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Related to Machine learning: Imagine that you would like to predict if your favorite table will...

Related to Machine learning:

Imagine that you would like to predict if your favorite table will be free at your favorite restau-
rant. The only additional piece of information you can collect, however, is if it is sunny or not
sunny. You collect paired samples from visit of the form (is sunny, is table free), where it is either
sunny (1) or not sunny (0) and the table is either free (1) or not free(0).


(a) [10 marks] How can this be formulated as a maximum likelihood problem? Explain what the
distributions are, what parameters need to be learned and write the (log) likelihood explicitly for
those distributions and parameters. You do not need to solve this maximum likelihood problem.


(b) [10 marks] Assume you have collected data for the last 10 days and computed the maximum
likelihood solution to the problem formulated in (a). You do not actually have to do this, just
assume that you did and now have estimated the parameter for your distribution. If it is sunny
today, how would you predict if your table will be free?

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Answer #1


sol) collecting of paired samples from visit of the form is sunny and is table, face, we have p Gunny)=P, , P (free)= P2 P(RoNow, X+Xq Xp + X3 %9+xy log (1) - dog (og het dorg (ru) that log ou to the dog (e) ne doy ) = (x1+x2) dog le+ (*1923) dog p2Assuming collented data for Lagt to N = 10 Then Pe frais likelihood paoblem) – #sun diy Pelticis likelihood problem) = #day p

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