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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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Sequential inference with a chain of -machines.An initial population generator  produces a length- string  from which a new model  is inferred. These steps are repeated using  as the population generator and so on, until a terminating condition is met.
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pcbi-1002510-g005: Sequential inference with a chain of -machines.An initial population generator produces a length- string from which a new model is inferred. These steps are repeated using as the population generator and so on, until a terminating condition is met.

Mentions: We are now ready to describe sequential learning, depicted in Figure 5. We begin by selecting the -machine as an initial population generator. Following a path through , guided by its transition probabilities, produces a length- string that represents the first population of individuals possessing alleles . We then infer an -machine from the population . is then used to produce a new population , from which a new -machine is estimated. This new population has the same allele distribution as the previous, plus some amount of variance. The cycle of inference and re-inference is repeated while allele frequencies drift each generation until fixation or deletion is reached. At that point, the populations (and so -machines ) cannot vary further. The net result is a stochastically varying time series of -machines () that terminates when the populations stop changing.


Structural drift: the population dynamics of sequential learning.

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

Sequential inference with a chain of -machines.An initial population generator  produces a length- string  from which a new model  is inferred. These steps are repeated using  as the population generator and so on, until a terminating condition is met.
© Copyright Policy
Related In: Results  -  Collection

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

pcbi-1002510-g005: Sequential inference with a chain of -machines.An initial population generator produces a length- string from which a new model is inferred. These steps are repeated using as the population generator and so on, until a terminating condition is met.
Mentions: We are now ready to describe sequential learning, depicted in Figure 5. We begin by selecting the -machine as an initial population generator. Following a path through , guided by its transition probabilities, produces a length- string that represents the first population of individuals possessing alleles . We then infer an -machine from the population . is then used to produce a new population , from which a new -machine is estimated. This new population has the same allele distribution as the previous, plus some amount of variance. The cycle of inference and re-inference is repeated while allele frequencies drift each generation until fixation or deletion is reached. At that point, the populations (and so -machines ) cannot vary further. The net result is a stochastically varying time series of -machines () that terminates when the populations stop changing.

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