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RI: Small: Dynamics of repulsion and reinforcement in point process, latent variable, and trajectory models

RI：小：点过程、潜变量和轨迹模型中排斥和强化的动力学

基本信息

批准号：
1816499
负责人：
Vinayak Rao
金额：
$ 23.4万
依托单位：
Purdue University
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2018
资助国家：
美国
起止时间：
2018-08-15 至 2022-07-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1816499&HistoricalAwards=false
关键词：
RI Small Dynamics repulsion reinforcement

项目摘要

Most traditional ways of analyzing data assume that data points are sampled independently of one another. In many problems, however, this assumption is incorrect. This project focuses on data where one observation influences others, either as reinforcing (likely to have a similar value) or repulsing (likely to have a greatly different value). Such interactions might arise between static measurements, between trajectories evolving in space/on a network, or may be desirable biases in algorithms to promote goals like robustness, diversity or fairness. These might arise as a consequence of competition for finite resources, because of rich-get-richer dynamics from propagating social influence, because of interacting processes in physical and biological systems, or out of a desire to learn compact representations of complex systems. Examples include the locations of cells or service stations, interactions among particles or populations, traffic trajectories, users navigating social media, the spiking of neurons or the spread of disease. The research brings together applied problems and theoretical ideas from fields like machine learning, statistics, physics and computer science. Such tools open new avenues to data-summarization, exploration and visualization, and allow practitioners to explore trade-offs between interpretability and predictive accuracy. The applied aspects of this project provide an opportunity for undergraduate research and for the integration of research and teaching through an undergraduate course on stochastic processes and simulation.At a technical level, this project develops principled statistical models and efficient algorithms that relax assumptions of independence among observations lying on a shared space. It considers interactions for three classes of problems: 1) point process models, 2) latent variable models and 3) trajectory models. Central to the work are two kinds of stochastic process models: the Hawkes process for reinforcement, and the Matern type-III process for repulsion. Both processes share intuitive and mechanistic generative schemes from an underlying Poisson process, whose rate is modulated by event history. This allows a framework that jointly models richer repulsive and reinforcing interactions in stationary and trajectory data. The connection with the Poisson process allows novel models and mechanisms of reinforcement and repulsion, as well as new, scalable algorithms, allowing investigations into the fundamental role of non-Poissonness in real applications. Incorporating repulsive priors into latent variables of hierarchical models also allow novel repulsive latent variable models with biases towards parsimony and interpretability.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

大多数传统的数据分析方法都假设数据点是彼此独立地采样的。然而，在许多问题中，这种假设是不正确的。该项目关注的是一个观察影响其他观察的数据，无论是加强（可能具有相似的值）还是排斥（可能具有非常不同的值）。这种相互作用可能出现在静态测量之间，在空间/网络上演变的轨迹之间，或者可能是算法中的期望偏差，以促进鲁棒性，多样性或公平性等目标。这些可能是由于对有限资源的竞争，由于传播社会影响的富-富动态，由于物理和生物系统中的相互作用过程，或者出于学习复杂系统的紧凑表示的愿望而产生的。例子包括细胞或服务站的位置，粒子或群体之间的相互作用，交通轨迹，用户浏览社交媒体，神经元的尖峰或疾病的传播。该研究汇集了来自机器学习，统计学，物理学和计算机科学等领域的应用问题和理论思想。此类工具为数据汇总、探索和可视化开辟了新的途径，并允许从业者探索可解释性和预测准确性之间的权衡。该项目的应用方面提供了一个机会，本科研究和研究与教学的整合，通过本科课程随机过程和模拟。在技术层面上，该项目开发原则的统计模型和有效的算法，放松假设的独立性之间的观察躺在一个共享的空间。它考虑了三类问题的相互作用：1）点过程模型，2）潜变量模型和3）轨迹模型。中心的工作是两种随机过程模型：霍克斯过程的强化，和马特恩III型过程的排斥。这两个过程共享直观和机械生成方案从一个潜在的泊松过程，其速率是由事件历史调制。这允许一个框架，联合模型更丰富的排斥和加强相互作用的静止和轨迹数据。与泊松过程的连接允许新的模型和机制的强化和排斥，以及新的，可扩展的算法，允许调查的基本作用，非泊松在真实的应用。将排斥性的先验知识转化为层次模型的潜在变量，也允许新颖的排斥性潜在变量模型偏向简约性和可解释性。该奖项反映了NSF的法定使命，并被认为值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估来支持。