OT learning 5. Learning a stochastic grammar


Having shown that the algorithm can learn deep obligatory rankings, we will now see that it also performs well in replicating the variation in the language environment.
Create a place assimilation grammar as described in §2.6, and set all its rankings to 100.000:

 ranking value  disharmony  plasticity 

*GESTURE  100.000  100.000  1.000 

*REPLACE (t, p)  100.000  100.000  1.000 

*REPLACE (n, m)  100.000  100.000  1.000 
Create a place assimilation distribution and generate 1000 string pairs (§3.1). Select the grammar and the two Strings objects, and learn with a plasticity of 0.1:

 ranking value  disharmony  plasticity 

*REPLACE (t, p)  104.540  103.140  1.000 

*REPLACE (n, m)  96.214  99.321  1.000 

The output distributions are now (using OTGrammar: To output Distributions..., see §2.9):




After another 10,000 new string pairs, we have:

 ranking value  disharmony  plasticity 

*REPLACE (t, p)  106.764  107.154  1.000 

*GESTURE  97.899  97.161  1.000 

*REPLACE (n, m)  95.337  96.848  1.000 
With the following output distributions (measured with a million draws):




The error rate is acceptably low, but the accuracy in reproducing the 80%  20% distribution could be better. This is because the relatively high plasticity of 0.1 can only give a coarse approximation. So we lower the plasticity to 0.001, and supply 100,000 new data:

 ranking value  disharmony  plasticity 

*REPLACE (t, p)  106.810  107.184  1.000 

*GESTURE  97.782  99.682  1.000 

*REPLACE (n, m)  95.407  98.760  1.000 
With the following output distributions:




So besides learning obligatory rankings like a child does, the algorithm can also replicate very well the probabilities of the environment. This means that a GLA learner can learn stochastic grammars.
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