Detection of regime switching points in non-stationary sequences using stochastic learning based weak estimation method

Abstract

In general, dynamic systems are systems with time-dependent behavior. Dynamic systems are characterized by the non-stationary data sequences they emit. One particular way to model these non-stationary sequences is to consider them as a sequence of stationary segments, regimes, where each regime is separated by regime switching points from both the preceding and subsequent regimes. In system identification and monitoring applications, it is crucial to correctly and timely detect these regime switching points. One promising estimation method that may be used for detecting regime switching points is the stochastic learning based weak estimation (SLWE) method by Oommen and Rueda. We use SLWE for estimating First Order Markov (FOM) probabilities between symbols emitted by a system and for predicting regime switching points. A switching point is detected when the SLWE estimator unlearns, i.e., adapts estimates of FOM probabilities to new observations, such that the estimate re-converges to a new value that reflects, for the new regime, the FOM dependency of system output tokens. In experiments with a real Dataset for Human Activity Recognition, we see that our method has attractive efficiency (time and space) and similar accuracy compared with the state-of the-art. Experiments with synthetic data, where we controlled noise and Hamming distance between regimes, show promising accuracy for noise rates up to 25%, a rate at which accuracy of state-of-the-art methods deteriorates. Our method is flexible and can be configured to use not only FOM but also second-order and prior symbol probabilities, and combinations thereof.