摘要翻译：
我们介绍了一种推断随机动力系统因果结构的方法，它扩展了率失真理论，使用因果屏蔽--一种自然的学习原理。我们研究了因果推理的两种不同情况：最优因果过滤和最优因果估计。滤波对应于测量序列的概率分布已知的理想情况，给出了在期望的表示水平上近似系统因果结构的原则性方法。我们证明，在模型复杂性约束放松的极限下，滤波可以找到随机动力系统的精确因果结构，称为因果状态划分。由此，可以估计进程存储的历史信息量。更一般地说，因果过滤发现了因果结构近似的分级模型复杂度层次。层次结构的突然变化，作为近似值的函数，捕捉到结构组织的不同尺度。对于有限数据的非理想情形，我们证明了如何通过最优因果估计来找到潜在因果状态的正确数目。先前导出的模型复杂性控制项允许我们校正概率估计中统计波动的影响，从而避免过拟合。
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英文标题：
《Optimal Causal Inference: Estimating Stored Information and
  Approximating Causal Architecture》
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作者：
Susanne Still, James P. Crutchfield, Christopher J. Ellison
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最新提交年份：
2010
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分类信息：

一级分类：Computer Science        计算机科学
二级分类：Information Theory        信息论
分类描述：Covers theoretical and experimental aspects of information theory and coding. Includes material in ACM Subject Class E.4 and intersects with H.1.1.
涵盖信息论和编码的理论和实验方面。包括ACM学科类E.4中的材料，并与H.1.1有交集。
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一级分类：Physics        物理学
二级分类：Statistical Mechanics        统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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一级分类：Computer Science        计算机科学
二级分类：Machine Learning        机器学习
分类描述：Papers on all aspects of machine learning research (supervised, unsupervised, reinforcement learning, bandit problems, and so on) including also robustness, explanation, fairness, and methodology. cs.LG is also an appropriate primary category for applications of machine learning methods.
关于机器学习研究的所有方面的论文（有监督的，无监督的，强化学习，强盗问题，等等），包括健壮性，解释性，公平性和方法论。对于机器学习方法的应用，CS.LG也是一个合适的主要类别。
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一级分类：Mathematics        数学
二级分类：Information Theory        信息论
分类描述：math.IT is an alias for cs.IT. Covers theoretical and experimental aspects of information theory and coding.
它是cs.it的别名。涵盖信息论和编码的理论和实验方面。
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一级分类：Mathematics        数学
二级分类：Statistics Theory        统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Statistics        统计学
二级分类：Statistics Theory        统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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英文摘要：
  We introduce an approach to inferring the causal architecture of stochastic dynamical systems that extends rate distortion theory to use causal shielding---a natural principle of learning. We study two distinct cases of causal inference: optimal causal filtering and optimal causal estimation.   Filtering corresponds to the ideal case in which the probability distribution of measurement sequences is known, giving a principled method to approximate a system's causal structure at a desired level of representation. We show that, in the limit in which a model complexity constraint is relaxed, filtering finds the exact causal architecture of a stochastic dynamical system, known as the causal-state partition. From this, one can estimate the amount of historical information the process stores. More generally, causal filtering finds a graded model-complexity hierarchy of approximations to the causal architecture. Abrupt changes in the hierarchy, as a function of approximation, capture distinct scales of structural organization.   For nonideal cases with finite data, we show how the correct number of underlying causal states can be found by optimal causal estimation. A previously derived model complexity control term allows us to correct for the effect of statistical fluctuations in probability estimates and thereby avoid over-fitting.
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PDF链接：
https://arxiv.org/pdf/708.158