Congrats, Zihan! Yuchen Zhou joined UIUC as an Assistant Professor in July 2024. Congrats, Yuchen! Hong Hu joined WUSTL as an Assistant Professor in August 2024. Congrats, Hong! Joshua Agterberg joined UIUC as an Assistant Professor in August 2024. Congrats, Joshua! Yuling Yan joined UW-Madison as an Assistant Professor in August 2024. Congrats, Yuling! Our new monograph "Spectral Methods for Data Science: A Statistical Perspective" is published in Foundations and Trends in Machine Learning. See slides for PKU summer school on theoretical statistics.

Topic courses I have developed

• Fall 2023: STAT9910-303: Large-Scale Optimization for Data Science (UPenn)
  

• Spring 2022: STAT991-302: Mathematics of High-Dimensional Data (UPenn)
  

• Fall 2020: ELE520: Mathematics of Data Science (Princeton)
  

Selected recent papers

• In-context learning

  • G. Li*, Y. Jiao*, Y. Huang, Y. Wei, Y. Chen, “Transformers meet in-context learning: A universal approximation theory,” 2025 (*=equal contributions). [slides]

• Diffusion models

  • J. Liang, Z. Huang, Y. Chen, “Low-dimensional adaptation of diffusion models: Convergence in total variation,” 2025 (accepted in part to COLT 2025). [slides]

  • Z. Huang, Y. Wei, Y. Chen, “Denoising diffusion probabilistic models are optimally adaptive to unknown low dimensionality,” 2024.

  • G. Li, Y. Wei, Y. Chi, Y. Chen, “A sharp convergence theory for the probability flow ODEs of diffusion models,” 2024. [slides]

  • G. Li*, Y. Huang*, T. Efimov, Y. Wei, Y. Chi, Y. Chen, “Accelerating convergence of score-based diffusion models, provably,” ICML 2024 (*=equal contributions). [slides][code]

• Optimization and statistical learning

  • Z. Zhang, J. D. Lee, S. S. Du, Y. Chen, “Anytime acceleration of gradient descent,” COLT 2025.

  • Z. Zhang, W. Zhan, Y. Chen, S. S. Du, J. D. Lee, “Optimal multi-distribution learning,” 2023 (appeared in part in COLT 2024). [slides]

• Reinforcement learning

  • Z. Zhang, Y. Chen, J. D. Lee, S. S. Du, “Settling the sample complexity of online reinforcement learning,” accepted to Journal of the ACM, 2025+ (appeared in part in COLT 2024). [slides]

  • G. Li, L. Shi, Y. Chen, Y. Chi, Y. Wei, “Settling the sample complexity of model-based offline reinforcement learning,” Annals of Statistics, vol. 52, no. 1, pp. 233-260, 2024. [paper][AoS version]

  • G. Li, Y. Wei, Y. Chi, Y. Chen, “Softmax policy gradient methods can take exponential time to converge,” Mathematical Programming, vol. 201, pp. 707-802, 2023 (appeared in part to COLT 2021). [paper][MP version][slides]

  • G. Li, C. Cai, Y. Chen, Y. Wei, Y. Chi, “Is Q-Learning minimax optimal? A tight sample complexity analysis,” Operations Research, vol. 72, no. 1, pp. 203-221, 2024 (appeared in part to ICML 2021). [paper][OR version]

  • S. Cen, C. Cheng, Y. Chen, Y. Wei, Y. Chi, “Fast global convergence of natural policy gradient methods with entropy regularization,” Operations Research, vol. 70, no. 4, pp. 2563–2578, 2022 (INFORMS George Nicholson award finalist, 2021). [ArXiv][OR version][slides]

  • G. Li, Y. Wei, Y. Chi, Y. Chen, “Breaking the sample size barrier in model-based reinforcement learning with a generative model,” Operations Research, vol. 72, no. 1, pp. 222-236, 2024 (appeared in part to NeurIPS 2020). [paper][OR version][slides]

• Nonconvex optimization for statistical estimation

  • Y. Chen, J. Fan, C. Ma, Y. Yan, “Bridging convex and nonconvex optimization in robust PCA: Noise, outliers, and missing data,” Annals of Statistics, vol. 49, no. 5, pp. 2948-2971, Oct. 2021. [ArXiv][AoS version]

  • C. Cai, G. Li, H. V. Poor, Y. Chen, “Nonconvex low-rank tensor completion from noisy data,” Operations Research, vol. 70, no. 2, pp. 1219–1237, 2022 (appeared in part in NeurIPS 2019). [ArXiv][OR version][slides]

  • Y. Chen, J. Fan, C. Ma, Y. Yan, “Inference and uncertainty quantification for noisy matrix completion,” Proceedings of the National Academy of Sciences (PNAS), vol. 116, no. 46, pp. 22931–22937, Nov. 2019. [ArXiv][PNAS version][slides]

  • Y. Chen, Y. Chi, J. Fan, C. Ma, Y. Yan, “Noisy matrix completion: Understanding statistical guarantees for convex relaxation via nonconvex optimization,” SIAM Journal on Optimization, vol. 30, no. 4, pp. 3098–3121, October 2020. [ArXiv][slides]

  • Y. Chen, Y. Chi, J. Fan, C. Ma, “Gradient descent with random initialization: Fast global convergence for nonconvex phase retrieval,” Mathematical Programming, vol. 176, no. 1-2, pp. 5-37, July 2019. [ArXiv][slides]

  • C. Ma, K. Wang, Y. Chi, Y. Chen, “Implicit regularization in nonconvex statistical estimation: Gradient descent converges linearly for phase retrieval, matrix completion, and blind deconvolution,” Foundations of Computational Mathematics, vol. 20, no. 3, pp. 451-632, June 2020 (SIAM Activity Group on Imaging Science Best Paper Prize). [main text][supplement][full paper (Arxiv)][slides]

  • Y. Chen and E. J. Candes, “Solving random quadratic systems of equations is nearly as easy as solving linear systems,” Communications on Pure and Applied Mathematics, vol. 70, issue 5, pp. 822-883, May 2017 (ICCM Best Paper Award (Gold Medal), and Finalist for Best Paper Prize for Young Researchers in Continuous Optimization). [slides][website]

• Spectral methods

  • Y. Zhou, Y. Chen, “Deflated HeteroPCA: Overcoming the curse of ill-conditioning in heteroskedastic PCA,” Annals of Statistics, vol. 53, no. 1, pp. 91-116, 2025. [ArXiv][AoS version][slides]

  • Y. Yan, Y. Chen, J. Fan, “Inference for heteroskedastic PCA with missing data,” Annals of Statistics, vol. 52, no. 2, pp. 729-756, 2024. [ArXiv][AoS version][slides]

  • C. Cai, G. Li, Y. Chi, H. V. Poor, Y. Chen, “Subspace estimation from unbalanced and incomplete data matrices, $\ell_{2,\infty}$ statistical guarantees ” Annals of Statistics, vol. 49, no. 2, pp. 944-967, 2021. [ArXiv][AoS version]

  • Y. Chen, J. Fan, C. Ma, K. Wang, “Spectral method and regularized MLE are both optimal for top-K ranking,” Annals of Statistics, vol. 47, no. 4, pp. 2204-2235, August 2019. [ArXiv][AoS version][slides]