This paper presents a novel extension of multi-task Gaussian Cox processes for modeling multiple heterogeneous correlated tasks jointly, e.g., classification and regression, via multi-output Gaussian processes (MOGP). A MOGP prior over the parameters of the dedicated likelihoods for classification, regression and point process tasks can facilitate sharing of information between heterogeneous tasks, while allowing for nonparametric parameter estimation. To circumvent the non-conjugate Bayesian inference in the MOGP modulated heterogeneous multi-task framework, we employ the data augmentation technique and derive a mean-field approximation to realize closed-form iterative updates for estimating model parameters. We demonstrate the performance and inference on both 1D synthetic data as well as 2D urban data of Vancouver.

翻译：本文提出了一种多任务高斯考克斯过程的新型扩展方法，通过多输出高斯过程（MOGP）对多个异质相关任务（如分类和回归）进行联合建模。在分类、回归和点过程任务的专用似然函数参数上施加多输出高斯过程先验，既能促进异质任务间的信息共享，又能实现非参数化参数估计。为规避多输出高斯过程调控的异质多任务框架中的非共轭贝叶斯推断问题，我们采用数据增广技术并推导出均值场近似，从而实现模型参数估计的闭式迭代更新。我们通过一维合成数据和温哥华二维城市数据验证了该方法的性能与推断能力。