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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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Related in: MedlinePlus

Top: Time to stasis of the Golden Mean, Even, and Biased Coin Processes. Middle: Stasis time of the Golden Mean Process as the weighted sum of stasis times for the Fixed Coin (FC) and Alternating Process (AP) pathways. Bottom: Stasis time of the FC pathway as the weighted sum of Golden Mean (GM) and Biased Coin (BC) subspace diffusion times.
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pcbi-1002510-g009: Top: Time to stasis of the Golden Mean, Even, and Biased Coin Processes. Middle: Stasis time of the Golden Mean Process as the weighted sum of stasis times for the Fixed Coin (FC) and Alternating Process (AP) pathways. Bottom: Stasis time of the FC pathway as the weighted sum of Golden Mean (GM) and Biased Coin (BC) subspace diffusion times.

Mentions: It should be noted that the memoryful Golden Mean and Even Processes reach stasis markedly faster than the memoryless Biased Coin. While Figure 8 shows only a single realization of each sampling process type, the top panel of Figure 9 shows the large disparity in stasis times holds across all settings of each process's initial bias. This is one of our first general observations about memoryful processes: The structure of memoryful processes substantially impacts the average time to stasis by increasing variance between generations. In the cases shown, time to stasis is greatly shortened.


Structural drift: the population dynamics of sequential learning.

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

Top: Time to stasis of the Golden Mean, Even, and Biased Coin Processes. Middle: Stasis time of the Golden Mean Process as the weighted sum of stasis times for the Fixed Coin (FC) and Alternating Process (AP) pathways. Bottom: Stasis time of the FC pathway as the weighted sum of Golden Mean (GM) and Biased Coin (BC) subspace diffusion times.
© Copyright Policy
Related In: Results  -  Collection

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

pcbi-1002510-g009: Top: Time to stasis of the Golden Mean, Even, and Biased Coin Processes. Middle: Stasis time of the Golden Mean Process as the weighted sum of stasis times for the Fixed Coin (FC) and Alternating Process (AP) pathways. Bottom: Stasis time of the FC pathway as the weighted sum of Golden Mean (GM) and Biased Coin (BC) subspace diffusion times.
Mentions: It should be noted that the memoryful Golden Mean and Even Processes reach stasis markedly faster than the memoryless Biased Coin. While Figure 8 shows only a single realization of each sampling process type, the top panel of Figure 9 shows the large disparity in stasis times holds across all settings of each process's initial bias. This is one of our first general observations about memoryful processes: The structure of memoryful processes substantially impacts the average time to stasis by increasing variance between generations. In the cases shown, time to stasis is greatly shortened.

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