Research

Research Interests

• Mathematical data science

• High-dimensional statistics

• Reinforcement learning

• Convex and non-convex optimization

Publications and Preprints

• Provable Acceleration for Diffusion Models under Minimal Assumptions
  Gen Li*, Changxiao Cai* (* = equal contribution)
  

• Minimax-Optimal Trust-Aware Multi-Armed Bandits
  Changxiao Cai, Jiacheng Zhang (alphabetical order)
  

• Transfer Learning for Contextual Multi-Armed Bandits
  Changxiao Cai, T. Tony Cai, Hongzhe Li
  The Annals of Statistics 52.1 (2024): 207-232.

• Minimax Estimation of Linear Functions of Eigenvectors in the Face of Small Eigen-Gaps
  Gen Li, Changxiao Cai, H. Vincent Poor, Yuxin Chen.

• Is Q-Learning Minimax Optimal? A Tight Sample Complexity Analysis
  Gen Li, Changxiao Cai, Yuxin Chen, Yuting Wei, Yuejie Chi
  Operations Research 72.1 (2024): 222-236.
  accepted in part to ICML 2021 [ICML version].

• Subspace Estimation from Unbalanced and Incomplete Data Matrices: \(\ell_{2,\infty}\) Statistical Guarantees
  Changxiao Cai, Gen Li, Yuejie Chi, H. Vincent Poor, Yuxin Chen
  The Annals of Statistics, 49 (2): 944–967, 2021.

• Uncertainty Quantification for Nonconvex Tensor Completion: Confidence Intervals, Heteroscedasticity and Optimality
  Changxiao Cai, H. Vincent Poor, Yuxin Chen
  IEEE Transactions on Information Theory, 69 (1): 407-452, 2023
  accepted in part to ICML 2020 [ICML version].

• Nonconvex Low-Rank Tensor Completion from Noisy Data
  Changxiao Cai, Gen Li, H. Vincent Poor, Yuxin Chen
  Operations Research, 70 (2): 1219-1237, 2022
  accepted in part to Conference on Neural Information Processing Systems (NeurIPS) 2019 [NeurIPS version].

• Conditional Rényi Divergence Saddlepoint and the Maximization of \(\alpha\)-Mutual Information
  Changxiao Cai, Sergio Verdú
  Entropy, Special Issue on Probabilistic Methods in Information Theory, Hypothesis Testing, and Coding, 21 (10): 969, 2019.

• Structured Low-Rank Matrix Factorization for Haplotype Assembly
  Changxiao Cai, Sujay Sanghavi, Haris Vikalo
  IEEE Journal of Selected Topics in Signal Processing, Special Issue on Structured Matrices in Signal and Data Processing, 10 (4): 647–657, 2016.

• Structurally-constrained Gradient Descent for Matrix Factorization in Haplotype Assembly Problems
  Changxiao Cai, Sujay Sanghavi, Haris Vikalo
  IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2016.