Signal and System Minimum Mismatch Modeling (3M) with Order Selection Analysis

In the data-driven modeling of linear, time-invariant structures, the choice of the number of parameters (order selection) is critical. It is known that the modeling error, resulting from the maximum likelihood estimate, cannot be directly used for order estimation as this error is a monotonically decreasing function of model order. The most well-known order selection methods, including Akaike information criterion (AIC), Bayesian information criterion (BIC), and minimum description length (MDL), propose an additive penalty term to the modeling error. A more recently proposed method, reconstruction error minimization (REM) concentrates on a different error to provide optimal order selection using a statistical learning approach. A closed-form expression of REM has been provided for the order selection in linear models, including finite impulse responses and has shown superiority over other order selection methods. The existing method of REM calculation uses a Gaussian approximation of the Chi- squared distribution. This work first provides the exact modeling of REM using the Chi-squared distribution. Next, the use of REM is extended for all-pole modeling and pole-zero modeling. For autoregressive (AR) order selection, a method denoted by minimum mismatch modeling (3M) is introduced. It has also been shown that REM is a special case of 3M. Simulation results show the advantages of the proposed method over the existing order selection methods by avoiding overparametrization or underpamaterization in favour of mean squared error (MSE) minimization. In addition, a practical application of eye blink artifact removal from electroencephalogram (EEG) data shows that the proposed method efficiently models the true background EEG while eliminating artifacts efficiently. Furthermore, the application of 3M for EEG sleep-stage classification enabled the classification process to be automated. It is worth mentioning that the use of 3M shows that different sleep-stages have different orders, which can be further used as a feature for classification.