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

数据采集技术的进步导致了越来越复杂的数据集的可用性。通常，收集的变量具有根本不同的统计数据，一些是连续的，而另一些是离散的。在许多领域中，记录变量之间的关系特别重要，并且随时间变化。其中一个领域是计算神经科学，最近的研究表明，即使在早期的感觉脑区，对刺激的神经反应也会受到行为背景的调节。这种调节背后的精确功能相互作用目前尚不清楚，但对于理解感觉处理的惊人多功能性是如何产生的非常重要。从分析的角度来看，理解神经活动，行为和任务变量之间的复杂的相互作用，都受到不同的统计和时间尺度，是一个重大的挑战。在这个项目中，我们将解决的一般问题，评估概率描述的时间依赖性的元素之间的关系与混合统计的动机，在神经科学中遇到的上下文相关的感觉处理问题。为了加入混合元素，我们将使用嵌入时变参数贝叶斯框架中的参数copula模型。对于模型拟合，我们将使用基于期望传播的推理方案结合高斯过程先验，后者自然适合考虑不同的时间尺度。与其他常用的方法相反，这种方法将使随机关系显式化，并生成具有显著不同统计数据的元素的可解释的联合模型。为了研究神经反应调制，特别是上下文相关的视觉处理，我们将把我们的分析框架应用于项目合作伙伴Nathalie Rochefort博士已经记录的数据。这些数据包括使用双光子钙成像从清醒行为小鼠的初级视觉皮层记录的大量神经元中的荧光变化。这些数据还包括从虚拟现实环境中收集的同时记录的行为和任务变量。我们的分析将加深我们对初级视皮层功能关系的理解，使视觉系统如此多才多艺，从而提供新的系统状态表征以及改进的感觉解码器。通用的时间依赖关系模型的发展将由特定的神经科学应用驱动，以理解初级视皮层中的上下文依赖关系，但是将更广泛地应用于随机关系分析重要的许多其它领域。

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.