On the criticality of inferred models
AbstractAdvanced inference techniques allow one to reconstruct the pattern of interaction from high dimensional data sets. We focus here on the statistical properties of inferred models and argue that inference procedures are likely to yield models which are close to a phase transition. On one side, we show that the reparameterization invariant metrics in the space of probability distributions of these models (the Fisher Information) is directly related to the model's susceptibility. As a result, distinguishable models tend to accumulate close to critical points, where the susceptibility diverges in infinite systems. On the other, this region is the one where the estimate of inferred parameters is most stable. In order to illustrate these points, we discuss inference of interacting point processes with application to financial data and show that sensible choices of observation time-scales naturally yield models which are close to criticality.
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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1102.1624.
Date of creation: Feb 2011
Date of revision: Sep 2011
Publication status: Published in J. Stat. Mech. (2011) P10012
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Web page: http://arxiv.org/
This paper has been announced in the following NEP Reports:
- NEP-ALL-2011-02-19 (All new papers)
- NEP-CIS-2011-02-19 (Confederation of Independent States)
- NEP-ECM-2011-02-19 (Econometrics)
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- Thomas Bury, 2013. "A statistical physics perspective on criticality in financial markets," Papers 1310.2446, arXiv.org, revised Jan 2014.
- Hongli Zeng & R\'emi Lemoy & Mikko Alava, 2013. "Financial interaction networks inferred from traded volumes," Papers 1311.3871, arXiv.org.
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