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• • • Digitale Intelligenz – Emergenzbasierte Statistik

    • Anwendungen emergenzbasierter KI in Produktion und Betriebswirtschaft
      

  
  
  
  

  Emergent Law Based Statistics

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  “I think […] that mathematical ideas originate in empirics. But, once they are conceived, the subject begins to live a peculiar life of its own and is […] governed by almost entirely aesthetical motivations. In other words, at a great distance from its empirical source, or after much “abstract” inbreeding, a mathematical subject is in danger of degeneration.

  Whenever this stage is reached the only remedy seems to me to be the rejuvenating return to the source: the reinjection of more or less directly empirical ideas.”

  John von Neumann – “The Mathematician” in The Works of the Mind (1947)

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  In our opinion “probability” is such a degenerated concept.

  There is neither an objective way (without any assumptions) to arrive at a probability statement from observations nor does the probability statement predict any possible concrete observation.

  Taking the statement “if it has rained today, then the probability that it will rain tomorrow is equal to 60%” as an example, neither the statement can be objectively derived from observations nor can the statement as such be objectively and finally falsified.

  In order to “reinject” empirical content into the fundament of statistical reasoning, we replace the concept of probability by the concept of “emergent laws”.

  Emergent Laws are descriptions of patterns that always were observed in the past.

  “In every sequence of 10 days (each following a rainy day) the relative frequency of rain was at least 60%.”

  We call this an “emergent law” because we only state a feature (relative frequency) of sequences of measurements (10 measurements) was always observed and this is explicitly not a feature of a single measurement.

  This law is also deterministic, because it states that some kind of complex but nevertheless exact observation has always been true until now. Taking into account that only what has always been true in the past can possibly be true in general emergent laws create the chance to make falsifiable predictions: “The relative frequency of rain in the next 10 days following a rainy day will be at least 60%.”

  In case such a prediction is falsified once the falsified universal statement will remain false forever. If we can find enough not falsified deterministic laws and if we can identify general consequences from sequences of such predictions we can build up empirical science on a very solid methodological fundament.

  Based on the methods of emergent-law-based statistics we found billions of emergent laws, in lots of databases. So there is no doubt that there are enough empirical laws to base statistics only on emergent laws.

  Further the performance of the prediction strategy that a pattern that was always true until now, will appear again the next time, can be evaluated empirically and we found that certain patterns of prediction quality were always observed in lots of different prediction tasks, and as a consequence they can be described by emergent laws as well. We call laws about the universal performance (independent of the type of prediction task) of a prediction strategy Meta-Laws.

  So we think that we solved the epistemological “induction problem”.

  By applying emergent laws and meta-laws to statistical problems we found far reaching consequences:

  • • • • Machine Learning (ML) Algorithms that search for emergent laws guided by meta-laws demonstrate a prediction performance at least comparable with the most advanced ML-Algorithms (e.g. Deep Neural Nets or XG-Boosting).

        • Because emergent laws and meta-laws were empirically true until now they never can contradict each other. So Databases containing knowledge defined by emergent laws can be easily combined without any limitation. A meaning-full kind of KnowledgeBase becomes possible.

        • A learning system that is based on a KnowledgeBase and evaluates the laws in real-time reveals aspects of the world that were always true until now.

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