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Structural drift: the population dynamics of sequential learning.

Crutchfield JP, Whalen S - PLoS Comput. Biol. (2012)

Bottom Line: We introduce a theory of sequential causal inference in which learners in a chain estimate a structural model from their upstream "teacher" and then pass samples from the model to their downstream "student".It extends the population dynamics of genetic drift, recasting Kimura's selectively neutral theory as a special case of a generalized drift process using structured populations with memory.We also demonstrate how the organization of drift process space controls fidelity, facilitates innovations, and leads to information loss in sequential learning with and without memory.

View Article: PubMed Central - PubMed

Affiliation: Complexity Sciences Center, Physics Department, University of California Davis, Davis, California, United States of America. chaos@ucdavis.edu

ABSTRACT
We introduce a theory of sequential causal inference in which learners in a chain estimate a structural model from their upstream "teacher" and then pass samples from the model to their downstream "student". It extends the population dynamics of genetic drift, recasting Kimura's selectively neutral theory as a special case of a generalized drift process using structured populations with memory. We examine the diffusion and fixation properties of several drift processes and propose applications to learning, inference, and evolution. We also demonstrate how the organization of drift process space controls fidelity, facilitates innovations, and leads to information loss in sequential learning with and without memory.

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Drift of Pr[Heads] for a single realization of the Biased Coin, Golden Mean, and Even Processes, plotted as a function of generation.The Even and Biased Coin Processes become the Fixed Coin Process at stasis, while the Golden Mean Process becomes the Alternating Process. Note that the definition of structural stasis recognizes the lack of variance in the Alternating Process subspace even though the allele probability is neither 0 nor 1.
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pcbi-1002510-g008: Drift of Pr[Heads] for a single realization of the Biased Coin, Golden Mean, and Even Processes, plotted as a function of generation.The Even and Biased Coin Processes become the Fixed Coin Process at stasis, while the Golden Mean Process becomes the Alternating Process. Note that the definition of structural stasis recognizes the lack of variance in the Alternating Process subspace even though the allele probability is neither 0 nor 1.

Mentions: To compare structural drift behaviors, consider also the Even Process. Similar in form to the Golden Mean Process, the Even Process produces populations in which blocks of consecutive s must be even in length when bounded by s [24]. Figure 8 compares the drift of Pr[Heads] for a single realization of the Biased Coin, Golden Mean, and Even Processes. One observes that the Even and Biased Coin Processes reach stasis as the Fixed Coin Process, while the Golden Mean Process reaches stasis as the Alternating Process. For different realizations, the Even and Golden Mean Processes might instead reach different stasis points.


Structural drift: the population dynamics of sequential learning.

Crutchfield JP, Whalen S - PLoS Comput. Biol. (2012)

Drift of Pr[Heads] for a single realization of the Biased Coin, Golden Mean, and Even Processes, plotted as a function of generation.The Even and Biased Coin Processes become the Fixed Coin Process at stasis, while the Golden Mean Process becomes the Alternating Process. Note that the definition of structural stasis recognizes the lack of variance in the Alternating Process subspace even though the allele probability is neither 0 nor 1.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3369870&req=5

pcbi-1002510-g008: Drift of Pr[Heads] for a single realization of the Biased Coin, Golden Mean, and Even Processes, plotted as a function of generation.The Even and Biased Coin Processes become the Fixed Coin Process at stasis, while the Golden Mean Process becomes the Alternating Process. Note that the definition of structural stasis recognizes the lack of variance in the Alternating Process subspace even though the allele probability is neither 0 nor 1.
Mentions: To compare structural drift behaviors, consider also the Even Process. Similar in form to the Golden Mean Process, the Even Process produces populations in which blocks of consecutive s must be even in length when bounded by s [24]. Figure 8 compares the drift of Pr[Heads] for a single realization of the Biased Coin, Golden Mean, and Even Processes. One observes that the Even and Biased Coin Processes reach stasis as the Fixed Coin Process, while the Golden Mean Process reaches stasis as the Alternating Process. For different realizations, the Even and Golden Mean Processes might instead reach different stasis points.

Bottom Line: We introduce a theory of sequential causal inference in which learners in a chain estimate a structural model from their upstream "teacher" and then pass samples from the model to their downstream "student".It extends the population dynamics of genetic drift, recasting Kimura's selectively neutral theory as a special case of a generalized drift process using structured populations with memory.We also demonstrate how the organization of drift process space controls fidelity, facilitates innovations, and leads to information loss in sequential learning with and without memory.

View Article: PubMed Central - PubMed

Affiliation: Complexity Sciences Center, Physics Department, University of California Davis, Davis, California, United States of America. chaos@ucdavis.edu

ABSTRACT
We introduce a theory of sequential causal inference in which learners in a chain estimate a structural model from their upstream "teacher" and then pass samples from the model to their downstream "student". It extends the population dynamics of genetic drift, recasting Kimura's selectively neutral theory as a special case of a generalized drift process using structured populations with memory. We examine the diffusion and fixation properties of several drift processes and propose applications to learning, inference, and evolution. We also demonstrate how the organization of drift process space controls fidelity, facilitates innovations, and leads to information loss in sequential learning with and without memory.

Show MeSH
Related in: MedlinePlus