Periodic Reporting for period 1 - BioCointegration (Biological rhythms: Do they cointegrate?)
Okres sprawozdawczy: 2021-09-01 do 2023-08-31
Many biological systems can be seen as networks of interconnected units. Understanding synchronization is key to understand some biological networks. A long-standing problem in neuroscience is to recover the network structure in a coupled system, such as a neuronal network represented by extracellularly recorded spike trains or traces of EEG signals from different locations on the scalp. Statistical inference of such systems has only recently caught interest as technological advances allow for simultaneous recordings of many interacting units. Therefore, a solid statistical treatment to properly test hypotheses on the network structure has not yet been established.
To solve this problem, the project elaborated the methodology of cointegration analysis. The theory of cointegration has developed within the field of econometrics and offers a refined statistical toolbox to analyze non-stationary multidimensional time series. The key idea is to estimate the long-run equilibrium relationships between several variables, which are captured by cointegrating vectors. The cointegration analysis provides estimation of the number of cointegration relations and allows to identify the coupling strengths and directions of the couplings.
This project aimed to extend the standard cointegration method for the needs of analyzing biological oscillators and hence to provide a more principled way to infer functional structure of biological networks. We addressed three main gaps in the methodology:
1. The standard cointegration analysis was used earlier with success up to about 10 dimensions. Nevertheless, biological networks are often of a much higher dimension. In this project, we found ways how to apply this methodology to high-dimensional data.
2. Couplings in many biological networks are not linear or constant and the standard model of cointegration was not ready for that. We suggested a more complex model that mimics nonlinear effects.
3. Not all coordinates of the investigated systems can be observed directly and are thus imputed. This causes identifiability issues, when some aspects of the systems cannot be inferred. We resolved this problem for EEG data.
To solve this problem, the project elaborated the methodology of cointegration analysis. The theory of cointegration has developed within the field of econometrics and offers a refined statistical toolbox to analyze non-stationary multidimensional time series. The key idea is to estimate the long-run equilibrium relationships between several variables, which are captured by cointegrating vectors. The cointegration analysis provides estimation of the number of cointegration relations and allows to identify the coupling strengths and directions of the couplings.
This project aimed to extend the standard cointegration method for the needs of analyzing biological oscillators and hence to provide a more principled way to infer functional structure of biological networks. We addressed three main gaps in the methodology:
1. The standard cointegration analysis was used earlier with success up to about 10 dimensions. Nevertheless, biological networks are often of a much higher dimension. In this project, we found ways how to apply this methodology to high-dimensional data.
2. Couplings in many biological networks are not linear or constant and the standard model of cointegration was not ready for that. We suggested a more complex model that mimics nonlinear effects.
3. Not all coordinates of the investigated systems can be observed directly and are thus imputed. This causes identifiability issues, when some aspects of the systems cannot be inferred. We resolved this problem for EEG data.
We investigated a range of strategies that would address the problem of fitting the cointegration model to high-dimensional data and identified 11 well-working estimation methods. For the nonlinear couplings, we identified a model with structural breaks as a viable and computationally achievable model description and adapted an algorithm for identifying the unknown parameters of the model. The problem of imputed coordinates was solved by an appropriate reparameterization of the model.
The newly developed methods have been implemented in R programming environment. We tested that our improved methodology provides good and reliable results by running numerous simulations and performing several example analyses of real data, namely EEG data from a visual identification experiment and accelerometer data from a study of narwhals’ diving behaviour.
The achieved results are summarized in 2 already published scientific papers and 1 paper in preparation. They were also presented at a number of conferences and workshops. All newly developed algorithms were implemented in R programming environment and are publicly available.
The newly developed methods have been implemented in R programming environment. We tested that our improved methodology provides good and reliable results by running numerous simulations and performing several example analyses of real data, namely EEG data from a visual identification experiment and accelerometer data from a study of narwhals’ diving behaviour.
The achieved results are summarized in 2 already published scientific papers and 1 paper in preparation. They were also presented at a number of conferences and workshops. All newly developed algorithms were implemented in R programming environment and are publicly available.
Compared to the state-of-the-art at the beginning of the project, we managed to extend the cointegration methodology in several important directions, so that it can be applied to a number of high-dimensional biological systems with nonlinear time-varying couplings. The achieved results are useful to scientists in primary research in neuroscience, medicine and biology, where they enable much more accurate inference of biological systems. The methodology has a potential to find use in diagnostics as well.