标题： 预测的分类 显示英文标题

标题： Taxonomy of Prediction

摘要： 预测是对系统未来做出的声明，基于对其过去的了解。 回溯是对系统过去做出的声明，基于对其未来的了解。 双向机器是一种左右手都能使用的隐马尔可夫链，它通过在其状态结构中明确所有统计相关性，从而最优地完成这两种任务。 我们引入了一种信息分类法，通过一系列多变量信息度量来分析这些相关性。 虽然之前的结果阐述了孤立比特测量中包含的不同类型的信息，但相关的信息难以显式计算。 通过双向机器的状态克服这一问题，我们将该分析扩展到预测和回溯。 结果突出显示了十四种新的可解释且可计算的度量，这些度量描述了过程的信息结构。 此外，我们引入了一种标记和索引方案，系统化地进行复杂多变量系统的信息理论分析。 具体实施方面，我们提供了算法，直接以闭合形式计算有限建模过程的所有这些量。 显示英文摘要

摘要： A prediction makes a claim about a system's future given knowledge of its past. A retrodiction makes a claim about its past given knowledge of its future. The bidirectional machine is an ambidextrous hidden Markov chain that does both optimally by making explicit in its state structure all statistical correlation in a stochastic process. We introduce an informational taxonomy to profile these correlations via a suite of multivariate information measures. While prior results laid out the different kinds of information contained in isolated measurement of a bit, the associated informations were challenging to calculate explicitly. Overcoming this via bidirectional machine states, we expand that analysis to prediction and retrodiction. The result highlights fourteen new interpretable and calculable measures that characterize a process' informational structure. In addition, we introduce a labeling and indexing scheme that systematizes information-theoretic analyses of complex multivariate systems. Operationalizing this, we provide algorithms to directly calculate all of these quantities in closed form for finitely-modeled processes.