2020/06/15 by Georg Peter, Georg, Peter, Lars Grasedyck +9 · 1 citation
Engineering · Mathematics · Medicine · #15A69 #60J22 #60J28 #Advanced Neuroimaging Techniques and Applications #FOS: Mathematics #Numerical Analysis (math.NA) #Sparse and Compressive Sensing Techniques #Tensor decomposition and applications
paper · pdf · doi:10.48550/arxiv.2006.08135
openalex publication_date 2020/06/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Continuous-time Markov chains describing interacting processes exhibit a state space that grows exponentially in the number of processes. This state-space explosion renders the computation or storage of the time-marginal distribution, which is defined as the solution of a certain linear system, infeasible using classical methods. We consider Markov chains whose transition rates are separable functions, which allows for an efficient low-rank tensor representation of the operator of this linear system. Typically, the right-hand side also has low-rank structure, and thus we can reduce the cost for computation and storage from exponential to linear. Previously known iterative methods also allow for low-rank approximations of the solution but are unable to guarantee that its entries sum up to one as required for a probability distribution. We derive a convergent iterative method using low-rank formats satisfying this condition. We also perform numerical experiments illustrating that the marginal distribution is well approximated with low rank.