We generalize the log Gaussian Cox process (LGCP) framework to model multiple correlated point data jointly. The observations are treated as realizations of multiple LGCPs, whose log intensities are given by linear combinations of latent functions drawn from Gaussian process priors. The combination coefficients are also drawn from Gaussian processes and can incorporate additional dependencies. We derive closed-form expressions for the moments of the intensity functions and develop an efficient variational inference algorithm that is orders of magnitude faster than competing deterministic and stochastic approximations of multivariate LGCP, coregionalization models, and multi-task permanental processes. Our approach outperforms these benchmarks in multiple problems, offering the current state of the art in modeling multivariate point processes.
翻译:我们将日志高西亚考克斯进程(LGCP)框架普遍化,以共同模拟多个相关点数据。观测被视为多个LGCP的实现,其日密度由从高西亚进程前期提取的潜在函数的线性组合给出。组合系数还来自高山进程,可以纳入更多的依赖性。我们为强度函数的时段生成闭式表达式,并开发一种高效的变异推断算法,其数量级比多变点LGCP、共同区域化模型和多任务永久进程相竞的确定性和随机近似速度要快。我们的方法在多个问题上超越了这些基准,为多变量点进程的建模提供了艺术的当前状态。