主讲本科课程：《概率论》、《数理统计》、《多元统计分析》、《寿险精算》等。
主讲研究生课程:《高等数理统计》、《统计学习理论》、《多元统计分析》等。
统计学习理论、稳健统计、深度学习等相关领域。
1． 对一系列高维学习算法的理论研究，国家自然科学基金青年基金，2011.01-2013.12，主持；
2. 信息论学习中的正则化及相关高维数据分析方法的数学理论，国家自然科学基金面上项目，2015.01-2018.12，主持；
3. 半监督流形学习的数学理论，国家自然科学基金面上项目，2019.01-2022.12， 主持；
4． 稀疏与冗余表征的理论及应用研究，国家自然科学基金面上项目，2012.01-2015.12，参与，第三；
5. 基于小波框架的散乱数据重构及其在计算生物中的应用，国家自然科学基金面上项目，2018.01-2021.12，参与，第二。
1. D. R. Chen and D. H. Xiang, The consistency of multicategory support vector machines, Advances in Computational Mathematics 24 (2006), 155-169.
2. D. R. Chen and D. H. Xiang, A construction of multiresolution analysis on interval, Acta Mathematica Sinica (English Series) 23 (2007), 705-710.
3. Z. W. Pan, D. H. Xiang, Q. W. Xiao, and D. X. Zhou, Parzen windows for multi-class classification, Journal of Complexity 24 (2008), 606-618.
4. D. H. Xiang and D. X. Zhou, Classification with Gaussians and convex loss, Journal of Machine Learning Research 10 (2009), 1447-1468.
5. H. Y. Wang, D. H. Xiang and D. X. Zhou, Moving least-square method in learning theory, Journal of Approximation Theory 162 (2010), 599-614.(Corresponding author)
6. B. H. Sheng and D . H. Xiang, The convergence rate for a K-functional in learning theory, Journal of Inequalities and Applications, 2010, doi:10.1155/2010/249507.
7. D. H. Xiang, Classification with Gaussians and convex loss II : improving error bounds by noise conditions, Sci China Math 54 (2011), 165-171.
8. D. H. Xiang, Logistic classification with varying Gaussians, Computers and Mathematics with Applications, 61 (2011), 397-407.
9. D. H. Xiang, T. Hu and D. X. Zhou, Learning with varying insensitive loss, Applied Mathematics Letters, 24 (2011), 2107-2109.
10. D. H. Xiang, Conditional quantiles with varying Gaussians, Advances in Computational Mathematics, 2011, doi: 10.1007/s10444-011-9257-5.
11. B. H. Sheng and D. H. Xiang, The consistency analysis of coefficient regularized classification with convex loss, WSEAS Transactions on Mathematics, 10 (2011), 291-300.
12. D. H. Xiang, A new comparison theorem on conditional quantiles, Applied Mathematics Letters, 25 (2012), 58-62, doi:10.1016/j.aml.2011.05.048.
13. D. H. Xiang, T. Hu and D. X. Zhou, Approximation analysis of learning algorithms for support vector regression and quantile regression, Journal of Applied Mathematics, 2012(2012), 17 pages, doi:10.1155/2012/902139.
14. B. H. Sheng and D. H. Xiang, Bound the learning rates with generalized gradients, WSEAS Transactions on Signal Processing, 8(2012), 1-10.
15. T. Hu, D. H. Xiang and D. X. Zhou, Online learning for quantile regression, Journal of Statistical Inference and Planning, 142(2012), 3107-3122.
16. D. H. Xiang, ERM scheme for quantile regression, Abstract and Applied Analysis, 2013(2013), 1-6, http://dx.doi.org/10.1155/2013/148490.
17. B. H. Sheng and D. H. Xiang, The learning rate of l2-coefficient regularized classification with strong loss, Acta Mathematica Sinica, English Series,29 (2013),2397-2408.
18. B. H. Sheng, D. H. Xiang and P. X. Ye,Convergence rate of semi-supervised gradient learning. International Journal of Wavelets, Multiresolution and Information Processing,13 (2015), 26 pages, doi:10.1142/S0219691315500216.
19. J. Cai and D. H. Xiang, Statistical consistency of coefficient-based conditional quantile regression, Journal of Multivariate Analysis,149 (2016), 1-12.
20. A. Christmann, F. Dumpert and D. H. Xiang, On extension theorems and their connection to universal consistency in machine learning. Analysis and Applications, 14 (2016), 795-808.
21. Z. C. Guo, D. H. Xiang, X. Guo and D. X. Zhou, Thresholded spectral algorithms for sparse approximations. Analysis and Applications, 15 (2017), 433-455. （高被引论文）
22. B. H. Sheng and D. H. Xiang, The performance of semi-supervised Laplacian regularized regression with the least square loss. International Journal of Wavelets, Multiresolution and Information Processing, 15 (2017), 1-31.
23. A. Christmann, D. H. Xiang and D. X. Zhou, Total stability of kernel methods, Neurocomputing, 289(2018), 101–118.
1. City University of Hong Kong Outstanding Academic Performance Award for Research Degree Students, HK$ 1,000, 2008.
2. City University of Hong Kong Research Tuition Scholarship, HK$ 15,000, 2008.