Deep conditional distribution learning via conditional Föllmer flow
Joint Laboratory of Data Science and Business Intelligence（数据科学与商务智能联合实验室）；Southwestern University of Finance and Economics（西南财经大学）；State Key Laboratory of Mathematical Sciences（数学科学国家重点实验室）；Academy of Mathematics and Systems Science（数学与系统科学学院）；Chinese Academy of Sciences（中国科学院）；School of Mathematics and Statistics（数学与统计学学院）；Wuhan University（武汉大学）；Hubei Key Laboratory of Computational Science（湖北省计算科学重点实验室）
Jinyuan Chang, Zhao Ding, Yuling Jiao, Ruoxuan Li, Jerry Zhijian Yang
备注：
The original title of this paper is "Deep Conditional Generative Learning: Model and Error Analysis"
We introduce an ordinary differential equation (ODE) based deep generative method for learning conditional distributions, named Conditional Föllmer Flow. Starting from a standard Gaussian distribution, the proposed flow could approximate the target conditional distribution very well when the time is close to 1. For effective implementation, we discretize the flow with Euler's method where we estimate the velocity field nonparametrically using a deep neural network. Furthermore, we also establish the convergence result for the Wasserstein-2 distance between the distribution of the learned samples and the target conditional distribution, providing the first comprehensive end-to-end error analysis for conditional distribution learning via ODE flow. Our numerical experiments showcase its effectiveness across a range of scenarios, from standard nonparametric conditional density estimation problems to more intricate challenges involving image data, illustrating its superiority over various existing conditional density estimation methods.
A generative flow for conditional sampling via optimal transport
University of the Philippines Diliman（菲律宾大学迪里曼分校）；California Institute of Technology（加州理工学院）；Columbia University（哥伦比亚大学）；Baruch College（巴鲁克学院）；University of Edinburgh（爱丁堡大学）；Georgia Institute of Technology（佐治亚理工学院）；Grinnell College（格林内尔学院）；University of Michigan（密歇根大学）；Yale University（耶鲁大学）
Semi-Conditional Normalizing Flows for Semi-Supervised Learning
National Research University Higher School of Economics（国家研究型高等经济大学）；Skolkovo Institute of Science and Technology（斯科尔科沃科学技术研究院）；Moscow Institute of Physics and Technology（莫斯科物理技术学院）；Yandex School of Data Analysis（Yandex数据分析学院）；Samsung AI Center Moscow（三星莫斯科人工智能中心）；University of Amsterdam（阿姆斯特丹大学）
Conformalised Conditional Normalising Flows for Joint Prediction Regions in time series
Hasso Plattner Institute for Digital Engineering（哈索·普拉特纳数字工程学院）；University of California, Irvine（加利福尼亚大学欧文分校）；Hasso Plattner Institute for Digital Health at the Icahn School of Medicine at Mount Sinai（西奈山伊坎医学院哈索·普拉特纳数字健康研究所）
Conditional Normalizing Flows for Forward and Backward Joint State and Parameter Estimation
Department of Computer Science and Engineering University of Notre Dame（计算机科学与工程系诺特达姆大学）；Department of Pediatrics Stanford University（儿科系斯坦福大学）；Department of Applied and Computational Mathematics and Statistics University of Notre Dame（应用与计算数学与统计系诺特达姆大学）
Conditional Flow Variational Autoencoders for Structured Sequence Prediction
Max Planck Institute for Informatics（马克斯·普朗克信息学研究所）；Bosch Center for Artificial Intelligence（博世人工智能中心）；CISPA Helmholtz Center for Information Security（CISPA亥姆霍兹信息安全中心）
