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.

Multivariate stochastic volatility modeling of neural data

Because multivariate autoregressive models have failed to adequately account for the complexity of neural signals, researchers have predominantly relied on non-parametric methods when studying the relations between brain and behavior. Using medial temporal lobe (MTL) recordings from 96 neurosurgical patients, we show that time series models with volatility described by a multivariate stochastic latent-variable process and lagged interactions between signals in different brain regions provide new insights into the dynamics of brain function. The implied volatility inferred from our process positively correlates with high-frequency spectral activity, a signal that correlates with neuronal activity. We show that volatility features derived from our model can reliably decode memory states, and that this classifier performs as well as those using spectral features. Using the directional connections between brain regions during complex cognitive process provided by the model, we uncovered perirhinal-hippocampal desynchronization in the MTL regions that is associated with successful memory encoding.

Strong self-regulation and widespread facilitative interactions in phytoplankton communities

The persistence of phytoplanktonic diversity in spite of competition for basic resources has long been a source of wonder and inspiration to ecologists. To sort out, among the many coexistence mechanisms suggested by theory and experiments, which ones actually maintain diversity in natural ecosystems, long-term field studies are paramount.We analysed a large dataset of phytoplankton abundance time series using dynamic, multivariate autoregressive models. Phytoplankton was counted and identified down to the genus level, every two weeks over twenty years, at ten sites along the French coastline. Multivariate autoregressive models allowed to estimate biotic interaction networks, while also accounting for abiotic variables that may drive part of the phytoplankton fluctuations. We then analysed the ratio of intra-to inter-taxa interactions (measuring self-regulation, itself a measure of niche differentiation), the frequency of negative vs positive interactions, and how stability metrics (both at the network and genus level) relate to network complexity and genus self-regulation or abundance.We showed that a strong self-regulation, with competition strength within a taxon (genus) an order of magnitude higher than between taxa, was present in all phytoplanktonic interaction networks. This much stronger intragenus competition suggests that niche differentiation - rather than neutrality - is commonplace in phytoplankton. Furthermore, interaction networks were dominated by positive net effects between phytoplanktonic taxa (on average, more than 50% of interactions were positive). While network stability (sensu resilience) was unrelated to complexity measures, we unveiled links between self-regulation, intergenus interaction strengths and abundance. The less common taxa tend to be more strongly self-regulated and can therefore maintain in spite of competition with more abundant ones.Synthesis: We demonstrate that strong niche differentiation, widespread facilitation between phytoplanktonic taxa and stabilizing covariances between interaction strengths should be common features of coexisting phytoplankton communities in the field. These are structural properties that we can expect to emerge from plausible mechanistic models of phytoplankton communities. We discuss mechanisms, such as predation or restricted microscale movement, that are consistent with these findings, which paves the way for further research.

Multivariate Stochastic Volatility Modeling of Neural Data

Because multivariate autoregressive models have failed to adequately account for the complexity of neural signals, researchers have predominantly relied on non-parametric methods when studying the relations between brain and behavior. Using medial temporal lobe (MTL) recordings from 96 neurosurgical patients, we show that time series models with volatility described by a multivariate stochastic latent-variable process and lagged interactions between signals in different brain regions provide new insights into the dynamics of brain function. The implied volatility inferred from our process positively correlates with high-frequency spectral activity, a signal that correlates with neuronal activity. We show that volatility features derived from our model can reliably decode memory states, and that this classifier performs as well as those using spectral features. Using the directional connections between brain regions during complex cognitive process provided by the model, we uncovered perirhinal-hippocampal desynchronization in the MTL regions that is associated with successful memory encoding.