In this paper, we present a kernel-based, multi-task Gaussian Process (GP) model for approximating the underlying function of an individual's mobility state using a time-inhomogeneous Markov Process with two states: moves and pauses. Our approach accounts for the correlations between the transition probabilities by creating a covariance matrix over the tasks. We also introduce time-variability by assuming that an individual's transition probabilities vary over time in response to exogenous variables. We enforce the stochasticity and non-negativity constraints of probabilities in a Markov process through the incorporation of a set of constraint points in the GP. We also discuss opportunities to speed up GP estimation and inference in this context by exploiting Toeplitz and Kronecker product structures. Our numerical experiments demonstrate the ability of our formulation to enforce the desired constraints while learning the functional form of transition probabilities.

翻译：本文提出一种基于核函数的多任务高斯过程（GP）模型，用于通过时间非齐次马尔可夫过程（包含"移动"与"停留"两种状态）逼近个体移动状态的基础函数。该方法通过构建任务间协方差矩阵来刻画转移概率之间的相关性，同时假设个体转移概率随外生变量呈时变特性以引入时间变化性。通过在GP中引入约束点集，我们强制实现马尔可夫过程概率的随机性和非负性约束。本文还探讨了利用Toeplitz与Kronecker积结构加速GP估计与推理的可行方案。数值实验表明，该模型在学习转移概率函数形式的同时，能够有效施加所需约束条件。