次模信息测度的因果马尔可夫条件
Causal Markov condition for submodular information measures
摘要：
因果马尔可夫条件（CMC）是一个将观察结果与因果关系联系起来的假设。它描述了一个因果假设所涉及的观测之间的条件独立性，在一个有向无环图。在传统环境中，观察值是随机变量，独立性是统计独立性，即，观测的信息量用香农熵来度量。我们制定了一个广义CMC的任何一种独立的意见，通过任意的子模块信息测度定义。最近，这已经被讨论的观察在二进制字符串的信息理解的意义上的柯尔莫哥洛夫复杂性。我们的方法使我们能够找到Kolmogorov复杂性的可计算替代方案，例如，应用现有数据压缩方案后的文本长度。我们表明，我们的CMC是合理的，如果限制注意一类因果机制，是适应于各自的信息措施。我们的理由是类似于从因果关系的函数模型中推导出统计CMC，其中每个变量都是其观察到的原因和未观察到的噪声项的确定性函数。我们在真实数据上的实验证明了基于压缩的因果推理的性能。
英文摘要：
The causal Markov condition (CMC) is a postulate that links observations to causality. It describes the conditional independences among the observations that are entailed by a causal hypothesis in terms of a directed acyclic graph. In the conventional setting, the observations are random variables and the independence is a statistical one, i.e., the information content of observations is measured in terms of Shannon entropy. We formulate a generalized CMC for any kind of observations on which independence is defined via an arbitrary submodular information measure. Recently, this has been discussed for observations in terms of binary strings where information is understood in the sense of Kolmogorov complexity. Our approach enables us to find computable alternatives to Kolmogorov complexity, e.g., the length of a text after applying existing data compression schemes. We show that our CMC is justified if one restricts the attention to a class of causal mechanisms that is adapted to the respective information measure. Our justification is similar to deriving the statistical CMC from functional models of causality, where every variable is a deterministic function of its observed causes and an unobserved noise term. Our experiments on real data demonstrate the performance of compression based causal inference.
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