Multivariate autoregressive model estimation for high dimensional intracranial electrophysiological data

Fundamental to elucidating the functional organization of the brain is the assessment of causal interactions between different brain regions. Multivariate autoregressive (MVAR) modeling techniques applied to multisite electrophysiological recordings are a promising avenue for identifying such causal links. They estimate the degree to which past activity in one or more brain regions is predictive of another region’s present activity, while simultaneously accounting for the mediating effects of other regions. Including in the model as many mediating variables as possible has the benefit of drastically reducing the odds of detecting spurious causal connectivity. However, effective bounds on the number of MVAR model coefficients that can be estimated reliably from limited data make exploiting the potential of MVAR models challenging. Here, we utilize well-established dimensionality-reduction techniques to fit MVAR models to human intracranial data from ∽100 – 200 recording sites spanning dozens of anatomically and functionally distinct cortical regions. First, we show that high dimensional MVAR models can be successfully estimated from long segments of data and yield plausible connectivity profiles. Next, we use these models to generate synthetic data with known ground-truth connectivity to explore the utility of applying principal component analysis and group least absolute shrinkage and selection operator (LASSO) to reduce the number of parameters (connections) during model fitting to shorter data segments. We show that group LASSO is highly effective for recovering ground truth connectivity in the limited data regime, capturing important features of connectivity for high-dimensional models with as little as 10 s of data. The methods presented here have broad applicability to the analysis of high-dimensional time series data in neuroscience, facilitating the elucidation of the neural basis of sensation, cognition, and arousal.

Modelling Covid-19 Pandemic in Nigeria using Multivariate Autoregressive Distributed Lag-Moving Average Models

The aim of this paper was to study the trend of COVID-19 cases and fit appropriate multivariate time series models as research to complement the clinical and non-clinical measures against the menace. The cases of COVID-19, as reported by the National Centre for Disease Control (NCDC) on a daily and weekly basis, include Total Cases (TC), New Cases (NC), Active Cases (AC), Discharged Cases (DC) and Total Deaths (TD). The three waves of the COVID-19 pandemic are graphically represented in the various time plots, indicating the peaks as (June–August, 2020), (December–February, 2021), and (July–September, 2021). Multivariate Autoregressive Distributed Lag Models (MARDLM) and Multivariate Autoregressive Distributed Lag Moving Average (MARDL-MA) models have been found to be suitable for fitting different categories of the COVID-19 pandemic in Nigeria. The graphical representation and estimates have shown a gradual decline in the reported cases after the peak in September 2021. So far, the introduction of vaccines and non-pharmaceutical measures by relevant organisations are yielding plausible results, as evident in the recent decrease in New Cases, Active Cases and an increasing number of Discharged Cases, with fewer deaths. This paper advocates consistency in all clinical and non-clinical measures as a way towards the extinction of the dreaded COVID-19 pandemic in Nigeria and the world.

Comparison Between Lotka-Volterra and Multivariate Autoregressive Models of Ecological Interaction Systems

Lotka-Volterra (LV) and Multivariate Autoregressive (MAR) models are computational frameworks with different mathematical structures that have both been proposed for the same purpose of extracting governing features of dynamic interactions among coexisting populations of different species from observed time series data.We systematically compare the feasibility of the two modeling approaches, using four synthetically generated datasets and seven ecological datasets from the literature.The overarching result is that LV models outperform MAR models in most cases and are generally superior for representing cases where the dependent variables deviate greatly from their steady states. A large dynamic range is particularly prevalent when the populations are highly abundant, change considerably over time, and exhibit a large signal-to-noise ratio. By contrast, MAR models are better suited for analyses of populations with low abundances and for investigations where the quantification of noise is important.We conclude that the choice of either one or the other modeling framework should be guided by the specific goals of the analysis and the dynamic features of the data.Availability of algorithms usedhttps://github.com/LBSA-VoitLab/Comparison-Between-LV-and-MAR-Models-of-Ecological-Interaction-Systems

Evaluating the effectiveness of a multivariate autoregressive model in predicting the time course of dynamic facial behaviours

Faces convey critical information about people, such as cues to their identity and emotional state. In the real world, facial behaviours evolve dynamically and encapsulate a range of biological motion signals. Furthermore, behavioural and neuroimaging studies have demonstrated that human observers are sensitive to this temporal information. The presence of systematic temporal changes in the face implies the possibility of predicting the evolution of dynamic facial behaviours. We video recorded subjects delivering positive or negative phrases, and used a PCA-based active appearance model to capture critical dimensions of facial variation over time. We applied multivariate autoregressive models to predict PCA scores of future frames from the frames immediately preceding them, up to a lag of 200ms prior to the target frame. These models did successfully predict future frames, but they did not benefit from extending the temporal support, suggesting they relied primarily on image similarity between consecutive frames. We next used hidden Markov models to segment videos into shorter sequences comprising more consistent facial behaviours. The Markov models successfully extracted distinct facial basis states, however segmenting the data by state did not yield any predictive benefit to autoregressive models fit within those states. We conclude that autoregressive models have only limited predictive power in the context of facial expression analysis.