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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.

Show MeSH
-Machine for the Golden Mean Process consisting of two causal states  that generates a population with no consecutive s.In state  the probabilities of generating a 0 or 1 are  and , respectively.
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pcbi-1002510-g004: -Machine for the Golden Mean Process consisting of two causal states that generates a population with no consecutive s.In state the probabilities of generating a 0 or 1 are and , respectively.

Mentions: Enforcing the alternating period-2 pattern requires two states, and , as well as two positive probability transitions and . Branching transitions are required for a process to structurally drift; the Alternating Process has none. Two simple -machines with branching structure are the smaller Fair Coin Process (Figure 3) and more complex Golden Mean Process (Figure 4). Both are discussed in detail later.


Structural drift: the population dynamics of sequential learning.

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

-Machine for the Golden Mean Process consisting of two causal states  that generates a population with no consecutive s.In state  the probabilities of generating a 0 or 1 are  and , respectively.
© Copyright Policy
Related In: Results  -  Collection

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

pcbi-1002510-g004: -Machine for the Golden Mean Process consisting of two causal states that generates a population with no consecutive s.In state the probabilities of generating a 0 or 1 are and , respectively.
Mentions: Enforcing the alternating period-2 pattern requires two states, and , as well as two positive probability transitions and . Branching transitions are required for a process to structurally drift; the Alternating Process has none. Two simple -machines with branching structure are the smaller Fair Coin Process (Figure 3) and more complex Golden Mean Process (Figure 4). Both are discussed in detail later.

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