# Estimating the size of training data for grammer extraction

I have a dependency treebank including 100 sentences, which I divide into a training set and a test set. I extract some rules ((DS,PS) pairs) to convert the treebank to phrase structures. When I extract such rules from the training set, I can measure the percentage of rules (DS patterns) that cover the test set, suppose

(10, 24%), (20, 34%), (30,40%), (40,44%), (50, 55%),(60, 58%), (70, 61%)...

As you see as I increase the size of the training set, the coverage of extracted patterns increases! however its not linear!, I want to see how many data I need to reach 100% coverage? I guess I can use a regression, but which regression? logarithmic?

Is this related to 'learning curve'? if yes how can I use regression for a learning curve?

• I don't know which curve your data leads to, but I think the results are not too unsurprising: When extending your training set, the new one won't contain exclusively new rules, but the ones that are more frequent (and therefore occur at smaller data sizes already) will occur in the newly added data to, while the patterns that occur less frequently won't occur with the same percentage as the more frequent ones (e.g., not with 24%) and hence you can not expect the pattern occurences to grow lineary. Jun 25 '16 at 14:54
• Since there unfortunately don't seem to be that many fellow computational linguists here (although I think your question is definitely within the declared scope of Ling.SE), maybe you can also seek for help at Cross Validated SE. Jun 25 '16 at 14:56
• @lemontree we know the best percentage it can reach is 100%, I don't think just by linearly increasing the size of training set I reach to 100%.... we can see it inversely, suppose the uncovered rules are decreasing and we are going to reach to 0%,,, maybe an exponential regression be suitable not? Jun 25 '16 at 16:06
• Could be, but I'm not really expertised in regression modeling so unfortunatlely can't answer that question. Jun 25 '16 at 16:34