Interacting Particle Systems on Networks: joint inference of the network and the interaction kernel
Department of Mathematics, Duke University, Durham, USA（杜克大学数学系，美国达勒姆）；School of Mathematics, Sun Yat-sen University, Guangzhou, China（中山大学数学学院，中国广州）；Department of Mathematics, Johns Hopkins University, Baltimore, USA（约翰霍普金斯大学数学系，美国巴尔的摩）；Department of Applied Mathematics and Statistics, Johns Hopkins University, Baltimore, USA（约翰霍普金斯大学应用数学与统计学系，美国巴尔的摩）
Modeling multi-agent systems on networks is a fundamental challenge in a wide variety of disciplines. Given data consisting of multiple trajectories, we jointly infer the (weighted) network and the interaction kernel, which determine, respectively, which agents are interacting and the rules of such interactions. Our estimator is based on a non-convex optimization problem, and we investigate two approaches to solve it: one based on an alternating least squares (ALS) algorithm, and another based on a new algorithm named operator regression with alternating least squares (ORALS). Both algorithms are scalable to large ensembles of data trajectories. We establish coercivity conditions guaranteeing identifiability and well-posedness. The ALS algorithm appears statistically efficient and robust even in the small data regime, but lacks performance and convergence guarantees. The ORALS estimator is consistent and asymptotically normal under a coercivity condition. We conduct several numerical experiments ranging from Kuramoto particle systems on networks to opinion dynamics in leader-follower models.
BOOST: A Data-Driven Framework for the Automated Joint Selection of Kernel and Acquisition Functions in Bayesian Optimization
Department of Chemical and Biomolecular Engineering, Korea Advanced Institute of Science and Technology（化学与生物分子工程系，韩国科学技术院）；Department of AX, Korea Advanced Institute of Science and Technology（AX系，韩国科学技术院）；Saudi Aramco-KAIST CO2 Management Center（沙特阿美-KAIST二氧化碳管理中心）
Kernel spectral joint embeddings for high-dimensional noisy datasets using duo-landmark integral operators
Department of Statistics, University of California, Davis（统计系，加州大学戴维斯分校）；Department of Biostatistics, T.H. Chan School of Public Health, Harvard University（生物统计系，哈佛大学T.H. Chan公共卫生学院）；Department of Data Science, Dana-Farber Cancer Institute（数据科学系，达纳-法伯癌症研究所）；Broad Institute of MIT and Harvard（哈佛大学和MIT Broad研究所）
Learning Multi-type heterogeneous interacting particle systems
Department of Mathematics, Duke University（杜克大学数学系）；School of Mathematics, Sun Yat-sen University（中山大学数学学院）；Department of Mathematics, Johns Hopkins University（约翰霍普金斯大学数学系）；Department of Applied Mathematics and Statistics, Johns Hopkins University（约翰霍普金斯大学应用数学与统计学系）
