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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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Time to fixation for a population of  individuals (sample size ) plotted as a function of initial allele probability  under the Monte Carlo (MC) sampling regime and as given by theoretical prediction (solid line) of Eq. (4).Time to deletion is also shown (dashed line), Eq. (5).
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pcbi-1002510-g001: Time to fixation for a population of individuals (sample size ) plotted as a function of initial allele probability under the Monte Carlo (MC) sampling regime and as given by theoretical prediction (solid line) of Eq. (4).Time to deletion is also shown (dashed line), Eq. (5).

Mentions: Figure 1 illustrates this, showing both the simulated and theoretically predicted number of generations until fixation occurs for , as well as the predicted time to deletion for reference. Each simulation was performed for a different initial value of and averaged over 400 realizations. Using the same methodology as Kimura and Ohta [5], we include only those realizations whose mutant allele reaches fixation.


Structural drift: the population dynamics of sequential learning.

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

Time to fixation for a population of  individuals (sample size ) plotted as a function of initial allele probability  under the Monte Carlo (MC) sampling regime and as given by theoretical prediction (solid line) of Eq. (4).Time to deletion is also shown (dashed line), Eq. (5).
© Copyright Policy
Related In: Results  -  Collection

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

pcbi-1002510-g001: Time to fixation for a population of individuals (sample size ) plotted as a function of initial allele probability under the Monte Carlo (MC) sampling regime and as given by theoretical prediction (solid line) of Eq. (4).Time to deletion is also shown (dashed line), Eq. (5).
Mentions: Figure 1 illustrates this, showing both the simulated and theoretically predicted number of generations until fixation occurs for , as well as the predicted time to deletion for reference. Each simulation was performed for a different initial value of and averaged over 400 realizations. Using the same methodology as Kimura and Ohta [5], we include only those realizations whose mutant allele reaches fixation.

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