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.

翻译：自回归模型是计算神经科学和生物医学工程等多个领域中分析时间序列的常用工具。在这些领域中，数据通常来自脑部活动的测量。关键在于，这些数据存在测量误差，且底层系统模型具有不确定性。因此，使用自回归模型估计器进行标准信号处理可能会产生偏差。我们提出了一种自回归建模框架，通过一个过参数化的损失函数显式地纳入这些不确定性。为优化该损失函数，我们推导出一种在状态估计与参数估计之间交替的算法。我们的研究表明，该过程能够成功地对时间序列进行去噪，并有效重构系统参数。这一新范式可用于神经科学领域的众多应用，例如脑机接口数据分析，以及更好地理解癫痫等疾病的大脑动力学。