The goal is to develop a family of provable stochastic algorithms for e.g. large scale optimization and training deep neural networks. The provability is established by probabilistic weak approximation and the ordinary differential equation theory. 
My goal is to develop methods that can be smoothly implemented in the ecosystem of data science, and perform provabiy accurate statistical analysis including hypothesis testing on statistical models and causal effect.
I develop quantile regression methods for economic and financial datasets that allow nonparametric modeling and/or high dimensionality $p>n$. 
Clinicians rely on medical imaging to make diagonosis. I develop machine learning methods that discover subtle patterns in brain fRMI and lung MRI. 
Chao, S.-K., Härdle, W. Wang, W. (2015). Quantile Regression in Risk Calibration, in Lee, C.-F., and Lee, J. C. (eds), Handbook of Financial econometrics and statistics, Springer, New York.
Chao, S.-K., Ning, Y. and Liu, H. (2015). On High Dimensional Post-Regularization Prediction Intervals. Unpublished manuscript.
Chao, S.-K., Proksch, K., Dette, H. and Härdle, W. (2017). Confidence corridors for nonparametric multivariate generalized quantile regression. Journal of Business and Economic Statistics, 35(1): 70-85.
Chao, S.-K., Volgushev, S. and Cheng, G. (2017). Quantile Process for Semi and Nonparametric Regression Models. Electronic Journal of Statistics, 11(2): 3272-3331.
Chao, S.-K., Härdle, W. and Huang, C. (2018). Multivariate Factorizable Expectile Regression with Application to fMRI Data. Computational Statistics and Data Analysis, 121: 1-19.
Volgushev, S., Chao, S.-K. and Cheng, G. (2019). Distributed inference for quantile regression processes. Annals of Statistics, 47(3): 1634-1662.
Chao, S.-K. and Cheng, G. (2019). A generalization of regularized dual averaging and its dynamics. Arxiv: 1909.10072.
Wang B. Z., Sheen, J., Trück, S., Chao, S.-K. and Härdle, W. (2020). A note on the impact of news on US household inflation expectations. Macroeconomic Dynamics.
Yu, Y., Chao, S.-K. and Cheng, G. (2020). Simultaneous Inference for Massive Data: Distributed Bootstrap. ICML 2020 (acceptance rate: 21.8%).
Chao, S.-K., Wang, Z., Xing, Y. and Cheng, G. (2020). Directional Pruning of Deep Neural Networks. Advances in Neural Information Processing Systems 33.
Yang, Y., Chao, S.-K.* and Cheng, G. (2021). Distributed Bootstrap for Simultaneous Inference Under High Dimensionality. Journal of Machine Learning Research (Forthcoming).
Kim, K. H., Chao, S.-K. and Härdle, W. (2021). Simultaneous Inference of Partially Linear Error-in-Covariate Models: an Application to the U.S. Gasoline Demand. Journal of Statistical Planning and Inference, 213: 93-105.
Chao, S.-K., Härdle, W. and Yuan, M. (2021). Factorisable Multitask Quantile Regression. Econometric Theory, 37(4): 794-816.
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Undergraduate course, University 1, Department, 2014
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Workshop, University 1, Department, 2015
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