Autoregressive models for biomedical signal processing

Autoregressive models are ubiquitous tools for the analysis of time series in many domains such as computational neuroscience and biomedical engineering. In these domains, data is, for example, collected from measurements of brain activity. Crucially, this data is subject to measurement errors as well as uncertainties in the underlying system model. As a result, standard signal processing using autoregressive model estimators may be biased. We present a framework for autoregressive modelling that incorporates these uncertainties explicitly via an overparameterised loss function. To optimise this loss, we derive an algorithm that alternates between state and parameter estimation. Our work shows that the procedure is able to successfully denoise time series and successfully reconstruct system parameters. This new paradigm can be used in a multitude of applications in neuroscience such as brain-computer interface data analysis and better understanding of brain dynamics in diseases such as epilepsy

Path Signatures for Seizure Forecasting

Forecasting the state of a system from an observed time series is the subject of research in many domains, such as computational neuroscience. Here, the prediction of epileptic seizures from brain measurements is an unresolved problem. There are neither complete models describing underlying brain dynamics, nor do individual patients exhibit a single seizure onset pattern, which complicates the development of a `one-size-fits-all' solution. Based on a longitudinal patient data set, we address the automated discovery and quantification of statistical features (biomarkers) that can be used to forecast seizures in a patient-specific way. We use existing and novel feature extraction algorithms, in particular the path signature, a recent development in time series analysis. Of particular interest is how this set of complex, nonlinear features performs compared to simpler, linear features on this task. Our inference is based on statistical classification algorithms with in-built subset selection to discern time series with and without an impending seizure while selecting only a small number of relevant features. This study may be seen as a step towards a generalisable pattern recognition pipeline for time series in a broader context