Information geometry of graphs

例如，熵量化了一种方式，即抛出一枚公平的硬币比抛出一枚有偏见的硬币更难预测结果。它在了解信息如何通过嘈杂的通信网络传输，以及如何在尽可能小的设备中存储大量信息(数据压缩)方面发挥着重要作用。最近，通过新兴的信息几何领域，人们已经清楚地看到，熵可以提供对统计推理中更基本问题的理解。具体地说，信息几何提供了一种定义随机事件分布之间的“距离”的方法，给出了一种明确的方法来确定两种随机性模型到底有多不同。然而，这些结果通常只在实值随机事件的上下文中被理解，而许多随机事件(例如，与计数有关的事件)仅在集合0，1，2，...中取值。我们建议将PI在信息论领域的专业知识与RA在泛函分析方面的背景相结合，以便以类似的方式为这些计数过程定义距离度量，并了解由此产生的度量的性质。

Entropy quantifies the way in which, for example, the outcome of tossing a fair coin is harder to predict than with a biased one. It plays a fundamental role in understanding how information is transmitted over noisy communication networks, and how large amounts of information can be stored in as small devices as possible (data compression). More recently, through the emerging field of Information Geometry, it has become clear that entropy can provide understanding of more fundamental questions of statistical inference. Specifically, Information Geometry offers a way to define a `distance' between distributions of random events, giving an unambiguous way to decide how different two models of randomness really are. However, these results are generally only understood in the context of real-valued random events, whereas many random events (those to do with counting, for example) take values in just the set 0,1,2,.... We propose to combine the expertise of the PI in the field of Information Theory with the RA's background in functional analysis, in order to define distance measures in a similar way for these counting processes, and to understand the properties of the resulting measures.