Novel techniques for stochastic modelling of time-dependent multivariate relationships with application to primary visual cortex

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Advances in data acquisition technologies lead to the availability of ever more complex datasets. Often, the gathered variables have fundamentally different statistics, some being continuous while others are discrete. In many domains, the relationships between the recorded variables are of particular importance and also changing in time. One such domain is computational neuroscience where it was recently shown that even in early sensory brain areas, neural responses to stimuli are modulated by behavioural context. The precise functional interactions underlying this modulation are currently unknown but nonetheless important for understanding how the amazing versatility of sensory processing comes about. From an analytical point of view, understanding the complex interactions between neural activity, behaviour and task variables, all being subject to different statistics and timescales, is a major challenge.In this project, we will address the general problem of assessing probabilistic descriptions of time-dependent relationships between elements with mixed statistics as motivated by the context-dependent sensory processing problem encountered in neuroscience. To join mixed elements, we will use parametric copula models embedded in a Bayesian framework for time-varying parameters. For model fitting, we will use an inference scheme based on Expectation Propagation in conjunction with Gaussian Process priors, the latter being naturally suited to take into account different timescales. Contrary to other commonly applied methods, this approach will make stochastic relationships explicit and generate interpretable joint models of elements with strikingly different statistics.In order to investigate neural response modulation and in particular context-dependent visual processing, we will apply our analysis framework to data already recorded by project partner Dr Nathalie Rochefort. The data consist of fluorescence changes in large populations of neurons as recorded from primary visual cortex of awake behaving mice using two-photon calcium imaging. The data also include concurrently recorded behavioural and task variables gathered from a virtual reality environment. Our analysis will deepen our understanding of functional relationships in primary visual cortex that make the visual system so versatile, thereby providing new system state characterizations as well as improved sensory decoders.The development of versatile time-dependent relationship models will be driven by the particular neuroscience application to understand context-dependent relationships in primary visual cortex, but will be more broadly applicable to many other domains where stochastic relationship analysis is of importance.