Educations

• Ph.D. (2010) in Mathematics,  Massachusetts Institute of Technology

Research Interests

• • Dimension Reduction, Kernel Methods, Deep Learning

Publications

Neural Networks and Kernel Regression

1. The phase diagram of kernel interpolation in large dimensions

2. On the asymptotic learning curves of kernel ridge regression under power-law decay

3. The Optimality of Kernel Classifiers in Sobolev Space

4. Generalization Error Curves for Analytic Spectral Algorithms under Power-law Decay

5. Optimal Rates of Kernel Ridge Regression under Source Condition in Large Dimensions

6. Yicheng Li, Haobo Zhang and Qian Lin*, "On the Asymptotic Learning Curves of Kernel Ridge Regression under Power-law Decay", NeurIPS2023

7. Weihao Lu, Haobo Zhang, Yicheng Li, Manyun Xu, and Qian Lin*, "Optimal rate of kernel regression in large dimensions", arXiv

8. Yicheng Li, Zixiong Yu, Guhan Chen and Qian Lin*, "On the Eigenvalue Decay Rates of a Class of Neural-Network Related Kernel Functions Defined on General Domains"( originally named "Statistical optimality of deep wide neural networks"), arXiv, Journal of Machine Learning Research, 2024

9. Haobo Zhang, Yicheng Li and Qian Lin*, "On the optimality of misspecified spectral algorithms", arXiv, Journal of Machine Learning Research, 2024

10. Haobo Zhang, Yicheng Li, Weihao Lu and Qian Lin*, "On the optimality of misspecified kernel ridge regression",ICML2023

11. Yicheng Li, Haobo Zhang and Qian Lin*, "Kernel interpolation generalizes poorly", arXiv , Biometrika ( to appear)

12. Jianfa Lai, Manyun Xu, Rui Chen and Qian Lin*, "Generalization ability of wide neural network on R", arXiv

13. Yicheng Li, Haobo Zhang and Qian Lin*, "On the Saturation effects of kernel ridge regression ", ICLR 2023

Sufficient Dimension Reduction

1. Qian Lin, "Sparse sliced average variance estimation"

2. Dongming Huang, Songtao Tian, Qian Lin*, "Sliced inverse regression with large structural dimension", arXiv

3. Qian Lin, X. Li, D. Huang and J. S. Liu.   "On Optimality  of Sliced Inverse Regression in High Dimensions",  Annals of Statistics. 2021. Volume 49, Number 1 (2021): 1-20;

4. Qian Lin, Z. Zhao and J. S. Liu.  "Sparse Sliced Inverse Regression via Lasso", Journal of the American Statistical Association. Volume 114 , Issue 528 (2019): 1726-1739;

5. Qian Lin,  Z. Zhao and J. S. Liu.     "On Consistency and Sparsity of Sliced Inverse Regression in High Dimensions,"    Annals of Statistics. Volume 46, Number 2 (2018): 580-610.  arXiv   

6. M. Neykov, Qian Lin and J. S. Liu.    "Signed Support Recovery for Single Index Models  in High Dimensions",    Annals of Mathematical Sciences and Applications Vol. 1 No. 2 (2016): 379-426   arXiv

7. Qian Lin, Z. Zhao and J. S. Liu.     "Global Testing under the Sparse Alternatives for Single Index Models",   Festschrift in Honor of R. Dennis Cook, 2021, (Book Chapter) ; 

8. Qian Lin, Y. Li and J. S. Liu.     "Inverse Modeling: A strategy to cope with nonlinearity,  Handbook of Big Data Analytics", Springer ; In Press, 2016,   (Book Chapter) ;   

Causal Inference

1. X. Li, P. Ding , Qian Lin, D. Yang and J. S. Liu.  "Randomization-based inference for peer effects",   Journal of the American Statistical Association.  Volume 114 , Issue 528 (2019): 1651-1664;

Others:

1. Qian Lin and M. Wang.     "Isogeny orbits in a family of abelian varieties",   Acta Arithmetica 170(2015), 161-173 ,   arxiv:1403.3976 

2. Roman Bezrukavnikov and Qian Lin.    "Highest weight modules at the critical level and noncommutative Springer resolution", Algebraic Groups and Quantum Groups, Contemp. Math 565 (2012): 15-27 ,   arxiv:1108.1906   

3. Qian Lin, Z. Liu and Y. Sheng.     "Quadratic Deformations of Lie-Poisson Structures", Letters in Mathematical Physics 83 (2008): 217-229,    arxiv:0707.2867