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Homework answers / question archive / In this question, you are going to implement the asymmetric PMI (pointwise mutual information) measure I(x, y) from Church and Hanks and explore it on the UD English-EWT training portion

In this question, you are going to implement the asymmetric PMI (pointwise mutual information) measure I(x, y) from Church and Hanks and explore it on the UD English-EWT training portion

Computer Science

In this question, you are going to implement the asymmetric PMI (pointwise mutual information) measure I(x, y) from Church and Hanks and explore it on the UD English-EWT training portion. Let ν and η be any two arbitrary word types. To implement PMI, we'll refer to p(ν), p(η), and p(ν, η). Your I will measure how likely η "occurs after" ν within the same "window." Define each sentence as the "window": if two word (types) ν and η appear in the same sentence, then they adjust the counts used to compute p(ν, η). Otherwise they don't. 
A). Use those functions to implement PMI. Answer the following sub-questions by looking at lowercased versions of the FORM column. i. Do you agree with their rough rule-of-thumb that "interesting" word pairs (x, y) have I(x, y) > 3? Provide some examples to help support your assessment. ii. What are the 10 values of η that return the largest positive values of I(ν, η) if ν ="doctor?" In your writeup, provide both the pairs (ν, η) and the PMI value. iii. For pairs (ν, η) that actually occurred within the same window, what are the 10 values of η that return the smallest (largest negative, or least positive) values of I(ν, η) if ν ="doctor?" In your writeup, provide both the pairs (ν, η) and the PMI value.


(B). Now let λ be any positive (real) number: it could be 0.000001, 10, 203983204981, or any other valid number. Define gλ = c + λ, and redefine each of the p distributions in terms of gλ instead of c. Call this new function pλ. i. If g(cat) = 42 (which it does), and there are 204, 607 tokens, what is pλ(cat) if λ = 3. ii. Why can't λ be negative? iii. Now re-implement I in terms of pλ (letting λ be a variable, i.e., it is not always 3). Try 5 values of λ: two values below 1 (λ1, λ2 < 1), one value at 1 (λ3 = 1), and two values above 1 (λ4, λ5 > 1). How much do the top 10 I(ν, η) words change as you decrease, or increase, λ.


(C) Finally, using the above results (and any other results you feel you need to gather to answer this), discuss potential implications for the "power" (ability to find "interesting word pairs") and "stability" (consistency/variability in results) of these methods. What are some of the potential risks in using a method like this to find interesting words, and how could you mitigate that risk?

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