Title: Estimating Markov Chain Transition Probabilities for Steady Aging Models from $n$-step Data
Primary area: learning on time series and dynamical systems
Keywords: Markov Chains, Transition Probabilities, Estimation, Diagonalization, Battery Aging

Abstract: Usage-dependent aging processes of products such as batteries have become increasingly important. However, in general, revealing aging dynamics of discrete time Markov Decision Processes (MDP) from sparse $n$-step data is challenging as multi-step transition probabilities become complex and make it impossible to efficiently optimize the likelihood function for larger $n$. In this paper, we consider classes of steady-aging processes, which can be characterized by band matrices. Based on explicit diagonalizations of such matrices, we are able to optimally solve the likelihood in an efficient manner. In contrast to existing benchmark approaches our approach scales well and remains applicable for large $n$. Further, our evaluations for synthetic as well as real-world data verify a high estimation accuracy (about 98\%) with comparably few data (about 10$\times$ more observations as states).

TL;DR: We show how to effectively estimate aging dynamics of discrete time Markov Chains from sparse multi-step data using explicit diagonalization techniques.