Heterogeneous Multi-Task Gaussian Cox Processes

TL;DR

This paper introduces a multi-task Gaussian Cox process framework that models heterogeneous tasks like classification and regression jointly, enabling shared information and nonparametric estimation, with efficient inference methods demonstrated on synthetic and urban data.

Contribution

It extends multi-task Gaussian Cox processes to handle heterogeneous tasks using multi-output Gaussian processes with a novel inference approach.

Findings

Effective modeling of heterogeneous tasks demonstrated

Closed-form iterative inference achieved

Successful application on synthetic and real urban data

Abstract

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.