1. Tolerant Retrieval Review Questions

2. Storing a Rotated Lexicon
Suggest a structure that could be used to store a rotated lexicon
Supposing that you had
W words
Average word length of n
Longest word of length x
How much space would the rotated lexicon require?

3. Storing a Digram Index
Suggest a structure that could be used to store a digram index
Supposing that you had
W words
Average word length of n
Longest word of length x
How much space would the digram index require?

4. Questions Suppose that: What is the precision? Recall?
there are 1000 documents
50 documents are relevant to the query
30 query results are returned, including 20 relevant documents
What is the precision? Recall?
How can perfect precision be achieved?
How can perfect recall be achieved?
Using these scores, how can search engine quality be automatically assessed?

5. Edit Distance
What is the edit distance between hello and yelp, assuming a unit cost function?
What is the edit distance if the cost of insert is 1, the cost of delete is 1, and the cost of rename is 3?

6. Jaccard Coefficient
Given sets S of size n and T of size m, with S∩T of size k, what is the Jaccard coefficient of S and T?
Compute the Jaccard coefficient of the bigrams of
believe
beleive
If the edit distance of words s and t is 1, what is the maximum/minimum size of the Jaccard coefficient of the bigrams of s and t?

7. Spelling Correction Suppose the user typed the words “plane piot”
Piot is a real word (Peter Piot was under Secretary-General of the United Nations)
possible corrections (as determined by your dictionary) are pivot and pilot
the probability of deleting a “v” immediately after an “i” is 0.02 and the probability of deleting a “l” immediately after an “i” is 0.01, the probability of correctly typing a word is 0.9
there are 1000 words in the corpus
the word “piot” appears once, “pivot” appears twice, “pilot” appears 10 times and “plane” appears 20 times
the phrase “plane pilot” appears 9 times, “plane pivot” and “plane piot” do not appear at all
What is the best spelling correction when using an interpolation of bigram and unigram models, choosing  = 0.5