Learning Graphons via Structured Gromov-Wasserstein Barycenters

We propose a novel and principled method to learn a nonparametric graph model called graphon, which is defined in an infinite-dimensional space and represents arbitrary-size graphs. Based on the weak regularity lemma from the theory of graphons, we leverage a step function to approximate a graphon. We show that the cut distance of graphons can be relaxed to the Gromov-Wasserstein distance of their step functions. Accordingly, given a set of graphs generated by an underlying graphon, we learn the corresponding step function as the Gromov-Wasserstein barycenter of the given graphs. Furthermore, we develop several enhancements and extensions of the basic algorithm, $e.g.$, the smoothed Gromov-Wasserstein barycenter for guaranteeing the continuity of the learned graphons and the mixed Gromov-Wasserstein barycenters for learning multiple structured graphons. The proposed approach overcomes drawbacks of prior state-of-the-art methods, and outperforms them on both synthetic and real-world data. The code is available at https://github.com/HongtengXu/SGWB-Graphon

Multi-Task Multi-Dimensional Hawkes Processes for Modeling Event Sequences

We propose a Multi-task Multi-dimensional Hawkes Process (MMHP) for modeling event sequences where there exist multiple triggering patterns within sequences and structures across sequences. MMHP is able to model the dynamics of multiple sequences jointly by imposing structural constraints and thus systematically uncover clustering structure among sequences. We propose an effective and robust optimization algorithm to learn MMHP models, which takes advantage of alternating direction method of multipliers (ADMM), majorization minimization and Euler-Lagrange equations. Our experimental results demonstrate that MMHP performs well on both synthetic and real data

State and Market in Socialist Development: the case of Chinese industrial planning

SUMMARY This article examines the capacities and limits of the socialist state as an instrument of industrialisation in China. Chinese experience suggests that state involvement at all stages of socialist industrialisation should become more selective in its scope and more flexible in its managerial forms. It highlights the importance of developing a lively industrial microeconomy and striking a balance between state agencies and industrial enterprises. RESUMEN Estado y mercado en el desarrollo socialista: el caso de la planificación industrial china. Este articulo examina la capacidad y límites del estado socialista como instrumento de industrialización en China. La experiencia de este país sugiere que la participación estatal en todas las etapas de la industrialización socialista, debería ser más selectiva en su campo de acción y más flexible en sus formas administrativas. Subraya la importancia de desarrollar una microeconomía industrial dinámica y de lograr un equilibrio entre las agencias estatales y las empresas industriales. RESUMES Etat et marché dans le développement socialiste: le cas de la planification industrielle en Chine Cet article examine les capacités et les limites de l'état socialiste en tant qu'instrument d'industrialisation en Chine. L'expérience chinoise suggère que l'implication de l'état à tous les niveaux de l'industrialisation socialiste devrait devenir plus sélective dans son but et plus flexible dans ses formes directoriales. Elle souligne l'importance de développer une micróeconomie industrielle bien vivante et d'établir un équilibre entre les agences d'état et les entreprises industrielles