講演者：Han Li
タイトル： Learning algorithm based on random projection
アブストラクト： 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. A main theme of learning is to approximate a function from random samples, maybe perturbed by noise. Learning theory provides a mathematical foundation for machine learning and its applications.
The main issue of this report is to design the learning algorithm based on the 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 Tikhonov regularization learning algorithm based on random projection in the case of convex loss and establish its convergence rates. This algorithm processes directly in the projected space, and need not to return to the original space. Therefore it greatly reduces the computational complexity. Thirdly, we study the functional regularization regression algorithms. By using the Rademacher average method we bound its excess error. This will effectively reduce or even eliminate the impact of dimension. We preprocess the functional data using the random projection and obtain the projection data set through projecting the observed samples onto the finite dimensional space. Finally, the coefficient regularized regression algorithm with random projection is proposed. The key idea is to compute the coefficients of the regression estimator by solving a system of linear equations in the latent space (the projected domain). Theoretical analysis and experiments show that learning directly in the random projected space is possible.
cc.osaka-kyoiku.ac.jp