Online Learning Algorithms for Quaternion ARMA Model
This work addresses adaptive learning for quaternion ARMA models, which is incremental as it extends existing methods to the quaternion domain with specific algebraic properties.
The paper tackles adaptive learning for quaternion ARMA models by transforming it into an optimization problem and developing two online algorithms using gradient descent and Newton analogues, with regret bound analysis showing asymptotic performance approaching the best model in hindsight.
In this paper, we address the problem of adaptive learning for autoregressive moving average (ARMA) model in the quaternion domain. By transforming the original learning problem into a full information optimization task without explicit noise terms, and then solving the optimization problem using the gradient descent and the Newton analogues, we obtain two online learning algorithms for the quaternion ARMA. Furthermore, regret bound analysis accounting for the specific properties of quaternion algebra is presented, which proves that the performance of the online algorithms asymptotically approaches that of the best quaternion ARMA model in hindsight.