On Tuesday 10th of September 2019 Rachele Anderson has nailed her PhD Thesis titled "Statistical inference and time-frequency estimation for non-stationary signal classification".
This thesis focuses on statistical methods for non-stationary signals. The methods considered or developed address problems of stochastic modeling, inference, spectral analysis, time-frequency analysis, and deep learning for classification. In all the contributions, an example of a biomedical application of the proposed method is provided, either to electroencephalography (EEG) data or to Heart Rate Variability (HRV) data. In paper A, we propose a method for estimating the parameters of a Locally Stationary Process (LSP). The proposed inference method is based on the separation of the two factors defining the LSP covariance function in order to take advantage of their individual structure. We prove theoretical convergence of the estimate provided to the true covariance. In a simulation study, we show that the method outperforms existent estimators in terms of speed of convergence, accuracy, and robustness. Finally, we provide an illustrative example of parameter estimation from EEG signals, measured from one person during several trials of a memory encoding task of different categories of visual memories. In paper B, we propose a novel framework for the analysis of task-related HRV. A model for the HRV and corresponding respiration signals is introduced, whose parameters are estimated through a novel inference method, extending the one proposed in paper A. The corresponding optimal mean-square error (MSE) Wigner-Ville spectrum (WVS) estimator is derived and evaluated with the individually estimated model parameters. The estimated parameters are considered as response variables in a regression analysis involving several physiological factors describing the test participants state of health, showing correlation with gender, age, stress, and fitness. This approach may be useful to search for physiological factors that determine individual differences. Paper C investigates the extraction of time-frequency (TF) features for classification of EEG signals and episodic memory. The model and inference method proposed in paper A are used to derive an MSE WVS estimator, which is compared with state-of-the-art TF representations. In a simulation study, the proposed estimator outperforms the other methods significantly in terms of MSE. Additionally, we evaluate the classification accuracy of a neural network classifier fed on TF features extracted with the different estimators, both for simulated data and in a real data example of EEG signals measured during a visual memory encoding task. Consistent improvement in classification accuracy is achieved by using the features extracted with the proposed optimal estimator, compared to the use of state-of-the-art methods, both for simulated and real data.
In paper D, we consider a non-parametric approach, based on multitaper spectral estimation, to frequency-domain Granger causality (GC), which can overcome the limits of the traditional linear vector autoregressive modeling of GC. In a simulation study, we compare the MSE of the estimated spectral GC using different multitaper spectral estimators for different numbers of tapers and data lengths. As an example of application, we utilize the multitaper approach to the analysis of brain functional connectivity in SSVEPs, collected from a subject both during wakeful resting and during visual stimulation with a flickering light, evaluating the changes in the information flow between the occipital and frontal lobes.