Inferring the causal structure that links n observables is usually based upon
detecting statistical dependences and choosing simple graphs that make the
joint measure Markovian. Here we argue why causal inference is also possible
when only single observations are present.
We develop a theory how to generate causal graphs explaining similarities
between single objects. To this end, we replace the notion of conditional
stochastic independence in the causal Markov condition with the vanishing of
conditional algorithmic mutual information and describe the corresponding
causal inference rules.
We explain why a consistent reformulation of causal inference in terms of
algorithmic complexity implies a new inference principle that takes into
account also the complexity of conditional probability densities, making it
possible to select among Markov equivalent causal graphs. This insight provides
a theoretical foundation of a heuristic principle proposed in earlier work.
We also discuss how to replace Kolmogorov complexity with decidable
complexity criteria. This can be seen as an algorithmic analog of replacing the
empirically undecidable question of statistical independence with practical
independence tests that are based on implicit or explicit assumptions on the
underlying distribution.

本文介绍了一种基于单个观测数据进行因果推断的方法，使用条件算法互信息代替因果马尔科夫条件中的条件随机独立性，解释了单个对象之间相似性的因果图生成，并使用可判定复杂度标准替代 Kolmogorov 复杂度，提出了一种新的因果推断原则，从而可以在 Markov 等价因果图之间进行选择。