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Problem 1. 
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There are many possible answers to this question.
Some problems with the proposed memory-based approach to chess include:
1) It is not known if the moves are by good players or bad players
2) The final outcome of the game, given that move, is also unknown.
3) Even the next move, given that move, is unknown, so it is unclear it
was even a good move.

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Problem 2
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One query : "formula 1 drivers"

Part 1.
Including morphological variations 
"formula formulate formulation formulas 1 one driver driving drivers"
The results of the query usually change, meaning that morphological variations
are treated many times as different words
Irrelevant documents can appear

Part 2.
Synonyms alter considerably the result of the query.
More irrelevant pages show up or the search engine does not produce
any result (too many (uncorrelated) words in the query)

Part 3.
Using only the intended synonyms instead of all of them,
the results can be slightly better than using the previous query,
but still too bad (probably you don't get any answer)

Part 4.
Long queries assign little weight to each term of the query
(increases the number of possible combinations of words)
Using only the right senses (but in a long query) still
assigns too little weight to each term.

Part 5.
Use relevance feedback method(Jurafsky & Martin book, pag 656-657)


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Problem 3. Recommender system
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We want to identify book shoppers with similar behavior, 
so we need to model book shoppers behaviour.

A shopper S is modeled as a vector with k entries,
in which each entry represents a predetermined category of books
(in example technology books, fiction, cooking, religion, ....)
in each entry we store a counter of the number of books the shopper S
has bought. We normalize by the total number of bought books in order 
allow comparison with all the other shoppers.

In example, if our bookstore only has 3 categories of books (k=3),
cooking, religion and technology, some example of shoppers can be,
Ann   (5,0,0)
David (1,1,3)
Eloise(0,2,2)

meaning that Ann has bought 5 books about cooking,
David has 3 books about cooking, one about religion and 
one about technology. Eloise seems not to like to cook,
she prefers religion and technology (strange combination).

Given the three previous shoppers, we are more likely to recommend
Eloise books like those that David bought instead of the books that 
Ann use to buy. 

The similarity function can be the dot product of the vectors,
but before we want to normalize them in order to avoid that one 
feature domain the similarity value. 
(See Jurafsky & Martin book, pag 650-651)