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arXiv 2018年

作者： Zenil, Hector Kiani, Narsis A. Tegnér, Jesper Algorithmic Dynamics Lab2 Unit of Computational Medicine Center for Molecular Medicine Department of Medicine Solna Karolinska Institute Stockholm Sweden Natural and Digital Sciences Paris France Oxford Immune Algorithmics Oxford University Innovation Oxford United Kingdom Saudi Arabia

The principle of maximum entropy (Maxent) suggests to select the distribution with maximal entropy. While this has served the community as a useful tool it has recently become clear that distributions with high entropy may indeed be produced by short generative programs. Here we refine the principle by considering recursive (computable) generative programs as a refinement to classical Maxent. We take advantage of a causal algorithmic calculus to derive a thermodynamic-like result based on how difficult it is to reprogram a computer code to produce an output with a different algorithmic probability. Using the distinction between computable and algorithmic randomness we quantify the cost in informa- tion loss associated with reprogramming. To illustrate this we construct reference graphs reversing the same algorithmic calculus and introduce a Maximal algorithmic Randomness Preferential Attachment (MARPA) Algorithm, a generalisation over previous approaches. Using MARPA and reprogrammability we refine Maxent by quantifying the algorithmic typicality of an object based on a combined distance from algorithmic randomness. Classical entropy-based Maxent collapse all random-looking cases despite the generating mechanism thereby confounding all distinct degrees of randomness and pseudo-randomness. We discuss practi- cal implications of evaluation of network randomness. Our analysis provides insight in that the reprogrammability asymmetry appears to originate from a non-monotonic relationship to algorithmic probability. Our analysis motivates further analysis of the origin and consequences of the aforementioned asymmetries, reprogrammability, and computation. Copyright © 2018, The Authors. All rights reserved.

关键词： Random processes

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