Integrated Information - Theory, Estimation, and Application

传统的信息论关注的是信息通过渠道从发送者到接收者的流动。然而，在交互元素的分布式网络中，任何元素(或元素集)都可以被视为发送者或接收者。在这种情况下，当没有特定的感兴趣的渠道，因此没有主要的发送者或接收者时，我们如何应用信息论的原理来研究网络？综合信息试图捕捉一种直观的概念，如果物理系统将信息作为一个整体来指定，而不是单独考虑其各部分时，则该物理系统将信息集成在一起。 整合信息最初是在神经科学中发展起来的，它试图在大脑中观察到的隔离和整合之间取得平衡。单独的大脑区域似乎执行特殊的功能(隔离)，但却共同工作以实现统一的反应(整合)。除了在神经科学中的应用外，综合信息还被用作复杂性的一般衡量标准，在包括生物学、计算机科学和物理学在内的自然科学中找到了应用。 在接下来的五年里，我将同时寻求推进综合信息领域的三个途径： 发展对集成信息的理论理解。具体地说，我们使用信息几何的工具来更好地理解物理系统中信息的结构。 改进估计综合信息的统计和计算技术。目前的方法将应用局限于小系统，但更好的工具将打开许多令人兴奋的可能应用。 展示集成信息在应用程序中的价值。应用程序将主要基于神经科学，但也将探索其他学科的机会。 我的研究是高度跨学科和协作性的，将对自然科学和工程学的几个领域产生直接影响。预期结果将为综合信息的结构提供一个新的(几何)视角。结果还将为连续变量建立综合信息的定义，使现有的综合信息方法暴露在新的应用领域。对综合信息的准确估计将为分析更大的模型提供新的机会。虽然最初是通过将大脑视为一个相互作用的神经元系统来开发的，但综合信息已经在其他自然科学领域找到了应用，从生物学到物理学。经过验证的估计综合信息的技术将促进因果模型和图形模型在这些领域的应用。

Traditional information theory is concerned with the flow of information through a channel, from sender to receiver. However, in distributed networks of interacting elements, any element (or set of elements) can be considered as a sender or a receiver. In such cases, when there is no specific channel of interest, and so no primary senders or receivers, how can we apply the principles of information theory to study the network? Integrated information attempts to capture an intuitive notion a physical system integrates information if it specifies more information as a whole than when its parts are considered independently. Originally developed in neuroscience, integrated information is an attempt to capture the balance between segregation and integration observed in the brain. Individual brain regions appear to perform specialized functions (segregation) yet work together to achieve a unified response (integration). In addition to applications in neuroscience, integrated information has been employed as a general measure of complexity, finding applications across the natural sciences, including biology, computer science, and physics. During the next five years I will concurrently pursue three avenues for advancing the field of integrated information: Develop the theoretical understand of integrated information. Specifically, we use the tools of information geometry to better understand the structure' of information in physical systems. Improve on statistical and computational techniques for estimating integrated information. Current methods limit applications to small systems, but better tools will open up many exciting possible applications. Demonstrate the value of integrated information in applications. Applications will be primarily based in neuroscience, but also exploring opportunities in other disciplines. My research is highly interdisciplinary and collaborative, and will have a direct impact on several fields within the natural sciences and engineering. The expected results will provide a new (geometric) perspective on the structure of integrated information. The results will also establish a definition of integrated information for continuous variables, exposing the existing methods of integrated information to new domains of application. Accurate estimates of integrated information will provide new opportunities to analyse larger models. While originally developed by considering the brain as a system of interacting neurons, integrated information has found applications in other natural science fields, from biology to physics. Validated techniques for estimating integrated information will stimulate the application of causal and graphical models in these fields.