Correlated Chained Gaussian Processes for Modelling Citizens Mobility Using a Zero-Inflated Poisson Likelihood
Correlated Chained Gaussian Processes for Modelling Citizens Mobility Using a Zero-Inflated Poisson Likelihood
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DOI：
10.1109/tits.2022.3171730
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发表时间：
2022-11
影响因子：
8.5
通讯作者：
Juan J. Giraldo;J. Zhang;Mauricio A Álvarez
中科院分区：
文献类型：
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作者：
Juan J. Giraldo;J. Zhang;Mauricio A Álvarez
对城市人口流动的建模依赖于对数据的计数，而数据本身就存在过度分散的问题。这种分散问题是由大量零值数据引起的。虽然传统的机器学习模型已经被用来克服上述问题，但它们缺乏适当地对数据中的时空相关性进行建模的能力。为了改善这种时空相关性的建模，在这项工作中，我们建议对中国城市广州的市民流动性进行建模，通过零膨胀泊松似然结合卷积过程产生的高斯过程先验。我们遵循将似然参数链接到从高斯过程先验中提取的潜在函数的想法;这种方式允许更高的灵活性来建模异方差。此外，我们推导出一个随机变分推理框架，使我们能够在大型数据集的背景下使用两种类型的卷积过程模型：相关链式高斯过程与卷积过程模型，以及相关链式高斯过程与变分诱导内核。我们提出了定量和定性的结果比较负二项和零膨胀泊松似然之间的性能，无论是结合三种类型的高斯过程先验：线性模型的coregionalisation，我们提出的两种方法的基础上卷积过程模型和变分诱导内核。
Modelling the mobility of people in a city depends on counting data with inherent problems of overdispersion. Such dispersion issues are caused by massive amounts of data with zero values. Though traditional machine learning models have been used to overcome said problems, they lack the ability to appropriately model the spatio-temporal correlations in data. To improve the modelling of such spatio-temporal correlations, in this work we propose to model the citizens mobility, for the Chinese city of Guangzhou, by means of a Zero-inflated Poisson likelihood in conjunction with Gaussian process priors generated from convolution processes. We follow the idea of chaining the likelihood’s parameters to latent functions drawn from Gaussian process priors; this way allowing a higher flexibility to model heteroscedasticity. Additionally, we derive a stochastic variational inference framework that allow us to use two types of convolution process models in the context of large datasets: correlated chained Gaussian processes with a convolution processes model, and correlated chained Gaussian processes with variational inducing kernels. We present quantitative and qualitative results comparing the performance between Negative Binomial and Zero-inflated Poisson likelihoods, both in combination with three types of Gaussian process priors: a linear model of coregionalisation, and our two proposed methods based on a convolution processes model and variational inducing kernels.