Practice Exercise 14.A
Probabilistic Relational Models

## 2: Learning Goals

• Represent a simple problem in plate notation.
• Derive and draw a grounded belief network.
• Calculate probabilities from a problem in the independent choice logic representation.

## 3: Directed Questions

1. In probabilistic relational models, do different individuals share the same probability parameters? [solution]

2. What are the three components of a plate model? [solution]

3. What type of dependency can a plate model not adequately represent? [solution]

## 4: Exercise: Movie Preferences

Suppose we have parametrized random variables likes(Person,Movie), young(Person) and genre(Movie,Genre) where there are 1000 people, 100 movies and 5 genres. Suppose young(Person) and genre(Movie,Genre) are parents of likes(Person,Movie).
1. Draw this in plate notation. [solution]

2. How many random variables are in the grounding of this model? [solution]

3. Draw the grounding belief network assuming the population of Person is {sam,chris,kim} and the population of Movie is {terminator,rango}. [solution]
Consider the following fragment of independent choice logic theory:
```likes(Person,Movie) <- young(Person) & genre(Movie,action) & young_likes_action(Person,Movie).
prob young_likes_action(Person,Movie):0.7.
likes(Person,Movie) <- ~young(Person) & genre(Movie,action) & old_likes_action(Person,Movie).
prob old_likes_action(Person,Movie):0.6.
likes(Person,Movie) <- genre(Movie,comedy) & likes_comedy(Person,Movie).
prob likes_comedy(Person,Movie):0.8.
young(sam).
young(chris).
genre(terminator,action).
genre(rango,comedy).
```
where <- means "if", ~ means "not", & means "and", and "prob a:p." means {a, ~a} is an alternative with P(a) = p.
1. What is the probability of likes(sam,rango)? [solution]

2. What is the probability of likes(chris,terminator)? [solution]

3. What is the probability of likes(kim,terminator)? [solution]

## 5: Learning Goals Revisited

• Represent a simple problem in plate notation.
• Derive and draw a grounded belief network.
• Calculate probabilities from a problem in the independent choice logic representation.