报告题目：Generative Learning with Euler Particle Transport
报告摘要：We propose an Euler particle transport (EPT) approach for generative learning. EPT is motivated by the problem of constructing the optimal transport map from a reference distribution to a target distribution characterized by the Monge-Ampere equation. Interpreting the infinitesimal linearization of the Monge-Ampere equation from the perspective of gradient flows in measure spaces leads to a stochastic McKean-Vlasov equation. We use the forward Euler method to solve this equation. The resulting forward Euler map pushes forward a reference distribution to the target. This map is the composition of a sequence of simple residual maps, which are computationally stable and easy to train. The key task in training is the estimation of the density ratios or differences that determine the residual maps. We estimate the density ratios (differences) based on the Bregman divergence with a gradient penalty using deep density-ratio fitting. We show that the proposed density-ratio estimators do not suffer from the “curse of dimensionality” if data is supported on a lower-dimensional manifold. Numerical experiments with multi-mode synthetic datasets and comparisons with the existing methods on real benchmark datasets support our theoretical results and demonstrate the effectiveness of the proposed method.
报告人简介：焦雨领，武汉大学数学与统计学院副教授，主要从事科学计算、机器学习方面研究, 主持国家自然科学基金面上项目、青年项目和湖北省自然科学基金面上项目各一项。在包括 SIAM Journal on Numerical Analysis, SIAM Journal on Scientific Computing, Applied and Computational Harmonic Analysis, Journal of Machine Learning Research, Statistical Science, Inverse Problems, IEEE Transactions on Signal Processing, ICML 等在内的期刊、会议上发表40余篇论文。