Parameter inference from a non-stationary unknown process

What is it about?

Time-series measurement and analysis is important in range of fields. For example, in neuroscience we can record electrical activity from a region of the brain, in finance we can observe the performance of an index fund, and in ecology we can track fluctuations in the population level of some species. Most tools used to analyse time-series data assume that the measured process is stationary, meaning that the statistical process underlying the time series doesn’t change over time, including properties like its mean and variance. However, many important processes are non-stationary, because many interesting systems interact with other processes in their environment, yielding drives that change the measured dynamics over time. For example, time series of brain activity during sleep exhibit considerable variation in statistical properties across wakefulness and different stages of sleep. To better study such phenomena we need ways to quantify non-stationarity. In our study we defined a problem that we called parameter inference from a non-stationary unknown process (PINUP). Suppose that the statistical properties of an observed system are changing over time under the influence of a hidden time-varying parameter, e.g., variations in brain activity influenced by the release of a neurotransmitter like noradrenaline from some brain region. Without needing a mathematical model of the observed system, PINUP starts with non-stationary time-series data and aims to directly infer a time series of the underlying parameter(s) or input(s) to the system that underpin the non-stationarity.

Featured Image

Photo by Adam Śmigielski on Unsplash

Photo by Adam Śmigielski on Unsplash

Why is it important?

To date, research on PINUP has been fragmented across different scientific fields such as physics, mechanical engineering, and cybernetics. By providing a clear problem definition and synthesising the existing literature we hope to accelerate progress on the PINUP problem. Additionally, we demonstrated that some of simulated systems commonly used benchmarking admit trivial solutions and we point the way to more challenging problems that can be used to drive improvements in PINUP algorithms. Our work will promote the study of a wide range of non-stationary phenomena.