Parameter estimation in abruptly changing dynamic environments using stochastic learning weak estimator

Abstract

Many real-life dynamical systems experience abrupt changes followed by almost stationary periods. In this paper, we consider streams of data exhibiting such abrupt behavior and investigate the problem of tracking their statistical properties in an online manner. We devise a tracking procedure where an estimator that is suitable for a stationary environment is combined together with an estimator suitable for a dynamic environment. The current estimate is based on the stationary estimator unless a statistically significant difference is observed between both estimators. The stationary estimate is deemed off track and a large update (jump) is given to get the stationary estimate back on track. We use the Stochastic Learning Weak Estimator (SLWE) as the dynamic estimator. The SLWE is known to be the state-of-the art solution to tracking the properties of nonstationary environments, due to its multiplicative update form. Therefore, the SLWE is a better choice to accompany a stationary estimator than the far more common sliding window based approach. A theoretically well founded statistical testing procedure is developed to detect a significant difference between the stationary and dynamical estimators. Although our procedure bears similarities to the event detection procedure suggested by Ross et al. (2012) [38], it is rather well founded theoretically. First, Ross et al. ignore the uncertainty in the stationary estimator in the detection procedure. Second, the detection threshold is determined based on heuristics and therefore lacks a solid statistical foundation. Extensive simulation results, based on both synthetic and real-life data related to news topic classification, demonstrate that our estimation procedure is easy to tune and outperforms legacy works.