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
   
*GESTURE 99.246 97.861

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

   
/an+pa/ → anpa14.3%
   
/an+pa/ → ampa85.7%
   
/at+ma/ → atma96.9%
   
/at+ma/ → apma3.1%

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):

   
/an+pa/ → anpa18.31%
   
/an+pa/ → ampa81.69%
   
/at+ma/ → atma99.91%
   
/at+ma/ → apma0.09%

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:

   
/an+pa/ → anpa20.08%
   
/an+pa/ → ampa79.92%
   
/at+ma/ → atma99.94%
   
/at+ma/ → apma0.06%

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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© ppgb, July 25, 2007