Regression Analysis for Multivariate Dependent Count Data Using Convolved Gaussian Processes

TL;DR

This paper introduces a semi-parametric regression model using convolved Gaussian processes for multivariate dependent count data, addressing covariance structure challenges and enabling flexible, accurate estimation and prediction.

Contribution

The paper proposes a novel convolved Gaussian process framework for multivariate count data regression, ensuring positive definiteness and flexibility in covariance modeling.

Findings

Effective modeling of multivariate count data with complex dependencies

Demonstrated superior performance through simulations and real data

Flexible covariance structures for diverse data sources

Abstract

Research on Poisson regression analysis for dependent data has been developed rapidly in the last decade. One of difficult problems in a multivariate case is how to construct a cross-correlation structure and at the meantime make sure that the covariance matrix is positive definite. To address the issue, we propose to use convolved Gaussian process (CGP) in this paper. The approach provides a semi-parametric model and offers a natural framework for modeling common mean structure and covariance structure simultaneously. The CGP enables the model to define different covariance structure for each component of the response variables. This flexibility ensures the model to cope with data coming from different resources or having different data structures, and thus to provide accurate estimation and prediction. In addition, the model is able to accommodate large-dimensional covariates. The definition of the model, the inference and the implementation, as well as its asymptotic properties, are discussed. Comprehensive numerical examples with both simulation studies and real data are presented.