Professor Jinchao Xu: Introduction to deep learning 

2020 PKU Biostatistics Summer School

On August 22 2020, Prof. Jinchao Xu was invited to give a mini-course “Introduction to deep learning” in “2020 PKU Biostatistics Summer School” hosted by PKU Department of Biostatistics and Beijing International Center for Mathematical Research.

In the three-hour lecture, Prof. Xu first gave an elementary introduction to deep learning, including deep neural network models, training algorithms and applications. Next, he introduced a general function class of deep neural networks and discuss their mathematical properties. As a special deep neural network, he discussed the convolutional neural network (CNN) and its application to image classification. In particular, he presented a new CNN framework, known as MgNet^[1], which is motivated and derived from the classic multigrid methods used for solving discretized partial differential equations. Later, he discussed and analyzed the commonly used training algorithms, stochastic gradient decent method (SGD), and introduced some alternative new training algorithms, known as extended regularized dual averaging (XRDA) method^[2][3], that can be effectively used for training sparse deep neural networks. Finally, he introduced some applications in biostatistics.

More than 200 participants, including graduate students and professors, attended this lecture. During the lecture and Q&A section, the participants had very actively discussion with Prof. Xu.  

Reference:

[1] He, Juncai, and Jinchao Xu. "MgNet: A unified framework of multigrid and convolutional neural network." Science china mathematics 62, no. 7 (2019): 1331-1354.

[2] He, Juncai, Xiaodong Jia, Jinchao Xu, Lian Zhang, and Liang Zhao. "Make \ell_1 regularization effective in training sparse CNN." Computational Optimization and Applications 77, no. 1 (2020): 163-182.

[3] Siegel, Jonathan W., and Jinchao Xu. "Extended Regularized Dual Averaging." arXiv preprint arXiv:1904.02316 (2019).