|
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.
Links to this page
© ppgb 20070725