  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.
