The multivariate probit model (MVP) is a popular classic model for studying binary responses of multiple entities. Nevertheless, the computational challenge of learning the MVP model, given that its likelihood involves integrating over a multidimensional constrained space of latent variables, significantly limits its application in practice. We propose a flexible deep generalization of the classic MVP, the Deep Multivariate Probit Model (DMVP), which is an end-to-end learning scheme that uses an efficient parallel sampling process of the multivariate probit model to exploit GPU-boosted deep neural networks. We present both theoretical and empirical analysis of the convergence behavior of DMVP's sampling process with respect to the resolution of the correlation structure. We provide convergence guarantees for DMVP and our empirical analysis demonstrates the advantages of DMVP's sampling compared with standard MCMC-based methods. We also show that when applied to multi-entity modelling problems, which are natural DMVP applications, DMVP trains faster than classical MVP, by at least an order of magnitude, captures rich correlations among entities, and further improves the joint likelihood of entities compared with several competitive models.

提出了基于GPU加速深度神经网络的端到端学习框架Deep Multivariate Probit Model（DMVP），比传统MVP方法结构更灵活， 收敛性良好，适用多实体建模，并可捕获实体间丰富的相关性，且训练速度至少比传统MVP快一个数量级。

深度多元Probit模型的端到端学习