O exercicio pode ser feito em grupo de até 3 pessoas
Para o dia 13/5 antes da meia noite
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Baseado nos Exercícios 15.13 e 15.14 do livro texto A versão em ingles:
15.13 A professor want to know if a student is getting enough sleep. Each day, the professor observe if the students sleep in class and whether they have red eyes. The professor has the following domain theory:
The prior probability of getting enough sleep with no observation is 0.6.
The probability of the student getting enough sleep on night on night t is 0.8 given that the student got enough sleep in the previous night, and 0.2 if not.
the probability of having red eyes is 0.2 if the student got enough sleep and 0.7 if not.
the probability of sleeping in class is 0.1 if the student got enough sleep and 0.3 if not.
Q1: Formulate this information as a dynamic Bayesian network that the professor could use to filter of predict from a sequence of observations.
Q2: Reformulate it as a hidden Markov model that has only a single observation variable. Give the complete probability tables for the model.
15.14 For the DBN in exercice 15.13 and for the evidence values
e1 = not red eyes, not sleeping in class
e2 = red eyes, not sleeping in class
e3 = red eyes, sleeping in class
perform the following computations:
Q3:. State estimation: Compute P(EnoughSleep_t | e_{1:t}) for $t=$1, 2, 3
Q4:: Smoothing: Compute P(EnoughSleep_t | e_{1:3}) for $t=$1, 2, 3
Q5:: Compare the filtered and the smoothed probabilities for t= 1 and 3.
Para representar o DBN (Q1) é so representar a rede bayesiana 2 vezes (tempo 0 e tempo 1).
Para Q2 de as tabelas de prior para o estado, as tabelas de treansição e o modelo de sensor.
Q3 é filtragem (as observações param em t) e Q4 é suavização (os observações vão até o 3).
Voce pode implementar os cálculos de Q3 e Q4 manualmente ou com um programa que vc mesmo implementou que implementa os algoritmos forward e forward-backward.