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/ → anpa | 14.3%

  /an+pa/ → ampa | 85.7%

  /at+ma/ → atma | 96.9%

  /at+ma/ → apma | 3.1%

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/ → anpa | 18.31%

  /an+pa/ → ampa | 81.69%

  /at+ma/ → atma | 99.91%

  /at+ma/ → apma | 0.09%

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/ → anpa | 20.08%

  /an+pa/ → ampa | 79.92%

  /at+ma/ → atma | 99.94%

  /at+ma/ → apma | 0.06%

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.

### Links to this page

- OT learning
- OTGrammar & 2 Strings: Learn...
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