报告题目：Learning algorithm based on random projection and applications
Sample-based machine learning is one of the most important research areas at the intersection of probability, statistics, computer science, and optimization that studies the performance of computer algorithms for making predictions on the basis of training data.
The main issue of this report is to design the learning algorithm based on random projection and to study its convergence. Firstly, we discuss the well-known Johnson-Lindenstrauss (JL) Lemma and establish the kernel form of JL Lemma. Secondly, we discuss the regularization learning algorithm based on random projection in the case of convex loss and establish its convergence rates. Thirdly, we study the functional regularization regression algorithms by using the Rademacher average method. Finally, the coefficient regularized regression algorithm with random projection is proposed.
In addition, the learning algorithm is applied to material design. Material design is contingent on the availability of reliable linkages between the microstructure and its associated mechanical properties. This work investigates a surrogate model, which is derived from 3D image-based simulation for revealing the optimum microstructure of particles in materials. The proposed methodology has good computational efficiency and accuracy.
Han Li received BS degree in mathematics and applied mathematics from Faculty of Mathematics and Computer Science in Hubei University in 2007. She received her Ph.D. degree in the School of Mathematics and Statistics at Beijing University of Aeronautics and Astronautics.Her research interests include neural networks, learning theory and pattern recognition. She now works as an assistant professor in College of Science and Engineering, Aoyama Gakuin University.